text:
Special Relativity/Mathematical approach

Vectors
Physical effects involve things acting on other things to produce a change of position, tension etc. These effects usually depend upon the strength, angle of contact, separation etc of the interacting things rather than on any absolute reference frame so it is useful to describe the rules that govern the interactions in terms of the relative positions and lengths of the interacting things rather than in terms of any fixed viewpoint or coordinate system. Vectors were introduced in physics to allow such relative descriptions.

The use of vectors in elementary physics often avoids any real understanding of what they are. They are a new concept, as unique as numbers themselves, which have been related to the rest of mathematics and geometry by a series of formulae such as linear combinations, scalar products etc.

Vectors are defined as "directed line segments" which means they are lines drawn in a particular direction. The introduction of time as a geometric entity means that this definition of a vector is rather archaic, a better definition might be that a vector is information arranged as a continuous succession of points in space and time. Vectors have length and direction, the direction being from earlier to later.

Vectors are represented by lines terminated with arrow symbols to show the direction. A point that moves from the left to the right for about three centimetres can be represented as:

If a vector is represented within a coordinate system it has components along each of the axes of the system. These components do not normally start at the origin of the coordinate system.

The vector represented by the bold arrow has components a, b and c which are lengths on the coordinate axes. If the vector starts at the origin the components become simply the coordinates of the end point of the vector and the vector is known as the position vector of the end point.

Addition of Vectors
If two vectors are connected so that the end point of one is the start of the next the sum of the two vectors is defined as a third vector drawn from the start of the first to the end of the second:

c is the sum of a and b:

c = a + b

If a components of a are x1, y1, z1 and the components of b are x2, y2, z2 then the components of the sum of the two vectors are (x1+x2), (y1+y2) and (z1+z2). In other words, when vectors are added it is the components that add numerically rather than the lengths of the vectors themselves.

Rules of Vector Addition

1. Commutativity a + b = b + a

2. Associativity (a + b) + c = a + (b + c)

If the zero vector (which has no length) is labelled as 0

3. a + (-a) = 0

4. a + 0 = a

Rules of Vector Multiplication by a Scalar
The discussion of components and vector addition shows that if vector a has components a,b,c then qa has components qa, qb, qc. The meaning of vector multiplication is shown below:

The bottom vector c is added three times which is equivalent to multiplying it by 3.

1. Distributive laws q(a + b) = qa + qb and (q + p)a = qa + pa

2. Associativity q(pa) = qpa

Also 1 a = a

If the rules of vector addition and multiplication by a scalar apply to a set of elements they are said to define a vector space.

Linear Combinations and Linear Dependence
An element of the form:

$$q_1\mathbf{a_1} + q_2\mathbf{a_2} + q_3\mathbf{a_3} +.... + q_m \mathbf{a_m}$$

is called a linear combination of the vectors.

The set of vectors multiplied by scalars in a linear combination is called the span of the vectors. The word span is used because the scalars (q) can have any value - which means that any point in the subset of the vector space defined by the span can contain a vector derived from it.

Suppose there were a set of vectors ($${a_1,a_2,.... ,a_m}$$), if it is possible to express one of these vectors in terms of the others, using any linear combination, then the set is said to be linearly dependent. If it is not possible to express any one of the vectors in terms of the others, using any linear combination, it is said to be linearly independent.

In other words, if there are values of the scalars such that:

(1). $$\mathbf{a_1} = q_2\mathbf{a_2} + q_3\mathbf{a_3} +.... + q_m\mathbf{a_m}$$

the set is said to be linearly dependent.

There is a way of determining linear dependence. From (1) it can be seen that if $$q_1$$ is set to minus one then:

$$q_1\mathbf{a_1} + q_2\mathbf{a_2} + q_3\mathbf{a_3} +.... + q_m\mathbf{a_m} = 0$$

So in general, if a linear combination can be written that sums to a zero vector then the set of vectors ($$\mathbf{a_1,a_2,.... ,a_m})$$ are not linearly independent.

If two vectors are linearly dependent then they lie along the same line (wherever a and b lie on the line, scalars can be found to produce a linear combination which is a zero vector). If three vectors are linearly dependent they lie on the same line or on a plane (collinear or coplanar).

Dimension
If n+1 vectors in a vector space are linearly dependent then n vectors are linearly independent and the space is said to have a dimension of n. The set of n vectors is said to be the basis of the vector space.

Scalar Product
Also known as the 'dot product' or 'inner product'. The scalar product is a way of removing the problem of angular measures from the relationship between vectors and, as Weyl put it, a way of comparing the lengths of vectors that are arbitrarily inclined to each other.

Consider two vectors with a common origin:

The projection of $$\mathbf{a}$$ on the adjacent side is:

$$P = | \mathbf{a} | cos \theta $$

Where $$| \mathbf{a} | $$ is the length of $$\mathbf{a}$$.

The scalar product is defined as:

(2) $$\mathbf{a. b} = | \mathbf{a} | | \mathbf{b} | cos \theta $$

Notice that $$cos \theta$$ is zero if $$\mathbf{a}$$ and $$\mathbf{b}$$ are perpendicular. This means that if the scalar product is zero the vectors composing it are orthogonal (perpendicular to each other).

(2) also allows $$cos \theta$$ to be defined as:

$$cos \theta = \mathbf{a. b} / ( | \mathbf{a} | | \mathbf{b} |)$$

The definition of the scalar product also allows a definition of the length of a vector in terms of the concept of a vector itself. The scalar product of a vector with itself is:

$$\mathbf{a. a} = | \mathbf{a} | | \mathbf{a} | cos 0$$

cos 0 (the cosine of zero) is one so:

$$\mathbf{a. a} = a^2$$

which is our first direct relationship between vectors and scalars. This can be expressed as:

(3) $$a = \sqrt{\mathbf{a. a}} $$

where a is the length of $$\mathbf{a}$$.

Properties:

1. Linearity $$[G\mathbf{a} + H\mathbf{b}].\mathbf{c} = G\mathbf{a.c} + H\mathbf{b.c}$$

2. symmetry $$\mathbf{a.b} = \mathbf{b.a}$$

3. Positive definiteness $$\mathbf{a.a}$$ is greater than or equal to 0

4. Distributivity for vector addition $$\mathbf{(a + b).c} = \mathbf{a.c + b.c}$$

5. Schwarz inequality $$| \mathbf{a.b} | \leq ab$$

6. Parallelogram equality $$| \mathbf{a} + \mathbf{b} |^2 + | \mathbf{a} - \mathbf{b} |^2 = 2( | \mathbf{a} |^2 + | \mathbf{b} |^2)$$

From the point of view of vector physics the most important property of the scalar product is the expression of the scalar product in terms of coordinates.

7. $$\mathbf{a.b} = a_1b_1 + a_2b_2 + a_3b_3$$

This gives us the length of a vector in terms of coordinates (Pythagoras' theorem) from:

8. $$\mathbf{a.a} = a^2 = a_1^2 + a_2^2 + a_3^2$$

The derivation of 7 is:

$$\mathbf{a} = a_1\mathbf{i} + a_2\mathbf{j} + a_3\mathbf{k}$$

where $$\mathbf{i}, \mathbf{j}, \mathbf{k}$$ are unit vectors along the coordinate axes. From (4)

$$\mathbf{a.b} = (a_1\mathbf{i} + a_2\mathbf{j} + a_3\mathbf{k}) .\mathbf{b} = a_1\mathbf{i}.\mathbf{b} + a_2\mathbf{j}.\mathbf{b} + a_3\mathbf{k}.\mathbf{b}$$

but $$\mathbf{b} = b_1\mathbf{i} + b_2\mathbf{j} + b_3\mathbf{k}$$

so:

$$\mathbf{a.b} = b_1a_1\mathbf{i .i} + b_2a_1\mathbf{i .j} + b_3a_1\mathbf{i .k} + b_1a_2\mathbf{j.i} + b_2a_2\mathbf{j.j} + b_3a_2\mathbf{j.k} + b_1a_3\mathbf{k.i} + b_2a_3\mathbf{k.j} + b_3a_3\mathbf{k.k}$$

$$\mathbf{i .j, i .k, j .k,}$$ etc. are all zero because the vectors are orthogonal, also $$\mathbf{i .i, j.j}$$ and $$\mathbf{k.k}$$ are all one (these are unit vectors defined to be 1 unit in length).

Using these results:

$$\mathbf{a.b} = a_1b_1 + a_2b_2 + a_3b_3$$

Matrices
Matrices are sets of numbers arranged in a rectangular array. They are especially important in linear algebra because they can be used to represent the elements of linear equations.

11a + 2b = c

5a + 7b = d

The constants in the equation above can be represented as a matrix:

 * $$\mathbf{A} =

\begin{bmatrix} 11 & 2 \\ 5 & 7 \\ \end{bmatrix}$$

The elements of matrices are usually denoted symbolically using lower case letters:

 * $$\mathbf{A} =

\begin{bmatrix} a_{11} & a_{12} \\ a_{21} & a_{22} \\ \end{bmatrix}$$

Matrices are said to be equal if all of the corresponding elements are equal.

Eg: if $$a_{ij}= b_{ij}$$

Then $$\mathbf{A} = \mathbf{B}$$

Matrix Addition
Matrices are added by adding the individual elements of one matrix to the corresponding elements of the other matrix.

$$c_{ij} = a_{ij} + b_{ij}$$

or $$\mathbf{C} = \mathbf{A} + \mathbf{B}$$

Matrix addition has the following properties:

1. Commutativity $$\mathbf{A} + \mathbf{B} = \mathbf{B} + \mathbf{A}$$

2. Associativity $$(\mathbf{A} + \mathbf{B}) + \mathbf{C} = \mathbf{A} + (\mathbf{B} + \mathbf{C})$$

and

3. $$\mathbf{A} + (-\mathbf{A}) = 0$$

4. $$\mathbf{A} + 0 = \mathbf{A}$$

From matrix addition it can be seen that the product of a matrix $$\mathbf{A}$$ and a number p is simply $$p\mathbf{A}$$ where every element of the matrix is multiplied individually by p.

Transpose of a Matrix

A matrix is transposed when the rows and columns are interchanged:

 * $$\mathbf{A} =

\begin{bmatrix} a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \\ a_{31} & a_{32} & a_{33} \\ \end{bmatrix}$$
 * $$\mathbf{A^T} =

\begin{bmatrix} a_{11} & a_{21} & a_{31} \\ a_{12} & a_{22} & a_{32} \\ a_{13} & a_{23} & a_{33} \\ \end{bmatrix}$$

Notice that the principal diagonal elements stay the same after transposition.

A matrix is symmetric if it is equal to its transpose eg: $$a_{kj} = a_{jk}$$.

It is skew symmetric if $$\mathbf{A^T} = -\mathbf{A}$$ eg: $$a_{kj} = -a_{jk}$$. The principal diagonal of a skew symmetric matrix is composed of elements that are zero.

Other Types of Matrix

Diagonal matrix: all elements above and below the principal diagonal are zero.

 * $$\begin{bmatrix}

4 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & 2 \\ \end{bmatrix}$$

Unit matrix: denoted by I, is a diagonal matrix where all elements of the principal diagonal are 1.

 * $$\begin{bmatrix}

1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \\ \end{bmatrix}$$

Matrix Multiplication
Matrix multiplication is defined in terms of the problem of determining the coefficients in linear transformations.

Consider a set of linear transformations between 2 coordinate systems that share a common origin and are related to each other by a rotation of the coordinate axes.

Two Coordinate Systems Rotated Relative to Each Other

If there are 3 coordinate systems, x, y, and z these can be transformed from one to another:

$$x_1 = a_{11}y_1 + a_{12}y_2 $$

$$x_2 = a_{21}y_1 + a_{22}y_2 $$

$$y_1 = b_{11}z_1 + b_{12}z_2 $$

$$y_2 = b_{21}z_1 + b_{22}z_2 $$

$$x_1 = c_{11}z_1 + c_{12}z_2 $$

$$x_2 = c_{21}z_1 + c_{22}z_2 $$

By substitution:

$$x_1 = a_{11}(b_{11}z_1 + b_{12}z_2) + a_{12}(b_{21}z_1 + b_{22}z_2) $$

$$x_2 = a_{21}(b_{11}z_1 + b_{12}z_2) + a_{22}(b_{21}z_1 + b_{22}z_2) $$

$$x_1 = (a_{11}b_{11} + a_{12}(b_{21})z_1 + (a_{11}b_{12} + a_{12}b_{22})z_2 $$

$$x_2 = (a_{21}b_{11} + a_{22}(b_{21})z_1 + (a_{21}b_{12} + a_{22}b_{22})z_2 $$

Therefore:

$$c_{11} = (a_{11}b_{11} + a_{12}(b_{21})$$

$$c_{12} = (a_{11}b_{12} + a_{12}b_{22})$$

$$c_{21} = (a_{21}b_{11} + a_{22}b_{21})$$

$$c_{22} = (a_{21}b_{12} + a_{22}b_{22})$$

The coefficient matrices are:

 * $$\mathbf{A} =

\begin{bmatrix} a_{11} & a_{12} \\ a_{21} & a_{22} \end{bmatrix}$$

 * $$\mathbf{B} =

\begin{bmatrix} b_{11} & b_{12} \\ b_{21} & b_{22} \end{bmatrix}$$

 * $$\mathbf{C} =

\begin{bmatrix} c_{11} & c_{12} \\ c_{21} & c_{22} \end{bmatrix}$$

From the linear transformation the product of A and B is defined as:

 * $$\mathbf{C} = \mathbf{AB} =

\begin{bmatrix} (a_{11}b_{11} + a_{12}b_{21}) & (a_{11}b_{12} + a_{12}b_{22}) \\ (a_{21}b_{11} + a_{22}b_{21}) & (a_{21}b_{12} + a_{22}b_{22}) \end{bmatrix}$$

In the discussion of scalar products it was shown that, for a plane the scalar product is calculated as: $$\mathbf{a.b} = a_1b_1 + a_2b_2$$ where a and b are the coordinates of the vectors a and b.

Now mathematicians define the rows and columns of a matrix as vectors:

A Column vector is $$\mathbf{b}= \begin{bmatrix} b_{11} \\ b_{21} \end{bmatrix}$$

And a Row vector $$\mathbf{a}= \begin{bmatrix} a_{11} & a_{12} \end{bmatrix}$$

Matrices can be described as vectors eg:

 * $$\mathbf{A} =

\begin{bmatrix} a_{11} & a_{12} \\ a_{21} & a_{22} \end{bmatrix} = \begin{bmatrix} \mathbf{a_{1}} \\ \mathbf{a_{2}} \end{bmatrix}$$

and

 * $$\mathbf{B} =

\begin{bmatrix} b_{11} & b_{12} \\ b_{21} & b_{22} \end{bmatrix} = \begin{bmatrix} \mathbf{b_{1}} \mathbf{b_{2}} \end{bmatrix}$$

Matrix multiplication is then defined as the scalar products of the vectors so that:

 * $$\mathbf{C} =

\begin{bmatrix} \mathbf{a_1.b_1} & \mathbf{a_1.b_2} \\ \mathbf{a_2.b_1} & \mathbf{a_2.b_2} \end{bmatrix} $$

From the definition of the scalar product $$\mathbf{a_1.b_1} = a_{11}b_{11} + a_{12}b_{21}$$ etc.

In the general case:

 * $$\mathbf{C} =

\begin{bmatrix} \mathbf{a_1.b_1} & \mathbf{a_1.b_2} &. & \mathbf{a_1.b_n} \\ \mathbf{a_2.b_1} & \mathbf{a_2.b_2} &. & \mathbf{a_2.b_n} \\ . & . & . & . \\ \mathbf{a_m.b_1} & \mathbf{a_m.b_2} &. & \mathbf{a_m.b_n} \end{bmatrix} $$

This is described as the multiplication of rows into columns (eg: row vectors into column vectors). The first matrix must have the same number of columns as there are rows in the second matrix or the multiplication is undefined.

After matrix multiplication the product matrix has the same number of rows as the first matrix and columns as the second matrix:

 * $$\begin{bmatrix}

1 & 3 & 4 \\ 6 & 3 & 2 \end{bmatrix} $$ times $$ \begin{bmatrix} 2 \\ 3 \\ 7 \end{bmatrix} $$ has 2 rows and 1 column $$ \begin{bmatrix} 39 \\ 35 \end{bmatrix} $$

ie: first row is $$1*2 + 3*3 + 4*7 = 39$$ and second row is $$6*2 + 3*3 + 2*7 = 35$$

 * $$\mathbf{AB} = \begin{bmatrix}

1 & 3 & 2 \\ 2 & -1 & 3 \end{bmatrix} $$ times $$ \begin{bmatrix} 2 & 3 & 4\\ 3 & 2 & 1\\ 5 & 1 & 3 \end{bmatrix} $$ has 2 rows and 3 columns$$ \begin{bmatrix} 21 & 11 & 13 \\ 16 & 7 & 16 \end{bmatrix} $$

Notice that $$\mathbf{BA}$$ cannot be determined because the number of columns in the first matrix must equal the number of rows in the second matrix to perform matrix multiplication.

Properties of Matrix Multiplication

1. Not commutative $$\mathbf{AB} \ne \mathbf{BA}$$

2. Associative $$\mathbf{A(BC)} = \mathbf{(AB)C}$$

$$(k\mathbf{A})\mathbf{B} = k(\mathbf{AB}) = \mathbf{A}(k\mathbf{B})$$

3. Distributative for matrix addition

$$(\mathbf{A} + \mathbf{B})\mathbf{C} = \mathbf{AC} + \mathbf{BC}$$

matrix multiplication is not commutative so $$\mathbf{C}(\mathbf{A} + \mathbf{B}) = \mathbf{CA} + \mathbf{CB}$$ is a separate case.

4. The cancellation law is not always true:

$$\mathbf{AB} = 0$$ does not mean $$\mathbf{A}=0$$ or $$\mathbf{B}=0$$

There is a case where matrix multiplication is commutative. This involves the scalar matrix where the values of the principle diagonal are all equal. Eg:

 * $$\mathbf{S} =

\begin{bmatrix} k & 0 & 0 \\ 0 & k & 0 \\ 0 & 0 & k \end{bmatrix} $$

In this case $$\mathbf{AS} = \mathbf{SA} = k\mathbf{A}$$. If the scalar matrix is the unit matrix: $$\mathbf{AI} = \mathbf{IA} = \mathbf{A}$$.

Linear Transformations
A simple linear transformation such as:

$$x_1 = a_{11}y_1 + a_{12}y_2 $$

$$x_2 = a_{21}y_1 + a_{22}y_2 $$

can be expressed as:

$$\mathbf{x} = \mathbf{Ay}$$

eg:

\begin{bmatrix} x_1 \\ x_2 \end{bmatrix} = \begin{bmatrix} a_{11} & a_{12} \\ a_{21} & a_{22} \end{bmatrix} \begin{bmatrix} y_1 \\ y_2 \end{bmatrix} $$

and $$y_1 = b_{11}z_1 + b_{12}z_2 $$

$$y_2 = b_{21}z_1 + b_{22}z_2 $$

as: $$\mathbf{y} = \mathbf{Bz}$$

Using the associative law:

$$\mathbf{x} = \mathbf{A}(\mathbf{Bz}) = \mathbf{ABz} = \mathbf{Cz}$$

and so:

 * $$\mathbf{C} = \mathbf{AB} =

\begin{bmatrix} (a_{11}b_{11} + a_{12}b_{21}) & (a_{11}b_{12} + a_{12}b_{22}) \\ (a_{21}b_{11} + a_{22}b_{21}) & (a_{21}b_{12} + a_{22}b_{22}) \end{bmatrix}$$

as before.

Indicial Notation
Consider a simple rotation of coordinates:

$$x^{\mu}$$ is defined as $$x_1$$, $$x_2$$

$$x^{\nu}$$ is defined as $$x_{1}^'$$, $$x_{2}^'$$

The scalar product can be written as:

$$\mathbf{s.s} =g_{\mu \nu} x^\mu x^\nu $$

Where:

 * $$g_{\mu \nu} =

\begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix} $$

and is called the metric tensor for this 2D space.

$$ \mathbf{s.s} = g_{11} x_1x_{1}^' + g_{12} x_1x_2^' + g_{21} x_2x_{1}^' + g_{22} x_2x_{2}^'$$

Now, $$g_{11} = 1$$, $$g_{12} = 0$$, $$g_{21} = 0$$, $$g_{22} = 1$$ so:

$$\mathbf{s.s} = x_1x_{1}^' + x_2x_{2}^'$$

If there is no rotation of coordinates the scalar product is:

$$\mathbf{s.s} = x_1x_1 + x_2x_2$$

$$s^2 = x_{1}^2 + x_{2}^2$$

Which is Pythagoras' theorem.

The Summation Convention
Indexes that appear as both subscripts and superscripts are summed over.

$$g_{\mu \nu} x^\mu x^\nu = g_{11} x_1x_{1}^' + g_{12} x_1x_2^' + g_{21} x_2x_{1}^' + g_{22} x_2x_{2}^'$$

by promoting $$\nu$$ to a superscript it is taken out of the summation ie:.

$$g_{\mu}^\nu x^\mu x^\nu = g_{1\nu} x_1x_{\nu}^' + g_{2\nu} x_2x_{\nu}^'$$

Matrix Multiplication in Indicial Notation
Consider:

Columns times rows:

$$ \begin{bmatrix} x_1 \\ x_2 \end{bmatrix} $$ times $$\begin{bmatrix}y_1 & y_2 \end{bmatrix} $$ = $$ \begin{bmatrix} x_1 y_1 & x_1 y_2 \\ x_2 y_1 & x_2 y_2 \end{bmatrix} $$

Matrix product $$\mathbf{XY} = x_iy_j $$ Where i = 1, 2 j = 1, 2

There being no summation the indexes are both subscripts.

Rows times columns: $$ \begin{bmatrix} x_1 & x_2 \end{bmatrix} $$ times $$ \begin{bmatrix} y_1 \\ y_2 \end{bmatrix} $$ = $$ \begin{bmatrix} x_1 y_1 & x_2 y_2 \end{bmatrix} $$

Matrix product $$\mathbf{XY} = \delta_{ij} x^iy^j $$

Where $$\delta_{ij}$$ is known as Kronecker delta and has the value 0 when $$i \ne j $$ and 1 when $$i = j $$. It is the indicial equivalent of the unit matrix:

$$\begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix} $$

There being summation one value of i is a subscript and the other a superscript.

A matrix in general can be specified by any of:

$$M_{i}^j$$, $$M_{ij}$$ , $$M^{i}_j$$ , $$M^{ij}$$ depending on which subscript or superscript is being summed over.

Vectors in Indicial Notation
A vector can be expressed as a sum of basis vectors.

$$\mathbf{x} = a_1\mathbf{e}_1 + a_2\mathbf{e}_2 + a_3\mathbf{e}_3 $$

In indicial notation this is: $$x = a^ie_i $$

Linear Transformations in indicial notation
Consider $$\mathbf{x} = \mathbf{Ay}$$ where $$\mathbf{A}$$ is a coefficient matrix and $$\mathbf{x}$$ and $$\mathbf{y}$$ are coordinate matrices.

In indicial notation this is:

$$x^{\mu} = A^{\mu}_{\nu} x^{\nu}$$

which becomes:

$$x_1 = a_{11} x^{'}_1+ a_{12} x^{'}_2+ a_{13} x^{'}_3$$

$$x_2 = a_{21} x^{'}_1+ a_{22} x^{'}_2+ a_{23} x^{'}_3$$

$$x_3 = a_{31} x^{'}_1+ a_{32} x^{'}_2+ a_{33} x^{'}_3$$

The Scalar Product in indicial notation
In indicial notation the scalar product is:

$$\mathbf{x.y} = \delta_{ij} x^i y^j $$

Analysis of curved surfaces and transformations
It became apparent at the start of the nineteenth century that issues such as Euclid's parallel postulate required the development of a new type of geometry that could deal with curved surfaces and real and imaginary planes. At the foundation of this approach is Gauss's analysis of curved surfaces which allows us to work with a variety of coordinate systems and displacements on any type of surface.

Elementary geometric analysis is useful as an introduction to Special Relativity because it suggests the physical meaning of the coefficients that appear in coordinate transformations.

Suppose there is a line on a surface. The length of this line can be expressed in terms of a coordinate system. A short length of line $$\Delta s$$ in a two dimensional space may be expressed in terms of Pythagoras' theorem as:

$$\Delta s^2 = \Delta x^2 + \Delta y^2$$

Suppose there is another coordinate system on the surface with two axes: x1, x2, how can the length of the line be expressed in terms of these coordinates? Gauss tackled this problem and his analysis is quite straightforward for two coordinate axes:

Figure 1:

It is possible to use elementary differential geometry to describe displacements along the plane in terms of displacements on the curved surfaces:

$$ \Delta Y = \Delta x_1 \frac {\delta Y}{\delta x_1} + \Delta x_2 \frac{\delta Y}{\delta x_2}$$

$$ \Delta Z = \Delta x_1 \frac {\delta Z}{\delta x_1} + \Delta x_2 \frac{\delta Z}{\delta x_2}$$

The displacement of a short line is then assumed to be given by a formula, called a metric, such as Pythagoras' theorem

$$\Delta S^2 = \Delta Y^2 + \Delta Z^2$$

The values of $$ \Delta Y $$ and $$ \Delta Z $$ can then be substituted into this metric:

$$\Delta S^2 = ( \Delta x_1 \frac {\delta Y}{\delta x_1} + \Delta x_2 \frac{\delta Y}{\delta x_2} )^2 + ( \Delta x_1 \frac {\delta Z}{\delta x_1} + \Delta x_2 \frac{\delta Z}{\delta x_2} )^2$$

Which, when expanded, gives the following:

$$\Delta S^2 = $$

$$( \frac{\delta Y}{\delta x_1}\frac{\delta Y}{\delta x_1} + \frac{\delta Z}{\delta x_1} \frac{\delta Z}{\delta x_1} ) \Delta x_1 \Delta x_1 $$

$$ +( \frac{\delta Y}{\delta x_2}\frac{\delta Y}{\delta x_1} + \frac{\delta Z}{\delta x_2} \frac{\delta Z}{\delta x_1} ) \Delta x_2 \Delta x_1 $$

$$ + ( \frac{\delta Y}{\delta x_1}\frac{\delta Y}{\delta x_2} + \frac{\delta Z}{\delta x_1} \frac{\delta Z}{\delta x_2} ) \Delta x_1 \Delta x_2 $$

$$ + ( \frac{\delta Y}{\delta x_2}\frac{\delta Y}{\delta x_2} + \frac{\delta Z}{\delta x_2} \frac{\delta Z}{\delta x_2} ) \Delta x_2 \Delta x_2 $$

This can be represented using summation notation:

$$\Delta S^2 = \sum_{i=1}^2 \sum_{k=1}^2 (\frac{\delta Y}{\delta x_i}\frac{\delta Y}{\delta x_k}  + \frac{\delta Z}{\delta x_i} \frac{\delta Z}{\delta x_k} ) \Delta x_i \Delta x_k $$

Or, using indicial notation:

$$\Delta S^2 = g_{ik} \Delta x^i \Delta x^k $$

Where:

$$ g_{ik} = (\frac{\delta Y}{\delta x^i}\frac{\delta Y}{\delta x^k} + \frac{\delta Z}{\delta x^i} \frac{\delta Z}{\delta x^k} ) $$

If the coordinates are not merged then $$\Delta s$$ is dependent on both sets of coordinates. In matrix notation:

$$\Delta s^2 = \mathbf{g} \Delta \mathbf{x} \Delta \mathbf{x}$$

becomes:

$$ \begin{bmatrix} \Delta x_1 & \Delta x_2 \end{bmatrix} $$ times $$ \begin{bmatrix} a & b \\ c & d \end{bmatrix} $$ times $$ \begin{bmatrix} \Delta x_1 \\ \Delta x_2 \end{bmatrix} $$

Where a, b, c, d stand for the values of $$g_{ik}$$.

Therefore:

$$ \begin{bmatrix} \Delta x_1a + \Delta x_2c & \Delta x_1b + \Delta x_2d \end{bmatrix} $$ times $$ \begin{bmatrix} \Delta x_1 \\ \Delta x_2 \end{bmatrix} $$

Which is:

$$(\Delta{x_1}a + \Delta{x_2}c) \Delta{x_1} + (\Delta{x_1}b + \Delta{x_2}d) \Delta{x_2} = \Delta{x_1}^2a + 2\Delta{x_1}\Delta{x_2}(c + b) + \Delta{x_2}^2d$$

So:

$$\Delta{s}^2 = \Delta{x_1}^2a + 2\Delta{x_1}\Delta{x_2}(c + b) + \Delta{x_2}^2d$$

$$\Delta{s}^2$$ is a bilinear form that depends on both $$\Delta{x_1}$$ and $$\Delta{x_2}$$. It can be written in matrix notation as:

$$\Delta{s}^2 = \mathbf{\Delta{x}^T A \Delta{x}}$$

Where A is the matrix containing the values in $$g_{ik}$$. This is a special case of the bilinear form known as the quadratic form because the same matrix ($$\mathbf{\Delta{x}}$$) appears twice; in the generalised bilinear form $$\mathbf{B} = \mathbf{x^TAy}$$ (the matrices $$\mathbf{x}$$ and $$\mathbf{y}$$ are different).

If the surface is a Euclidean plane then the values of gik are:

$$ \begin{bmatrix} \delta{Y}/\delta{x_1} \delta{Y}/\delta{x_1} + \delta{Z}/\delta{x_1} \delta{Z}/\delta{x_1} & \delta{Y}/\delta{x_2} \delta{Y}/\delta{x_1} + \delta{Z}/\delta{x_2} \delta{Z}/\delta{x_1} \\ \delta{Y}/\delta{x_2} \delta{Y}/\delta{x_1} + \delta{Z}/\delta{x_2} \delta{Z}/\delta{x_1} & \delta{Y}/\delta{x_2} \delta{Y}/\delta{x_2} + \delta{Z}/\delta{x_2} \delta{Z}/\delta{x_2} \end{bmatrix} $$

Which become:

 * $$g_{\mu \nu} =

\begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix} $$

So the matrix A is the unit matrix I and:

$$\Delta{s}^2 = \mathbf{\Delta{x^T} I \Delta{x}}$$

and:

$$\Delta{s}^2 = \Delta{x_1}^2 + \Delta{x_2}^2$$

Which recovers Pythagoras' theorem yet again.

If the surface is derived from some other metric such as $$\Delta{s^2} = -\Delta{Y}^2 + \Delta{Z}^2$$ then the values of gik are:

$$ \begin{bmatrix} -\delta{Y}/\delta{x_1} \delta{Y}/\delta{x_1} + \delta{Z}/\delta{x_1} \delta{Z}/\delta{x_1} & -\delta{Y}/\delta{x_2} \delta{Y}/\delta{x_1} + \delta{Z}/\delta{x_2} \delta{Z}/\delta{x_1} \\ -\delta{Y}/\delta{x_2} \delta{Y}/\delta{x_1} + \delta{Z}/\delta{x_2} \delta{Z}/\delta{x_1} & -\delta{Y}/\delta{x_2} \delta{Y}/\delta{x_2} + \delta{Z}/\delta{x_2} \delta{Z}/\delta{x_2} \end{bmatrix} $$

Which becomes:

 * $$g_{\mu \nu} =

\begin{bmatrix} -1 & 0 \\ 0 & 1 \end{bmatrix} $$

Which allows the original metric to be recovered ie: $$\Delta{s^2} = -\Delta{x_1}^2 + \Delta{x_2}^2$$.

It is interesting to compare the geometrical analysis with the transformation based on matrix algebra that was derived in the section on indicial notation above:

$$ \mathbf{s.s} = g_{11} x_1x_{1}^' + g_{12} x_1x_2^' + g_{21} x_2x_{1}^' + g_{22} x_2x_{2}^'$$

Now,

 * $$g_{\mu \nu} =

\begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix} $$

ie: $$g_{11} = 1$$, $$g_{12} = 0$$, $$g_{21} = 0$$, $$g_{22} = 1$$ so:

$$\mathbf{s.s} = x_1x_{1}^' + x_2x_{2}^'$$

If there is no rotation of coordinates the scalar product is:

$$\mathbf{s.s} = x_1x_1 + x_2x_2$$

$$s^2 = x_{1}^2 + x_{2}^2$$

Which recovers Pythagoras' theorem. However, the reader may have noticed that Pythagoras' theorem had been assumed from the outset in the derivation of the scalar product (see above).

The geometrical analysis shows that if a metric is assumed and the conditions that allow differential geometry are present then it is possible to derive one set of coordinates from another. This analysis can also be performed using matrix algebra with the same assumptions.

The example above used a simple two dimensional Pythagorean metric, some other metric such as the metric of a 4D Minkowskian space:

$$\Delta S^2 = - \Delta T^2 + \Delta X^2 + \Delta Y^2 + \Delta Z^2$$

could be used instead of Pythagoras' theorem.


text: Wikijunior talk:Dinosaurs/Pterosaurs

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Wikijunior talk:Dinosaurs/Pterosaurs


text:
User:Elonka

Hello! To see my main wikipedia page, please go to: http://en.wikipedia.org/wiki/User:Elonka

w:User:Elonka

title: User:Elonka


text:
User talk:84.12.24.49

Please stop adding nonsense to Wikibooks. It is considered vandalism. If you would like to experiment, use the sandbox. Thank you.

title: User talk:84.12.24.49


text:
Help talk:Print versions

upload to Wikimedia Commons forbidden?
This Help Page says: "PDF files can be uploaded to Wikimedia Commons just like images. [...] PDF files could previously be uploaded to Wikibooks but new files are now uploaded to Commons." I created a PDF for an article I wrote and uploaded it, but someone on Commons told me that this is out of scope of Wikimedia Commons and requested a deletion, see for the discussion. So, I'm confused - where should PDF files be uploaded? (I intend to write more articles and create PDFs. Where should I upload them?) I would like to have a definite answer, where the PDF gets either deleted or moved or the "deletion request" gets removed. --LarsWinterfeld (discuss • contribs) 12:42, 29 September 2015 (UTC)

the file should not be deleted on commons, there is even a category for pdf version of wikibooks on commons https://commons.wikimedia.org/wiki/Category:English_Wikibooks_PDF

--Dirk Hünniger (discuss • contribs) 17:08, 1 October 2015 (UTC)

Problem with step by step
If you do the following:

4. Insert every chapter like a template, preceded by chapter title. Remember about chapter with list of authors.

= Chapter name =

And the chapter already includes the chapter name then in the contents menu on the print version the chapter's name will appear twice, one as a subtitle of the other.

Doesn't this need to be changed? Glich (talk) 16:29, 23 July 2008 (UTC)

Deeper explanation of "Creating separate page for print version" required?
Could someone take some time to provide a more in depth explanation of the steps needed in the section "Creating separate page for print version". For example, step 3 mentions "Copy the TOC as an ordered list". Does this mean just the text on the web page as I see it, or the wikitext or html code which is behind the TOC? I looked at the proposed reference work (Python Programming) but don't quite understand whether they created their TOC, or whether there is a way for wikibooks to create it for me that I am supposed to use.

Can someone provide some clarification? Many thanks. --Codinghead (talk) 11:18, 4 September 2009 (UTC)

Copyright inclusion
In Ada Programming we already have a "print version" in Ada Programming/All Chapters so I followed the additional recomendations and have added the template and included the GFDL text. I wonder whether this last inclusion is really necessary; it adds too much text to the page and what is worst, it adds the page to the Category:Wikibooks enforced policies. Could an administrator at least use the noinclude tag around the category? Otherwise we need other method for including the GFDL text. ManuelGR 20:40, 9 January 2006 (UTC)

 * Ok, done, adding noinclude helped.
 * About GFDL problem: yes, it is strictly required that any print version of text under GFDL license has full text of the license. In fact, we should also include it in all our pages, but we "cheat" a bit by providing only link to the license text. Yes, GFDL is a stupid license, but unfortunately when Wikibooks were created there was no better alternative (like CC-BY-SA license). It's too late to change anything so we are stick to GFDL forever. Remember, when you create your own wiki, never ever use GFDL, maybe except dual-licensing ;-) --Derbeth talk 22:13, 9 January 2006 (UTC)

 * I reread the license and I don't think we are cheating since we follow the requirements of section titled GNU Free Documentation License.  Actually I don't see any problem on using the GFDL for a wiki. ManuelGR 23:08, 9 January 2006 (UTC)

Automatic generation of print version pages from a navigational map
Take a look at m:User:Nigelk/Nav and m:User:Nigelk/ConcatPages. This extension could be used to keep the TOC of the book synchronized with the print version. This extension also automatically adds next/up/previous links to the pages listed in the TOC page, aka nav map. ManuelGR 20:19, 10 January 2006 (UTC)

No Print Question
If I do the following:

 * To prevent block of text from being printed, cover it with  ... .

and the block of text contains a header. Is there a way to also not show the header in the TOC?
 * Try ...  It solved some problems for me Pluke 14:31, 18 June 2006 (UTC)

Inclusion of Module Sections?
Is there a way to link a module's section from the print version's page, but not include the entire module as well? I was thinking about creating an Endnotes page for some books instead of having footnotes at the end of each chapter. I tried, but no luck. --Everlong 23:28, 17 April 2006 (UTC)

 * Not quite sure what, precisely, you're asking. If you want to include only parts of the module in the "all-pages" version, you can use the <noinclude> tag to mark the parts that you don't want included. If you want all the endnotes included, you may have to make each module's endnote section a seperate page and include it both at the end of each module as well as in the "all-pages" endnote page. --Swift 18:47, 18 May 2007 (UTC)

Patent and PDF
I noticed that PDF is the file type of choice. Due to the various patents surrounding this format, it should be avoided. Wikimedia takes a stance against similar formats such as MP3, AVI and, to a lesser extent, GIF/JPG. How about promoting the use of ODF and other unencumbered (but equally powerful) formats? --OldakQuill 15:48, 27 April 2006 (UTC)
 * AFAIK JPG cannot be substituted and I haven't heard of any instructions from any Wikimedia project to avoid JPG files. Currently, PDF is the only reasonable publication format: it can be viewed in various web browsers and operating systems. I don't see any alternative and in my opinion it's not Wikimedia Foundation role to promote free software and new standards. --Derbeth talk 17:42, 27 April 2006 (UTC)
 * I'm not simply talking about advocacy. Patents often put a burden on Wikimedians to pay various companies whenever they create a file in a patented format. This is precisely the reason why we do not allow MP3 files. ODF is a very viable, flexible alternative. PNG can be used in the place of most JPG files. --OldakQuill 12:39, 28 April 2006 (UTC)

 * Certainly I'm all in favor of open file formats, including the OpenDocument format (ODF) developed by OASIS. Certainly *some* patent holders require a license fee to use their license. However, the wikipedia article on pdf pdf claims that PDF is also an open file format. Also, according to the wikipedia article on pdf, "Anyone may create applications that read and write PDF files without having to pay royalties to Adobe Systems; Adobe holds a number of patents relating to PDF but licenses them royalty-free for use in developing software that complies with its PDF specification."
 * Likewise, since the LZW patent has expired, GIF is now a open file format (and free). But PNG is technically superior to GIF, even if it is no longer "morally" superior, so I still recommend converting all GIFs to PNG.
 * I don't know enough about ODF vs PDF to know whether one is technically superior to another. But it seems reasonable to me for ODF advocates to post ODF versions, so that users have a choice of viewing a Wikibook in HTML/XHTML, PDF, or ODF.
 * --DavidCary 04:16, 5 April 2007 (UTC)

Don't over complicate task of book making
I can understand the open source community has its roots in programming but word processing is a common thing. You don't need to use a programming language to make pdfs or even E-books the programming has already been done for you from many many sources. If you can have an HTML page you can make it into an RTF page, if you can make it into an RTF page you can edit it in any number of word processing programs and print it out into PDF form or MSReader form or Palm Doc form. I've done all this countless times. I've taken text files off of Gutenberg.org and done everything from making them into paperbacks you can hold in your hand to e-books for e-readers -- ALL FROM COMMONLY AVAILABLE PROGRAMS (pardom my volume) -- MSWord and WordPerfect being the most common. The point is DON'T set it up as a specialist's task but one countless people can accomplish from their home computers. ALL the Wikibooks should be available in downloadable format. Infact MULTIPLE formats ... HTML, palm Doc, MSWord Doc, MSReader, PDF and whatever else format is requested. Set a place where the source text is available for book makers and you'll get them back from home book makers as quick as you can write or devise them. -- Thank you. JN

Print version tag prints!
I have including the tag on the A-level Computing page, as I am trying out the print version to see how it looks (no where near finished i know!). However the tag appears on the printed version, A-level Computing/Print version. Using the div noprint tag doesn't get rid of it!?! any suggestions Pluke 14:26, 18 June 2006 (UTC)

 * SolvedTry ... Pluke 14:32, 18 June 2006 (UTC)

More tips on PDF creation
Can you explain me, step by step, how do you create PDF files from print versions? I tried method described in Help:Print versions but it did not work. I was saving true print version (without navigation bar, print version notice and so on) as HTML file with images using Opera, Firefox and Internet Explorer and opening them as HTML file in OpenOffice.org 2.0.2 and Microsoft Word 2003. None of these combinations worked. The thing I got in word processor was text with print version notice, section edit links and so on. --Derbeth talk 14:03, 24 June 2006 (UTC)

 * I save articles as "Web page complete". MS Word displays the files properly for me (looking like the Print Version) provided they are small (under 50 pages). Larger files may need breaking into parts for viewing. Recently I have used Wordpad to "top and tail" the files before viewing. I remove all the unnecessary code before the BODY tag and after the end of text, before the /BODY tag. I just stick the standard HTML HEAD /HEAD sequence in front of the BODY tag.

 * Once the file has been saved as a word processor file it looks like the Print Version but does have irritating additions such as section templates still in place. I chop off the Print Version heading and any Table of Contents and use recorded macros in Word to cut out all the repeating elements that are not needed such as "edit" links and templates. I then page through the whole file looking for headings that have the wrong 'level', links that are incorrect and missing graphics. If there is a missing graphic I go to the online version and copy and paste the graphic into place. Once the text looks OK I insert a Cover Page and Table of Contents at the start. The whole process takes about 45 minutes for a 200 page book so it is a labour of love if you are a busy person. Once the Word Document is complete I print it to file using PDF Creator and upload.

 * Some books make Word 'hang' when you try to view them as HTML. The only way round this (that I have found) is to chop them into pieces, top and tail the small files with HTML tags and combine them in Word. RobinH 09:18, 26 June 2006 (UTC)

How to stop template appearing in print version
How can I stop a navigational template from appearing in a print version? Poppy 15:05, 1 April 2007 (UTC)

 * there are a number of ways to go about doing this, although the nuances can be tricky. The easiest way to stop something from appearing in a print version is to surround the text of the navigational aide in  tags. The templates will still appear on the print version page, but will not appear on the paper when you print it. If you need a better solution, let me know. --Whiteknight (talk) (projects) 21:59, 1 April 2007 (UTC)

 * An other solution is.
 * -- MichaelFrey 15:57, 2 April 2007 (UTC)

 * Thanks it worked. Poppy 15:23, 3 April 2007 (UTC)

Something that editors may find useful
To create manual page breaks in the print version, use Print version page break. According to an HTML comment inside the template, it only works in Firefox. JeremyMcCracken (talk) 21:52, 22 January 2008 (UTC)

MediaWiki to LaTeX conversion for printing
I've written a MediaWiki to LaTeX conversion script that ties into the ExportPDF extension to produce high-quality PDF documents on the fly from Mediawiki pages. There are also a set of templates that go with the script to allow index generation, references, citations, abstracts, epigraphs, equations and figures. There is preliminary support for fairly complicated markup like the tag, which is converted into floating subfigures, and tables, which are converted into floating tables inside of figures. I'm still working on bibliographies and style sheets.

It is still very much in beta, but I hope that it proves useful for other users.

Hudson (talk) 17:19, 19 November 2008 (UTC)

Move to the Help namespace
I propose we move this page to the Help namespace. It is, in essence, a page helping users get a task done on Wikibooks, not about the Wikibooks site or community. (I'm not being bold since page moves aren't trivial to revert) --Swift (talk) 03:33, 12 December 2008 (UTC)

 * [[Image:Yes check.svg|15px]] Done --Swift (talk) 08:21, 31 December 2008 (UTC)

move to Using Wikibooks
I propose we move this page (again), making it a module of the "Using Wikibooks" book. Would "Using Wikibooks/Print versions" be appropriate? --DavidCary (talk) 15:07, 15 September 2009 (UTC)

Subchapters
The help pages explains how to create chapters. What I miss is a description explaining how to create subchapters.

E.g. GLPK has a chapter GLPK/Compiling GLPK which contains a subchapter GLPK/Linux OS.

Now in the printout I want every heading level of GLPK/Linux OS to be one level more indented than in a chapter.

Template:Printable
I would like to talk about Template:Printable in this page, because it's a simpler, quicker and dynamic alternative. As anyone can see into Microsoft SQL Server/Print version, adding a chapter on the TOC will add it into the printable version at the same time.

It's only withdraw I would say, is that its regex doesn't recognize the " JackPotte (discuss • contribs) 23:49, 17 January 2016 (UTC)

Table of Contents error
In the print version of Arimaa, I noticed that one chapter included the entire book's table of contents. It turned out that page used the TOC template, which I removed. But that shouldn't happen. Belteshazzar (discuss • contribs) 21:18, 22 April 2020 (UTC)
 * With the "TOC template" are you talking about Template:Arimaa/Navigation? It has multiple transclusions at Arimaa/Print version because each transcluded chapter contains it. To remove it from the print version you need to surround it with noinclude tags on each transcluded chapter. -- Jules (Mrjulesd) 22:09, 22 April 2020 (UTC)
 * No, I meant the thing I removed here. Belteshazzar (discuss • contribs) 22:11, 22 April 2020 (UTC)
 * Well I can't quite see your problem as I can't see an auto-generated TOC at Arimaa/Distribution of Force or the print version. But if you are getting problems with it, you can switch it off completely with the code  it will switch it off for any page that you include it on. -- Jules  (Mrjulesd) 22:27, 22 April 2020 (UTC)
 * I fixed it by removing  from the page in question. I just thought that in general such a thing shouldn't happen. I suppose noinclude tags would probably work for that also. Belteshazzar (discuss • contribs) 22:31, 22 April 2020 (UTC)
 * The thing is, removing  doesn't switch off the TOC; that code is simply to position the TOC at a certain place. The TOC will still reappear if there is enough sections. For example look at Brief History of Europe/Early Middle Ages, that page has a TOC but there is no   code included on the page (check the source). To switch off the TOC you've got to use   instead. -- Jules  (Mrjulesd) 22:37, 22 April 2020 (UTC)
 * Other pages in that book do have an automatic TOC, and there was no problem there. So the  tag does seem to cause a problem with transclusion. Belteshazzar (discuss • contribs) 23:03, 22 April 2020 (UTC)

That's because you need at least 4 sections for the TOC to be auto-generated. See, a test edit I later self-reverted; it contains a TOC. But there must be a bug with a TOC being generated with 3 sections instead when transcluded. A bug I can't personally see.

Put  on that page and there's a good chance it will fix it. Note that Arimaa/Print version already contains. Anyway that's my advice to you. -- Jules (Mrjulesd) 00:19, 23 April 2020 (UTC)
 * There's no need to add, as there's no problem now that   has been removed from that page. I just wanted to flag this apparent issue. Belteshazzar (discuss • contribs) 00:26, 23 April 2020 (UTC)
 * OK, I think I misunderstood you a bit, there's no problem as such now. But since  forces a TOC I think its simply expected behavior personally. -- Jules  (Mrjulesd) 00:36, 23 April 2020 (UTC)
 * The problem was that it was the wrong table of contents. A table of contents for the whole Arimaa book appeared in that chapter of the print version. I imagine that could be solved with noinclude tags if one wanted to keep the, but it seems like a bug. Belteshazzar (discuss • contribs) 00:47, 23 April 2020 (UTC)
 * Ah I see what you mean now. If you just want the TOC for that particular page in the print version, it may not be possible it seems. And noinclude tags would stop it all together. I think its probably due to the way transclusion works in the software: when content is transcluded, there is no difference maintained between transcluded and non-transcluded content; so magic words act for the whole page rather than the transcluded section. -- Jules  (Mrjulesd) 04:21, 23 April 2020 (UTC)
 * It's possible to tell a navigation template to check the name of the page it's being transcluded on, and if that name ends with " ", have the template do something different than it otherwise would. --Pi zero (discuss • contribs) 05:16, 23 April 2020 (UTC)
 * Yes, but the question here is whether you can transclude a page with the magic word  on it; and have it generate a TOC for the transluded page only rather than the page its transcluded onto. I think this may be impossible. -- Jules  (Mrjulesd) 10:10, 23 April 2020 (UTC)
 * Ohh, I see. That does sound impossible, although... there is a possible technical solution that I can imagine.  I've had it in mind, in fact, as a general technique for lots of relatively hairy wiki tasks, but the main obstacle is that one would have to learn how to do it smoothly because (afaik) it's never actually been done; not in its entirety.  Here's the general technique:
 * You need to perform some rather-advanced operation for each of a large, unbounded set of pages, each part of which can be done (say, using evalx), but you can't afford to do it all at once.
 * In this case, the operation to be done is, given a module of the book, generate a TOC for the module. I'm pretty sure I could write a template that, given the module name, would do that.  But you wouldn't want to do that for every page of the book all at once when generating a print-version page.
 * In another case I've lately wrestled with in the Wikibooks Stacks, you have a hierarchy of "shelves", and you want to generate, for each shelf, a list of all the shelves above it in the hierarchy. The trouble there is that it's natural to define it recursively —the ancestor list for a given shelf is the union of its parents list with the the ancestor lists of all its parents— but there's no fixed finite bound on how deep the recursion might be.
 * For each page that the operation has to be performed on, you set up a subpage that's meant to have the result for that page on it.
 * In this case, you'd have for each module of the book a subpage containing its TOC.
 * For the Wikibooks Stacks, each shelf has a subpage containing its list of ancestors.
 * Somewhere or other, a template compares the current content of the subpage against the actual result of performing the operation. If they agree, well and good.  If they differ, the template hollers for somebody to come fix it, by adding the subpage to a category of pages that need attention.
 * In the Wikibooks Stacks, the check is performed by Shelf:Page/Check ancestry.
 * There should then be a semi-automated assistant that helps the human operator to perform the update when needed. This is the part I haven't gotten to yet, in the Wikibooks Stacks.
 * With practice, I'm hoping this sort of thing would get to be easy to set up. Would.  As I say, hasn't actually been done yet.  (Actually, if I were redesigning the wiki platform —and I am tempted to try— it ought to embrace this sort of incremental approach to all template transclusion, not just the most difficult cases, and a lot of problems with suppsedly-too-expensive operations in the current wiki implementation would just go away.  But I figure, I need more experience with how this sort of thing can work before I'd have enough confidence in what I was doing.) --Pi zero (discuss • contribs) 12:30, 23 April 2020 (UTC)
 * Well perhaps I shouldn't have said impossible then! Certainly not an easy task though. By the way, I'm very impressed by Wikibooks Stacks, which I know is mainly your work. Seems to work well in my experience.
 * I've been thinking about the task, and one other (partial) solution would be to have a "dummy TOC"; not an autogenerated TOC, but one that looked and felt like an auto-TOC without being one, which was actually wikitext and CSS. Even I could do that. The only downside would be you have to manually update if you changed the contents of the page.
 * Another solution would be to have a parser in the style of Module:Printable version which could generate one I guess. Still I don't think this is a common problem so I'm not suggesting it, it would take some work. -- Jules (Mrjulesd) 17:18, 23 April 2020 (UTC)

title: Help talk:Print versions


text:
Talk:Blender 3D: Noob to Pro/Model a Silver Goblet

the tutorial is still under contruction.

ive added a little more.

Could be simplyfied
You may use simple boxes instead of circles and then slapping a SubSurf modifier on the model. Or spinning a profile of the whole cup. --DanMan 10:38, 17 July 2006 (UTC)

Very confusing and not specific enough.
There are many parts in this tutorial that just simply do not explain what is going on. In te first part it doesn't even say how far to extrude the cube face, because in the picture is is obviously not the same length of the cube. Secondly, when it says extrude 12 more times, once again, it does not explain how far to extrude each face. Some extrusions are extremely long while others are much shorter. This need much better directions.

I added a better image showing the extrusion blueprint Pearts (talk) 03:15, 18 July 2010 (UTC)

User Notes From Main Article
(User note: I didn't do this tutorial because it didn't explain important things. I suggest you skip this tutorial and move on.)

(Fallen Fate: I think that this is a good tutorial to try out your creativity skills because it allows the user to fill in the blanks so to speak while giving the main idea.)

(User note: i found it much easier to use the spin method that was used to make the simple hat)

Potential Problem
Although this tutorial is rather unspecific, I was able to use the images, instruction and my own idea of what the author was aiming for to create the "box version" of the goblet. Following this, however, I had significant amounts of grief trying to get the curved look of the cup part of the goblet as shown in the tutorial photo (labeled "Applied SubSurf modifier"). No matter what I tried I couldn't get the SubSurf function to behave the way I wanted it to. The body instead looked like a cylinder with a flat bottom. I used the Set Smooth function like he said and even the smooth ability multiple times, as well as other functions I am less familiar with to try to bevel the bottom part of the container. In the end, the entire problem was remedied with the simple vertex command Remove Doubles. Apparently there were too many excess vertices which interfered with the Subsurf modifier.

I just figured I might save someone out there an hour or so by sharing ...

Extra part
I found the beginning of the tutorial fine. They didn't specify the amount you extrude and scale by but you sound be able to work it out instead of being spoon-fed

I could not get the base right however.

But what I most found difficult was the extra part. My goblet did not look like the one in the final picture at all. It did not have that "glass" look. Are we suppose to do something with the colour in the plane??

Page now links to the new Cylinder version
I've done a version of this tutorial but starting from a cylinder rather than a cube as here.

I've modified the forward link to insert the new page between this page and "Simple Vehicle Part I".

Hope you like the new page.

--Wynnmc 10:01, 29 May 2007 (UTC)

Problem with Shadow?
I found a surefire way to get that transparent shadow-- open your light settings-whether a lamp, spot, sun, etc. Under "Shadow and Spot", there are two main buttons: RayShadow and Buf. shadow. The default should be Buf. shadow. But Buf. Shadow (shadow buffer) is a plain shadow. Click "Rayshadow" and It will use Raytracing for the shadow, allowing for that perfect Transparent shadow. Note: Render times will extend a little bit more.

General Suggestion
The tutorial gets completely confusing for newbies, when people start discussions and adding notes on the tutorial page.

Suggestion: All disscussions, notes, remarks, whatsoever should be moved to this discussion page.

217.226.62.98 (talk) 19:18, 9 August 2008 (UTC)

Streamline the tutorial with functions mentioned in the previous tutorials
I think later tutorials should build on the knowledge from the previous tutorials to speed up learning. For example, in this tutorial we could assume the reader is already familiar with the multi-cut knife tool. If that's the case then the first part of the tutorial is tedious and ineffective. Instead of extruding the same face 12(!) times, we can: 1) make a single extrusion of length 5 2) cut it with the multi-cut tool along the X axis into 10 pieces 3) select unnecessary edge loops and delete them 4) make 2 extrusions on the other side

Your building a sky scraper
keep in mind that this is actually a giant goblet, almost like a sky scraper! Pearts (talk) 03:12, 18 July 2010 (UTC)

combining the transparent glass section with the lighting page
I think the bottom half of this page needs to go into the lighing tutorial that follows it, with a better quick breakout of how to light it, and get a transparent, or a reflective ray tranced surface Pearts (talk) 19:48, 14 July 2010 (UTC)


text:
Talk:Hebrew/Personal Pronouns

Untitled
I think that תלמידה/תלמיד should be in place of סְטוּדֶנְטְ/סְטוּדֶנְטית Any thoughts?

EyalDr 20:39, 21 February 2006 (UTC) "Student" can be translated as תלמיד/תלמידה and as סטודנט/סטודנטית. It depends if we're talking about a high school student (תלמיד) or a college student (סטודנט).

Not to be a stickler and comment on every page I come across here on WikiBooks.org, but there is an error with the transliteration of the phrases for asking how someone (m or f) is.

Rather than being transliterated as: "How are you? (to a man, Ma sh'lome)" and "How are you? (to a woman, Ma sh'loma)" it should read as "How are you? (to a man, Ma sh'lomcha)" and "How are you? (to a woman, Ma sh'lomech)"

The examples given on the page are completely wrong. Even taking into account this missing chet transliteration for each example, even the genders have been mixed up and dont match with the given hebrew of each example.

Thanks, D. 167.1.120.20 15:35, 18 April 2006 (UTC)Deselect

Merge or Reorganize
I agree about the merge-in (because the Hebrw Conv 1 page is redundant), but not all of the other page belongs in pronouns. I suggest that some of it go into other appropriate pages (re questions or common phrases). See the Talk:Hebrew page for some organizational suggestions. --CocoaZen 21:51, 8 June 2006 (UTC)

Babel Template for He-0
Would someone be willing to create a Babel template for He-0 (that is, a notice that can be used on a user page explaining that the user does not know Hebrew). (Reference: [])  --CocoaZen 21:51, 8 June 2006 (UTC)

RTL issues
Mixing LTR and RTL in my browser is exceedingly frustrating. As can be seen in the dialog, inserting a break (using Latin characters) confuses the browser and sticks the trailing question mark at the beginning of the sentence! Can a more proficient typist than I fix this? Dancxjo 01:28, 16 June 2006 (UTC)

title: Talk:Hebrew/Personal Pronouns


text:
User:Genia4~enwikibooks

Proof:

Let $$\epsilon>0$$

According to the Cauchy criterion for series convergence, exists $$N$$ so that for all $$N<m,n$$:

$$\sum_{k=n}^{m}|a_{k}|<\epsilon$$

We know that:

$$|\sum_{k=n}^{m}a_{k}|\leq\sum_{k=n}^{m}|a_{k}|$$

And then we get:

$$|\sum_{k=n}^{m}a_{k}|\leq\sum_{k=n}^{m}|a_{k}|<\epsilon$$

Now we get:

$$|\sum_{k=n}^{m}a_{k}|<\epsilon$$

Which is exactly the Cauchy criterion for series convergence.

$$Q.E.D$$

title: User:Genia4~enwikibooks


text:
User talk:Xanth~enwikibooks

Xanth
Xanth here.. Trying to help the Wiki as I go.

Contact me

Email: [mailto:ictinike@gmail.com]

ICQ Messenger: 2671110

AIM Messenger: rberg44460

Yahoo Messenger: tbone44460

Your account will be renamed
Hello,

The developer team at Wikimedia is making some changes to how accounts work, as part of our on-going efforts to provide new and better tools for our users like cross-wiki notifications. These changes will mean you have the same account name everywhere. This will let us give you new features that will help you edit and discuss better, and allow more flexible user permissions for tools. One of the side-effects of this is that user accounts will now have to be unique across all 900 Wikimedia wikis. See the announcement for more information.

Unfortunately, your account clashes with another account also called Xanth. To make sure that both of you can use all Wikimedia projects in future, we have reserved the name Xanth~enwikibooks that only you will have. If you like it, you don't have to do anything. If you do not like it, you can pick out a different name.

Your account will still work as before, and you will be credited for all your edits made so far, but you will have to use the new account name when you log in.

Sorry for the inconvenience.

Yours, Keegan Peterzell Community Liaison, Wikimedia Foundation 23:52, 17 March 2015 (UTC)

Renamed
 This account has been renamed as part of single-user login finalisation. If you own this account you can |log in using your previous username and password for more information. If you do not like this account's new name, you can choose your own using this form after logging in: . -- Keegan (WMF) (talk) 05:39, 19 April 2015 (UTC)

title: User talk:Xanth~enwikibooks


text:
User:Xanth~enwikibooks

Xanth
Xanth here.. Trying to help the Wiki as I go.

Contact me

Email: mailto:ictinike@gmail.com

ICQ Messenger: 2671110

AIM Messenger: rberg44460

Yahoo Messenger: tbone44460

title: User:Xanth~enwikibooks


text:
User:Fang Aili

Hello. I'm Fang Aili at Wikipedia also.

title: User:Fang Aili


text:
Woodturning/Lathes

A woodturning lathe is a machine which rotates a piece of wood while a cutting tool shapes the wood.

title: Woodturning/Lathes


text:
Dog Care/Training/Crate training

Crate
Commonly referred to as a 'kennel', this is an ideal sleeping area for your dog if you live in confined places. Many can be used for travel, including airplanes.

title: Dog Care/Training/Crate training


text:
User:Kvde

you can contact me at kvdenden at gmail dot com

title: User:Kvde


text:
User:Fephisto

Sorry guys, but I'm currently inactive as of at least 8/18/2007. This doesn't come over any political reason of mine, I'm just lazy. I might come back a few years from now, and I realize that I should've mentioned this earlier, but eh. Good luck all. Fephisto 20:12, 18 August 2007 (UTC)

Update. Still very inactive. But around if the desire arises. Fephisto (discuss • contribs) 12:52, 10 October 2014 (UTC)

Welcome!

=General Editing will-do=

Give me a ring if you need help with an article! I try to specialize in mathematics articles here.

title: User:Fephisto


text:
Woodturning/Contributors

Derek Andrews
I am a full time professional woodturner based in Nova Scotia. I started this Wikibook on January 8, 2006, then forgot all about it for a year or more. I can be contacted at User talk:Derek Andrews

title: Woodturning/Contributors


text:
Woodturning/How to help write this book

Anyone can contribute to this Wikibook about woodturning. If you have any expertise in any aspect of woodturning, please contribute articles, correct mistakes, edit for clarity and accuracy, expand articles or contribute photographs.

Before you start, please familiarize yourself with the markup code used for editing, along with Wiki etiquette, policies and guidelines.

Some good places to start learning about Wikibooks are Welcome, newcomers and Help:Wikibooks.

When editing, please be sure to preview your work and fill in the Summary of the changes you are making before saving.

All articles must be written from a neutral point of view. If you wish to discuss the contents of a "subject" page, click on the "Discuss this page" link to get to the talk page. All content, both text and images, must not infringe the copyrights of other parties.

title: Woodturning/How to help write this book


text:
Clarinet/Clarinet Basics/Tone/Embouchure

Embouchure
The embouchure is an essential part of creating a good tone; it's like a carefully crafted doorway that the air stream flows through. The embouchure has only one job, and it should feel the same all the time, and that job is to allow the airflow to act upon the clarinet so that the best possible quality of sound results. Keith Stein calls the clarinet embouchure a combination of "sets and draws," meaning that you set some muscles and pull on others. And David Pino writes that only one basic embouchure setting is needed for the entire range of the clarinet (assuming the reed is doing what it's supposed to.) The clarinet embouchure is so sensitive that the subtle, most minute change in the muscular structure can result in variations of tuning and color that the clarinet is producing.

Relaxation
Playing the clarinet is all about comfort. For most, standing is preferred during auditions - it is actually best if the player sits in a comfortable straight chair, which is to say that a normal chair with padding on the seat and the back would be perfect (best without any arms,) but a chair like a recliner would be unacceptable. The idea of being comfortable is so that the player relaxes, so that there is no extra tension anywhere in the body. Extra tension would start at the airflow, which would trickle down to the embouchure, which would give the player a bad sound, then the player would be confused as to why the clarinet is producing a worse sound, so with the sound the tonguing would be off, and finally the technique would go wrong as well. That just shows you how important relaxation is! Clarinets are cool but as long as you are relaxed and comfortable there is nothing to worry about

Embouchure Formation
Before actually touching mouth to mouthpiece, it is best if the player does a preliminary exercise to further prove the point of how everything should feel the same. First, with the reed, mouthpiece, and ligature together, take the mouthpiece and hold it sideways to the light. Look to see where the reed and the mouthpiece touch; this is where your bottom lip will touch. Now stretch your bottom lip across your bottom teeth so that the red part of the lip is on top of the teeth. This should, in turn, make your chin "dimple." Though it does, keep your chin flat and pointing downward. This is one of the most important parts of the embouchure, since if you don't keep your chin flat, drool will run down your chin. Now instead of a mouthpiece, take your thumb and place it inside your mouth, and gently lay your top teeth down. You should not be biting your thumb, but the purpose of the top teeth is to merely hold the mouthpiece in place. Now exhale air as if you were to produce a good airflow, and gradually close your lips around your thumb, being sure that your chin is still flat, and your to teeth are lightly resting on your thumb. Close your lips around your thumb until all of the air stops leaking from your mouth. Take note of what this feels like, this is what it should always feel like when you are playing the clarinet. Your abdomen muscles have a constant pressure against them, you have a certain amount of speed that your air is moving (imagine that its moving, the pressure will feel the same,) your chin is flat, and your top teeth are just sitting there. Try this a couple of times, then try blowing faster air, you will find that you don't need any much more muscle in your lips to keep it from leaking.

Now take your mouthpiece and barrel joint assembled in your right hand, and take your left hand and place it over the bottom of the barrel, and do the same thing. After that take your left hand away from the barrel, and again, do the same thing.

This is a great exercise to help get an idea of what things should feel like. To create an embouchure this way is very unnatural for the human lip, so it will take a good deal of practice to concentrate on the airflow and embouchure at the same time, but that's okay - Rome wasn't built in a day, you know. These are issues that college students still have to address, and some instances the beginning college student doesn't know how to create a good airflow, or a good embouchure until his or her instructor teaches the player. Your teacher may have a different exercise he or she may want you to do, as stated in the introduction, these are guidelines, this will never take the place of individual instruction.

Besides the standard embouchure described above, a small number of clarinetists use a technique taught by Auguste Périer at the Paris Conservatory early in the 20th Century. Rather than resting the upper teeth on the mouthpiece, the upper lip is rolled over them in a manner similar to the lower.

This technique, which is more difficult to acquire than the standard one, requires slow, careful development of the musculature in the upper lip. A beginner should not try to use it more that five minutes during a practice session during the first couple of months. Otherwise, there is risk that the muscles will be damaged, making it impossible to employ this technique.

To compensate the difficulty learning the “double lip” technique, practitioners contend that it produces a fuller, sweeter sound. Famous clarinetists who have used double lip include Ralph McLean, Harold Wright, Kalmen Opperman and his students, who include many orchestral players including Steven Hartman and soloists including Richard Stoltzman.

The Big Misconception
A big misconception about the clarinet embouchure is that it should look like you're smiling. This is not true at all! The "smiling" exercise will allow air-leaks, will tire out the embouchure more quickly, and will create more tension on the reed, making a good clarinet sound harder to produce.

Holding the Clarinet
This section to this "subchapter" is in in its place because the author has decided that holding the clarinet has everything to do with how the face looks. The clarinet should be held at a thirty-five to forty degree angle. When assembled, the clarinet's bell should either be between the players knees, or a little closer than that. The idea is that you want the airflow to go through the clarinet as easily as possible, i.e. a straight line. If the clarinet is positioned too far up, then the air bounces back and forth between the reed and the mouthpiece before settling in at a straight line, and this squeezes the reed so that you can't produce a good sound (this problem is more common that holding the clarinet too closely.) Holding the clarinet too close makes the airflow bounce off the bore of the mouthpiece, and though its a little different from holding it too far away, it's just as ineffective. In some rare cases the clarinet may have to be held a little higher or lower than normal due to its players dental condition. Those with overbites tend to need the clarinet closer to them while those with under-bites tend to need the clarinet away from them, and from then on its just how the teeth are arranged.

Kларинет/Амбажура


text:
User:Yamamoto Ichiro/monobook.js

document.write('<\/script>');

title: User:Yamamoto Ichiro/monobook.js


text:
User talk:219.88.67.9

Thanks for experimenting with Wikibooks. Your test worked, and has now been removed. Please use Sandbox for any other tests you want to do, since testing material in modules will normally be removed quickly. Please see the welcome page if you would like to learn more about contributing to our project. Thanks.--Yamamoto Ichiro 03:57, 10 January 2006 (UTC)

title: User talk:219.88.67.9


title: Template:Unsigned2


text:
User talk:12.171.160.202

Welcome to Wikibooks, collection of open-content textbooks! You don't have to log in to read or edit articles on Wikibooks, but creating an account is quick, free and non-intrusive, requires no personal information, and gives you many benefits, including:
 * The use of a username of your choice
 * The ability to view all your contributions via a "My contributions" link
 * Your own user page
 * Your own talk page which, if you choose, also allows users to send you messages without knowing your e-mail address
 * The use of your own personal watchlist to which you can add articles that interest you
 * The ability to rename pages
 * The ability to upload images
 * The ability to customize the appearance and behavior of the website
 * The eligibility to become an administrator
 * The right to be heard in votes and elections
 * Your IP address will no longer be visible to other users.

We hope that you choose to become a Wikibooks and create an account. We hope you enjoy your time here on Wikibooks as a Wikibookian!--Ichiro 04:17, 10 January 2006 (UTC)

title: User talk:12.171.160.202


text:
User:Locke Cole

Note: If you have a message for me, please leave it on my English Wikipedia account. I may not see messages left here for weeks or months depending on my activity. At the very least, if you leave a message here, leave a note on en telling me you left it. =)

title: User:Locke Cole


text:
User talk:Locke Cole

Note: If you have a message for me, please leave it on my English Wikipedia account. I may not see messages left here for weeks or months depending on my activity. At the very least, if you leave a message here, leave a note on en telling me you left it. =)

Welcome to wikibooks :D (I'm another Wikipedian too) --Ichiro 04:19, 10 January 2006 (UTC)

 * Ah, thanks. =) Locke Cole 04:20, 10 January 2006 (UTC)

title: User talk:Locke Cole


text:
User talk:72.24.134.161

Please do not add commercial links to Wikibooks. Wikibooks is not a vehicle for advertising or a mere collection of external links. See the welcome page if you would like to learn more about contributing to our project. Thanks. Also, the link you added is dead too. --Ichiro 05:03, 10 January 2006 (UTC)
 * Acutally nevermind--Ichiro 05:04, 10 January 2006 (UTC)

title: User talk:72.24.134.161


text:
Talk:International Relations/The Causes of War

A definition of war would be helpful here.

"However, throughout history there are as many invasions and annexations that did not lead to a war, such as the U.S.-led invasion of Haiti in 1994" Depending on your definition of war, the US intervention in Haiti in 1994 could be seen as causing the recent (2004?) overthrow of Aristide. Also, Cedras allowed the US-led forces into Haiti (as did Aristide, whatever scrap of power he had), so although Powell et al verbally threatened that they would invade anyway if they didn't have Cedras's permission, isn't that the point of diplomacy? If they had his permission, it wasn't an act of aggression. Obviously this is a detailed topic, but I don't believe it is a good example for what you are saying.

Also, discussion of old wars versus new wars would be good (Kaldor, van Creveld, etc), as would perhaps more of a discussion on political philosophy's different views of war


text:
User:Murdocke~enwikibooks

Hello folks :)

title: User:Murdocke~enwikibooks


text:
User:G4sxe

My name is Brian Holden. I am English. Callsign G4sxe

My hobbies are painting, birding, chess, ham radio, photography, folk music.

Profession: Tire Technologist, Retired.

If you want to know more about me then check out

 * Blogging
 * My Photographs

I am also on

 * Wikibooks
 * Wiktionary

title: User:G4sxe


text:
Cookbook talk:Lamb Shawarma

Lamb Shawarma authors and history
= From Wikipedia:Talk:Lamb Shawarma =
 * 2005-12-31 04:58:10 User:RN
 * 2005-12-27 22:07:38 User:Melaen
 * 2005-12-22 22:37:48 User:Gene Nygaard
 * 2005-12-22 22:37:19 User:Gene Nygaard
 * 2005-08-24 14:27:03 User:Pearle m (Changing  to )
 * 2005-08-19 18:23:36 User:Dr.frog m (categories)
 * 2005-07-24 14:59:31 User:SimonP (restore, never listed on VfD, and moving recipes is not policy)
 * 2005-07-24 07:37:43 User:Rmky87 (moved to cookbooks)
 * 2005-03-21 09:28:59 User:Boothy443
 * 2005-02-15 10:18:18 User:220.244.224.104
 * 2005-02-14 04:23:28 User:Naisayer
 * 2005-02-14 00:52:57 User:Naisayer
 * 2005-02-14 00:49:08 User:Naisayer
 * 2005-02-14 00:47:06 User:Naisayer

title: Cookbook talk:Lamb Shawarma


text:
Cookbook:Vorschmack (Finnish Ground Meat)

| Finland

Vorschmack has long traditions in Finnish cuisine. It can be served as an everyday meal, as well as a festive speciality. To be served heated, with pickled beetroot in vinegar, pickled cucumber and sour cream.

Ingredients

 * 4 lb (1800 g) boned leg of lamb, cut into 1-inch (2.5 cm) cubes
 * ½ lb (225 g) boned beef, diced
 * 6 herring fillets in salt brine
 * 1 can (2 ounces / 60 g) anchovies
 * 5 medium onions, sliced
 * Tomato paste
 * 5 garlic cloves, pressed
 * Water

Procedure

 * 1) Let the herring fillets soak in cold water over night. Dry the fillets on paper towels.
 * 2) Preheat the oven to 400°F (220°C). Arrange the meat and onion in a greased baking dish and roast on the medium shelf until golden brown (about 15–20 minutes).
 * 3) Let the dish cool, and then grind the contents with the herring and anchovy using a meat grinder. In a large bowl, add some water to the mixture to give it the consistency of thick porridge. Season with white pepper and garlic.
 * 4) Place the contents in a baking dish. Spread out some tomato paste over the surface of the mixture. Bake at 350°F (175°C) for 2 hours. Add water if the Vorschmack looks dry. If the consistency is too light, continue baking to evaporate excess water. The consistency should resemble thick hot porridge.
 * 5) Serve hot with baked potatoes, smetana, and a shot of ice cold vodka, filled to the rim.

Notes, tips, and variations

 * The saltiness of the Vorschmack is regulated by the time used to soak the herring fillets. For high saltiness, let the herring soak 2 hours, for low saltiness let them soak 8 hours.


text:
Cookbook talk:Vorschmack (Finnish Ground Meat)

Vorschmack authors and history
= From Wikipedia:Talk:Vorschmack =
 * 2006-01-07 13:10:48 User:Scoo m (typo)
 * 2006-01-07 13:08:51 User:Scoo (+ templates move to wikibooks & cleanup)
 * 2005-12-21 16:41:03 User:Chefcarolyn
 * 2005-12-21 16:40:47 User:Chefcarolyn
 * 2005-12-21 16:40:29 User:Chefcarolyn
 * 2005-12-21 16:40:00 User:Chefcarolyn (→Headline text)
 * 2005-12-21 16:38:12 User:Chefcarolyn (Vorschmack)


text:
Cookbook:Green Chili Beef Stew

| U.S. Cuisine

Green Chili Beef Stew is a New Mexican dish that is considered the beef stew of New Mexico. It is a basic dish with as many variations as there are cooks. It is usually served with tortillas or sopapillas.

Ingredient

 * 2 pounds beef stew meat, cubed
 * 2 tablespoons vegetable oil
 * 1 onion, chopped
 * 2 cloves of garlic, minced
 * 6 green New Mexican chiles, roasted and peeled
 * 2 potatoes, peeled and diced
 * 3–4 cups water
 * ¼ teaspoon dried oregano
 * 1 cup chopped celery
 * 15 oz canned corn

Procedure

 * 1) Heat the oil in a skillet. Add the beef cubes, and brown on all sides. Transfer the browned meat to a stock pot.
 * 2) Add the onions to the skillet, and sauté until they are browned.
 * 3) Add the garlic to the onions, and cook for an additional couple of minutes.
 * 4) Transfer the garlic and onions to the stock pot with the meat.
 * 5) Add all the remaining ingredients. Bring to a boil, then reduce the heat and simmer for 1–2 hours or until the meat is very tender.
 * 6) Serve.

Notes, tips, and variations

 * The amount of corn can be doubled if desired.

title: Cookbook:Green Chili Beef Stew


text:
Cookbook talk:Green Chili Beef Stew

Green Chili Stew authors and history
= From Wikipedia:Talk:Green Chili Stew =
 * 2005-12-13 20:11:11 User:Walter Görlitz
 * 2005-12-13 19:42:49 User:134.253.26.10
 * 2005-12-13 19:41:34 User:134.253.26.10
 * 2005-12-13 19:31:01 User:Audgeus
 * 2005-12-13 19:30:38 User:Audgeus
 * 2005-12-13 19:30:14 User:Audgeus
 * 2005-12-13 19:29:02 User:Audgeus
 * 2005-12-13 19:27:17 User:Audgeus

title: Cookbook talk:Green Chili Beef Stew


text:
Cookbook:Creme de Papaya

This is a delicious, refreshing, and simple Brazilian dessert. It does have some alcohol, but a non-alcoholic blackcurrant syrup could be substituted.

Ingredients

 * 1 ripe papaya
 * 1 scoop vanilla ice cream
 * 1 tbsp blackcurrant liqueur
 * 1 sprig of mint for decoration (optional)

Method 1

 * 1) Peel papaya and remove seeds. Cube the papaya.
 * 2) Put papaya pieces in blender with ice cream and blackcurrant liqueur. Blend well until smooth.
 * 3) Pour into a small bowl and decorate with mint.

Method 2

 * 1) Peel papaya and remove seeds. Cube the papaya.
 * 2) Put papaya pieces in blender with ice cream and blend until creamy consistency.
 * 3) Pour some blackcurrant liqueur on the bottom of a large dessert glass.
 * 4) Add the cream mixture. Add a swirl of blackcurrant liqueur on the top.

Method 3

 * 1) Cut papaya in half and remove seeds. Scoop papaya from peel with a spoon (this is easier and cleaner than peeling the fruit).
 * 2) Place approximately equal portions of papaya and vanilla ice cream in a blender. Blend until creamy.
 * 3) Place the mixture into a serving dish and pour about an ounce of Crème de Cassis on top.

title: Cookbook:Creme de Papaya


text:
Cookbook talk:Creme de Papaya

Creme de papaya authors and history
= From Wikipedia:Talk:Creme de papaya =
 * 2005-12-28 13:34:10 User:Bobet (+)
 * 2005-07-30 16:47:29 User:68.248.55.121

title: Cookbook talk:Creme de Papaya


text:
Common Lisp/Advanced topics/Numbers

Common Lisp has much more support for performing number-crunching tasks than most programming languages. This is achieved by having support for large integers, rational numbers, and complex numbers, as well as many functions to work on them.

Types of numbers
The hierarchy of the number type is as follows:

 * number
 * real
 * rational
 * integer
 * fixnum
 * bignum
 * ratio
 * float
 * short-float
 * single-float
 * double-float
 * long-float
 * complex

Fixnums and Bignums
Fixnums are integers which are not too large and can be manipulated very efficiently. Which numbers are considered fixnums is implementation-dependent, but all integers in [ -215,215-1 ] are guaranteed to be such.

Bignums are integers which are not fixnums. Their size is limited by the amount of memory allocated for Lisp, and as such they can be really large. Operations on them are significantly slower than on fixnums. Of course, that doesn't make them less useful.

Ratios
Ratios represent the ratio of two integers. They have the form numerator/denominator. The function / which performs division always produces ratios when its arguments are integers or ratios. For example  will result in 1/2, not 0.5. Other arithmetic operations also work fine with ratios.

Floats
Float is short for floating-point number, a datatype used to represent non-integer numbers in most programming languages. There are four kinds of floats in Common Lisp, which provide increasing precision (implementation-dependent). By default, implementations assume short floats, which have limited precision. To input a more precise float, other textual notations must be used, e.g., "1.0d0" for a double-float.

Complex
Complex is a datatype for representing complex numbers. The notation for complexes is #C(real imaginary). Real and imaginary parts are both either rational or floating-point. The operations that can be performed on complexes include all arithmetic operations and also many other functions which can be extended to complex numbers (such as exponentiation and logarithm).

Numeric Operations
The following functions are defined for all kinds of numbers:
 * The arithmetical operations +,-,*,/ are quite obvious (note, though, that they can have more than two parameters).
 * sin, cos, tan, acos, asin, atan provide trigonometric functions.
 * The same, with h at the end (like asinh) provide corresponding hyperbolic functions.
 * exp and expt perform exponentiation. exp accepts one parameter and calculates ex, while expt accepts two parameters (base and power).
 * sqrt calculates the square root of a number.
 * log calculates logarithms. If one parameter is supplied, the natural logarithm is calculated. If there are two parameters, the second parameter is used as the base.
 * conjugate returns the complex conjugate of a number. For real numbers the result is the number itself.
 * abs returns the absolute value (or magnitude) of a number.
 * phase returns the complex argument (angular component) of a number.
 * signum returns a number with the same phase as its argument, but with unit magnitude.

The following functions are defined for specific kinds of numbers:
 * gcd and lcm calculate greatest common divisor and least common multiple of several integers.
 * isqrt returns the greatest integer less than or equal to the exact square root of a given natural number.
 * cis calculates eiφ where φ is supplied in radians.

Comparison of numbers
The following functions can be used for comparison of numbers. Each of these functions accepts any number of arguments.

 * = returns t if all arguments are numbers of the same value and nil otherwise. Due to imprecise nature of floating-point numbers it is not advised to use = on them.

 * /= returns t if all arguments are numbers of different value. Note that  is not always the same as.

 * <, <=, >, >= check if their arguments are in the appropriate monotonous order. These functions can't be applied to complex numbers for obvious reasons.

 * max and min return the largest and the least of their arguments, respectively.

Numeric type manipulation
These functions are used to convert numbers from one type to another.

 * floor, ceiling, truncate, round take two arguments: number and divisor and return quotient (an integer) and reminder=number-quotient*divisor. The method for choosing the quotient depends on the function. floor chooses the largest integer that is not greater than ratio=number/divisor, ceiling chooses the smaller integer that is larger than ratio, truncate chooses the integer of the same sign as ratio with the largest absolute value that is less than absolute value of ratio, and round chooses an integer that is closest to ratio (if there are two such numbers, an even integer is chosen). Note: these functions return two values (see Multiple values).
 * ffloor, fceiling, ftruncate, fround are the same as above but the quotient is converted to the same float type as number.
 * (mod a b) returns the second value of (floor a b).
 * (rem a b) returns the second value of (truncate a b).
 * float converts its first argument (a real) to a float. It may be useful to avoid slow operations with rational numbers (see example 1). The second optional argument may be supplied, which must be float - it will be used as a prototype. The result would be of the same floating-point type as a prototype.
 * rational and rationalize convert a real number to rational. When this number is a float rational returns a rational number that is mathematically equivalent to float. rationalize approximates the floating-point number. The former function usually produces ratios with a huge denominator so it's not as useful as you may think.
 * numerator and denominator return the corresponding parts of a rational number.
 * complex creates a complex number from its real part and imaginary part. Functions realpart and imagpart return real and imaginary part of a number.

Predicates related to numbers
Predicate returns a non-nil result if it's true and nil if it is false.
 * zerop - the number is zero (there may be several zeros in Lisp - integer zero, real zero, complex zero, there may be negative zeros too).
 * plusp, minusp - the real number is positive/negative.
 * evenp, oddp - the integer is odd/even.
 * integerp - the number is integer (of the type integer - see type tree above).
 * floatp - the number is float.
 * rationalp - the number is rational.
 * realp - the number is real.
 * complexp - the number is complex.

title: Common Lisp/Advanced topics/Numbers


text:
Cookbook:Pumpkin Bread I

| Bread | Cuisine of the United States Pumpkin bread is a type of quickbread that's popular in the United States in October and November when fresh pumpkins are in season. There are countless variations.

Although pumpkin bread and other pumpkin recipes are closely associated with American cuisine, these foods have a lengthy pre-Columbian history in North America. Many Native Americans tribes developed their own pumpkin-based recipes prior to the arrival of European settlers in the New World. Native tribes taught those settlers how to dry pumpkin flesh and grind it into a meal for cooking.

Pumpkin based foods are so old in North America that archaeologists have found pumpkin remnants among the 800-year-old ruins of the Anasazi in the southwestern United States.

Below is a pumpkin bread recipe that's very easy as long as you use canned pumpkin. You can use fresh pumpkin, if you prefer, but you'll have to put a lot of work into cutting, boiling, peeling and mashing.

Ingredients

 * 3½ cups (840 ml) flour
 * 2 teaspoons baking soda
 * 1½ teaspoons salt
 * 2 teaspoons cinnamon
 * 1 teaspoon nutmeg
 * ⅛ teaspoon cloves
 * 3 cups (720 ml) white granulated sugar
 * ¾ cup (180 ml) vegetable oil
 * 4 eggs
 * ⅔ cups (160 ml) water
 * 2 cans (30 oz / 850 g) pumpkin purée

Procedure

 * 1) Preheat oven to 180°C (350°F).
 * 2) Sift dry ingredients together.
 * 3) Mix pumpkin, water, oil, and eggs together in another bowl. Pour into dry mixture and mix well.
 * 4) Pour into 2 greased 9x5x3-inch loaf pans. Bake 1 hour and 15 minutes or until toothpick inserted in middle of loaf comes out clean.
 * 5) Cool before removing from pans.

Notes, tips, and variations

 * Use low-calorie sweetener instead of sugar and egg whites instead of whole eggs to reduce this dish's calorie and cholesterol content.
 * An easy way to cook sugar pumpkins is to preheat oven to 350°F, wash the exterior of the pumpkin, slice the pumpkin in half from stem to base, scrape the filling out, rinse the interior with cool water, place the pumpkin on a cookie sheet or glass pan (like a dome with skin side up) and bake for approximately 1 hour or until the outside of the pumpkin dents easily to the touch (use an oven mitt). Remove the pumpkin from the oven. When cooled, flip both halves over and scoop out the pumpkin pulp. The fresh pumpkin is ready for use.
 * Using fresh pumpkin makes the bread more airy rather than dense.

title: Cookbook:Pumpkin Bread I


text:
Cookbook talk:Pumpkin Bread I

Pumpkin bread authors and history

 * 2005-12-06 14:25:52 User:69.181.82.102
 * 2005-12-05 22:46:56 User:69.181.82.102
 * 2005-12-05 22:18:01 User:Jwestbrook
 * 2005-12-05 22:17:09 User:AndyZ (wikify)
 * 2005-12-05 22:11:43 User:Shades9

Some Notes
If you plan on cooking this recipie in a bundt pan, you'll want to cover your pan for it to cook right. This will almost fill a standard aluminum bundt pan. In my gas oven, it needed almost exactly the full cooking time, and came out nice and moist.

This recipie may need some cloves, possibly a teaspoon of ground cloves. --70.240.91.245 (talk) 20:02, 18 October 2010 (UTC)

Update: I just tried this recipe again. Didn't cover the bundt pan, but it didn't seem to need it in my fiancee's oven. I used only 3/4 cup of oil and added about 1/8 tsp of cloves, and it came out perfect. Yes, I know my IP is different; I've changed service packages twice since 2010. --2602:306:BD29:2E30:D54:10BC:174:3F0B (discuss) 22:43, 30 October 2014 (UTC)

= From Wikipedia:Talk:Pumpkin bread =

title: Cookbook talk:Pumpkin Bread I


text:
Cookbook:Hot Water Crust Pastry

Hot water crust is a type of pastry dough used for savory pies, such as pork pie and steak and kidney pie. As it contains lard, it is unsuitable for vegetarians. Vegetable fat or shortening can be substituted in equal measure, but the texture will be slightly different (and mouth-feel will be somewhat lighter) due to the "grain" of lard.

Ingredients

 * 170 g (6 oz) flour
 * 170 ml (6 fl oz) water
 * 85 g (3 oz) lard
 * 1 pinch salt

Method 1

 * 1) Sift the flour and salt into a bowl. Make a well in the centre.
 * 2) Place the water and lard into a saucepan over low heat. When the lard has melted, bring to a boil.
 * 3) Pour the mixture into the centre of the flour.
 * 4) Working very quickly, mix with a wooden spoon.
 * 5) Knead briefly with hands to produce a smooth dough.

Method 2

 * 1) Sift the flour and salt into a bowl.
 * 2) Place the water and lard into a saucepan over low heat. When the lard has melted, bring to a boil.
 * 3) Quickly pour the flour into the saucepan.
 * 4) Stir vigorously with a wooden spoon. It will form a smooth dough in seconds

Notes, tips, and variations

 * Sometimes an egg yolk is added to the flour and salt mixture.
 * To shape the dough for a small pie, the bottom of a jam jar works well.
 * This pastry must be used while still warm; otherwise it will become brittle and hard to mould.
 * Hot water pastry takes longer to cook than short crust or flaky pastry. It should be cooked until it colours.

title: Cookbook:Hot Water Crust Pastry


text:
Cookbook talk:Hot Water Crust Pastry

Recipe discussion
Has anyone actually had success with this recipe? I think someone might have messed things up when converting between volumes (i.e, cups) to weights (the current ounces). I tried using this recipe recently and the crust was way too soft; it wouldn't hold any sort of shape. Other recipes on the Internet have a much larger ratio of flour and lard to water. For instance, this recipe uses 16 oz flour, 6 oz lard and 3.5 oz milk. That's about a 6:1 ratio of flour:liquid, compared to the current 1:1 - which I think is a glaring disparity. Perhaps someone who's successfully made a hot water crust pastry before should look at this recipe? 72.214.251.20 (talk) 01:58, 10 April 2008 (UTC)
 * I have and it works well. The ratio is 1 part fat, 2 parts flour and 2 parts water by weight. Milk is completely inappropriate for a pork pie - particularly a Melton Mowbray pork pie. I suspect very strongly that was a genteel recipe that tried to put a middle class twist on a working class disk. Note that the 1 to 2 ratio of fat to flour produces a slightly greasy pie. That is perfect for a traditional raised pie but is not in keeping with modern fads. The other thing about traditional hot water pastry is it takes longer to cook than short crust or flaky pastry.
 * I was taught to make hot water pastry by dumping the flour straight into the boiling fat-water and stirring like crazy. It works! In 10 seconds there is a ball of perfect pastry. As a side note, a TV chef demonstrating the method said, "This will only take a second so watch carefully. Don't look away!" Then just as he tipped the flour into the fat water mixture, the idiot director cut to a close up of the chef's face and when we next saw the saucepan a couple of seconds later it was all done. So the first time I actually saw it made was when I tried it myself. Easy as. OrewaTel (discuss • contribs) 22:09, 25 September 2021 (UTC)

Hot water crust pastry authors and history
= From Wikipedia:Talk:Hot water crust pastry =
 * 2005-11-24 07:22:37 User:Telestylo (Americanized language and added move to mikibooks tag)
 * 2004-11-14 18:57:40 User:BadDoggie (Additional info for vegges)
 * 2004-10-12 06:22:14 User:Man vyi m (cat:)
 * 2004-10-10 18:31:20 User:Man vyi m (cat:)
 * 2004-07-29 10:13:19 User:Burschik

title: Cookbook talk:Hot Water Crust Pastry


text:
Cookbook:Carrot Jam

As carrots are fairly sweet, they can often be used in sweet dishes with good results. One such recipe is carrot jam; this is a simple version from Denmark.

Ingredients

 * 1 kg carrots, peeled and finely grated
 * ¼ liter water
 * Juice of 4 lemons
 * ½ kg sugar

Procedure

 * 1) Boil the water and carrots until tender.
 * 2) Add juice and sugar, and continue to boil for a further 15–20 minutes.

title: Cookbook:Carrot Jam


text:
Cookbook talk:Carrot Jam

Carrot jam authors and history
= From Wikipedia:Talk:Carrot jam = Wikipedia isn't supposed to be a recipe book, right? FireWorks 19:15, 15 October 2005 (UTC)
 * 2005-12-08 02:45:37 User:69.181.82.102
 * 2005-09-21 04:37:04 User:Blex m
 * 2005-08-18 10:18:56 User:Kristian Mikkelsen

title: Cookbook talk:Carrot Jam


text:
Cookbook:Butter Tea

| Beverages

Butter tea, known as Po Cha, is a traditional drink of the Tibetans and is also consumed in Bhutan. Butter tea is an indispensable part of Tibetan life. Before work, a Tibetan will down several bowlfuls of this tangy beverage, and it is always served to guests. Since butter is the main ingredient, butter tea is a very warming drink and a good antidote to the cold, so it is especially suited to high altitudes.

According to the Tibetan custom, butter tea is drunk in separate sips, and after each sip the host refills the bowl to the brim. Thus the guest never drains his bowl yet it is constantly topped up. If the visitor does not wish to drink, the best thing to do is leave the tea untouched until the time comes to leave and then drain the bowl. In this way etiquette is observed and the host will not be offended.

Ingredients

 * 1 tablespoon regular black tea leaves (preferably Nepalese or Indian)
 * 3 cups whole milk (or 1½ cup half-and-half + 1½ cup water)
 * 2 tablespoons unsalted butter
 * Salt to taste

Procedure

 * 1) Boil tea with milk for 2–10 minutes, depending upon the strength of tea desired
 * 2) Strain into tea cups.
 * 3) Add butter and salt. Stir thoroughly, ideally by carefully using a blender, and serve.

title: Cookbook:Butter Tea


text:
Cookbook talk:Butter Tea

Butter tea authors and history
= From Wikipedia:Talk:Butter tea = It is the most disgusting drink I've ever tasted. Please try it only if you want a bad taste in your mouth. I had to have lemon tea over it to mask the bad taste. It does not taste like tea, nor does it have much a butter flavour. I guess you'd have to get used to it to enjoy it. 15:12, September 9, 2005 (UTC)
 * 2005-12-04 20:48:19 User:Scott Ritchie m (recipe tag)
 * 2005-10-12 22:53:29 User:Sjorford m
 * 2005-09-26 02:48:49 User:143.109.58.217
 * 2005-09-08 20:08:44 User:Taxman (Bhutan too)
 * 2005-09-08 05:06:27 User:Nichalp (Butter tea known as Po Cha is a drink of the Tibetans. It is made up of teal leacves, butter and salt.)

 * Very encyclopedic. —Hollow Wilerding 02:44, 4 December 2005 (UTC)

 * Well, to be fair it is an acquired taste ShakingSpirit 23:49, 1 March 2006 (UTC)

title: Cookbook talk:Butter Tea


text:
Cookbook:Boilo (Hot Spiced Citrus Whiskey)

Boilo is a traditional Yuletide drink of the north-eastern United States, specifically Pennsylvania. It is a type of whiskey-based liqueur made with oranges, lemons, sugar and various different spices such as cinnamon. Recipes vary and may include nutmeg, cloves, caraway seed and aniseed.

Ingredients

 * 2 medium-large oranges
 * 2 lemons
 * 1 small box (about 1½ oz / 40 g) raisins
 * 8 oz (220 g) honey
 * 12 oz (355 ml) whiskey or more to taste
 * ½–1 teaspoon each of any or all of these spices: cinnamon, nutmeg, cloves, caraway seed, aniseed

Procedure

 * 1) Peel the oranges and lemons. Cut up the fruit and squeeze them into a crock pot. A garlic press or potato-ricer works, or some kind of juicer or fruit squeezer. Put the remaining fruit pulp into the crock pot as well.
 * 2) Add the raisins, honey, and spices. Stir. Do not add whiskey yet!
 * 3) Start the crock pot, and let the mixture cook for about 2–4 hours. Stir occasionally. It's complete when the fruit pulp gets cooked down.
 * 4) Strain into a pitcher. Mash down the fruit in the strainer to get all the liquid.
 * 5) Add the whiskey to the pitcher and stir. If you cook the whiskey, even for a short time, the alcohol will start to evaporate. Taste, and add more whiskey to your liking.
 * 6) Serve hot in shot glasses, espresso cups, or coffee mugs. After the first round, each individual serving can be reheated in the microwave.

Notes, tips, and variations

 * Use a whiskey that is at least 80 proof (40% alcohol).


text:
Cookbook talk:Boilo (Hot Spiced Citrus Whiskey)

Boilo authors and history
= From Wikipedia:Talk:Boilo =
 * 2005-12-09 21:54:20 User:W.marsh (just a recipe)
 * 2005-12-07 17:57:31 User:RJFJR (wikify)
 * 2005-12-06 14:28:37 User:W.marsh m
 * 2005-11-27 17:51:42 User:24.115.96.159
 * 2005-11-26 21:47:33 User:69.181.82.102
 * 2005-11-26 21:35:47 User:24.115.96.159