text:
Haskell/Solutions/Higher-order functions

Choosing how to compare
Instead of comparing the two strings directly, we compare the all uppercase version. The order of the original two strings is then based on the order of the uppercase versions.

Higher-Order Functions and Types
Part 1:

1. A for loop in Haskell:

0 1 2
 * Main> for 0 (<3) (+1) (print)

2.  is an   action built recursively. At the beginning of each recursive step, the boolean  is checked. The base case, reached when  is , the result is the do-nothing action,. In the recursive case, the result is an action consisting of  followed by   called with   instead of   and with the same function arguments as before.

Part 2:

1. The naïve solution,, would not work. The type of is , a list of actions. There is nothing wrong with that per se, as actions are Haskell values like any others. However, a list of actions is not an action, and so it cannot e.g. be put in an  do-block and executed through.

2.

Or using :

3.

Alternatively,  can be implemented in terms of  :

Or point-free:

Function manipulation
1.

A stylistic alternative is using lambdas to emphasise that a function is being returned. If you ever get confused while trying to implement a function-returning function, doing that might make it easier to see what the implementation should be.

2.
 * passes the elements of a pair to, in order. As   always returns its first argument,   returns the first element of the pair; in other words, it is   in disguise.
 * converts, which returns the first element of a pair, into a function of two arguments which returns the first one; therefore,   is equivalent to.
 * Alternatively,  and   are inverses (that is, they undo each other;   amounts to  ), and so if   is   it is evident that   is.
 * A third approach is noting that, given the types of  and   type of   is an  function. The only possible function with this type is  ; therefore,   must be equivalent to it.
 * , given a pair, produces a pair with swapped elements., therefore, takes two arguments and pair them in swapped order; it is equivalent to.

All of the above answers can be rigorously checked by expanding and substituting definitions. Here is how it is done in the first case; we suggest you try it with the other two.

3. ''What follows is a meticulous step-by-step explanation. If you are here because you gave up the exercise, you might still enjoy skipping to the end and trying to understand what the implementation is doing before returning and seeing how it was built.''

There are two key insights needed to pull off this trick. The first one is remembering that a left fold

can be expanded as

and then realising that if we flip  and swap its arguments everywhere

we get an expression that associates to the right, just like a right fold!

The only problem is that the list elements in our right-associative expression are in the wrong order. The obvious way of fixing that is reversing the input list. That leads us to the first solution:

Reversing the list, however, is rather inelegant and takes time proportional to the length of the list. At this point, the second insight comes into play. By looking at the expression with the nested  and squinting a little

we can see we are actually taking  and applying several functions in sequence to it. We can make that transparent by rewriting the expression using.

If we switch the  to prefix notation

it becomes clear that the function at the left of  can be written as a fold with  :

Another way of thinking about this step is recovering the intuition that  takes a list and replaces   with the binary operator and   with the initial accumulator. In our case,, the do-nothing dummy function, is used as the initial accumulator. Next, we factor out the repeated  using  :

Here we meet the same problem: the list elements are not in the order we would like them to be. The reversal is consistent with the fact that functions composed with  are applied from right to left. However, this time we can, instead of reversing the list, simply flip :

Merely flipping the fold operator is not enough to turn  into   because in the general case the operator arguments have different types, and so flipping causes a mismatch. Folding a list with, however, can only work if the list elements are  functions, and  functions can be composed in both directions.

By abstracting from the concrete example we get the second solution:

If you find this final expression hard to grasp, making it more pointful by removing the s may help:

Alternatively, we could make it even more pointfree, though that would be rather excessive.


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Talk:How to Make a Comic/Equipment

We don't know how to use this kind of material. What kind of software is available also ? The list is not complete I think. Can a professional correct it please?

Better yet, can someone brush up that last bit? It's great to know something that can't be both actually funny and not based around humor, I mean here I was thinking you could do that but apparently I'm wrong.

two friends talking in the garden
Panel 1:

 * Show two friends, Alex and Sam, sitting on a park bench with a sunny sky and green trees in the background.
 * Alex: "Hey, Sam! What should we do today?"

Panel 2:

 * Illustrate Alex and Sam brainstorming with thought bubbles above their heads.
 * Sam: "How about a bike ride?"
 * Alex: "Or maybe a picnic?"

Panel 3:

 * Show both friends looking at each other with wide smiles.
 * Alex: "Why not both?"
 * Sam: "Great idea, Alex! Let's have a biking picnic adventure!"

This simple comic strip portrays the friendly interaction and decision-making process of two friends planning a fun day together. 39.62.4.198 (discuss) 12:15, 7 October 2023 (UTC)

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

title: Talk:How to Make a Comic/Equipment


text:
Wikibooks:Texas Master Technology Teacher

Texas Master Technology Teacher

 * 1) University of Houston
 * 2) Instructional Technology Program
 * 3) MTT - Master Technology Teacher Certificate Program

 * 1) Multimedia


text:
Finite Model Theory/FO Discrimination

The Property of Elementary Equivalence
FMT is about discrimination of structures. So the basic question is "Can I discriminate a structure from all different structures?", where different means not equal up to isomorphy. This can be done for finite structures (but not for infinite ones). E.g. ...

Properties for a finite Number of Structures
So being of a certain structure can be seen as an elementary property, that discriminates a class of isomorphic structures from all others. Now we can think of properties that discriminate 2 different (nonisomorphic) structures from the rest. They can also be discriminated by simply connecting the properties, like e.g. ...

This can be extended to properties for a finite number of structures, like e.g. ...

Properties for an infinite Number of Structures
Also properties that hold for an infinite number of structures can be thought of. But these are not discriminatable in the above way. E.g. ...

There are Logics that allow this sort of infinite disjunction, like ...

So, are there other ways to discriminate these structure in FO? Sometimes, like in the case of ...

So we need a decision tool (method) that decides if structures with a certain property can be discriminated or not, i.e. responds either "yes" or "no" for all possible properties, i.e. is sound and complete.

title: Finite Model Theory/FO Discrimination


text:
User:Dwlegg

Hello, my personal web site is http://www.legg.uklinux.net.

title: User:Dwlegg


text:
Talk:XForms/Apache

Can xforms work with tomcat? —The preceding unsigned comment was added by 80.251.207.40 (talk • contribs) 19:27, 26 May 2007 (UTC)

title: Talk:XForms/Apache


text:
User:Samuell

Hi Me on Wikipedia

title: User:Samuell


text:
Materials in Electronics/Confined Particles

Schrödinger's Equation can be used to find the electron distributions in a range of situations. The easiest to solve, theoretically, is the potential well. This is a region of space with a lower potential than neigbouring regions. The simplest case is where the well is infinitely deep, so electrons cannot ever escape. This is the Infinite Potential Well:
 * /1D Infinite Wells/
 * /2D Infinite Wells/
 * /3D Infinite Wells/

If you add more electrons to the box, the states are filled according to the Aufbau Principle:

 * ../The Aufbau Principle/

However, infinte wells don't exist and are just a convenient approximation. In real life, we deal with Finite Wells:
 * 1D Finite Potential Wells


text:
Materials in Electronics/Confined Particles/1D Infinite Wells

The 1D Infinite Well
Often, it is convenient to consider an electron "trapped" in a closed space, for example in a piece of semiconductor with a large bandgap between it and its surroundings. This kind of electron trap is called a 'potential well. The theoretically most straightforward case is the infinite potential well in one dimension, where an electron is confined completely and can never escape, as to do so would require an infinite amount of energy.

We will later expand this to more dimensions and the more realistic finite potential well, where the electron can escape.

For now, consider an electron trapped in an infinite potential well, of width L (right). The potential of this systems is given by:

 * $$V\left( x \right) = \begin{cases}

\infty ,\quad x < 0 \\ 0, \quad \,\,\, 0 \le x \le L \\ \infty, \quad x > L                            \end{cases} $$

The probability of finding an electron outside this region is zero. As the wavefunction of the electron in this well must be continuous according to the conditions on the wavefuction, we are seeking a solution to ψ(x) that is zero at x=0 and x=L. if this were not true, we would have a discontinuity here.

Solving for the Wavefunction
We need to solve Schrödingers Equation to find ψ(x):

$$ - {\hbar^2 \over {2m}}{{d^2 \psi \left( x \right)} \over {dx^2 }} + V\left( x \right)\psi \left( x \right) = E\psi \left( x \right), \quad \quad 0 \le x \le L$$.

Since V(x) is zero on this interval, we can write:

 * $$ - {\hbar^2 \over {2m}}{{d^2 \psi \left( x \right)} \over {dx^2 }}= E\psi \left( x \right) \quad \quad 0 \le x \le L$$.

Rearranging,

 * $${{d^2 \psi \left( x \right)} \over {dx^2 }} = - {{2mE} \over \hbar^2 }\psi \left( x \right)$$

Recall that the energy is given by

 * $$E\,$$
 * $$ = T\left( x \right) + V\left( x \right)\,$$
 * $$ = {{\hbar ^2 k^2 } \over {2m}}$$
 * }
 * $$ = {{\hbar ^2 k^2 } \over {2m}}$$
 * }

Substituting for E in our differential equation gives:

 * $${{d^2 \psi \left( x \right)} \over {dx^2 }} = - k^2 \psi \left( x \right)$$

This is now a second-order differential equation with a standard form. The general solution is given by:

 * $$\psi \left( x \right) = A \sin{kx} + B \cos{kx}$$

Applying Boundary Conditions
Applying the first boundary condition $$\left( \psi \left( 0 \right) =0 \right)$$:

 * $$\psi \left( 0 \right) = A\sin \left( 0 \right) + B\cos \left( 0 \right) = 0$$

Therefore, B=0.

Applying the second boundary condition $$\left( \psi \left( L \right) =0 \right)$$:

 * $$\psi \left( L \right) = A\sin \left( k L \right) = 0$$

Therefore, kL must be a multiple of π:

 * $$kL=n \pi \quad n=\{ 0,1,2,\ldots \} $$
 * $$k=\frac{n \pi}{L} \quad n=\{ 0,1,2,\ldots \} $$

We call A the normalisation coefficient, ψ0. This exists to ensure the probability of finding an electron in all of space is 1. Also, since when n=0 the whole equation goes to zero, the probability of an electron existing is zero, and thus, the solutions to the Schrödinger Equation for a particle in a 1D box start at n=1:

 * $$\psi _{n_x } \left( x \right) = \psi _0 \sin \left( {{{n_x \pi } \over L} }x \right), \quad n_x = \left\{ {1,2,3, \ldots } \right\}$$

Because we a working in the x-direction, we have called our indexing number nx. This is called the wavenumber. The energies associated with the above solutions are given by:

 * $$E_{n_x }$$
 * $$ = {{\hbar ^2 k^2 } \over {2m}}$$
 * $$= {{\hbar ^2 n_x^2 \pi ^2 } \over {2mL^2 }}, \quad n_x = \left\{ {1,2,3, \ldots } \right\}$$
 * }
 * $$= {{\hbar ^2 n_x^2 \pi ^2 } \over {2mL^2 }}, \quad n_x = \left\{ {1,2,3, \ldots } \right\}$$
 * }

There are two thing to note here.
 * A wavefunction solving the Schrödinger Equation exists only for integer wavenumbers, n.
 * Each wavefunction (eigenfunction) has a specific energy (eigenvalue) associated with it. This is proportional to the square of the wavenumber and the energy of the wavefunction with n=1, E1.

The diagram below shows the wavefunctions with wavenumbers 1, 2 and 3, plotted against the associated energy relative to E1:

The probability densities can be found easily once the wavefunctions have been found - simply take the modulus (in the case of complex wavefunctions) and square. This results in probability densities as shown below:

Normalisation Coefficient
We can find the normalisation coefficient, ψ0 using the knowledge that the electron must be somewhere in the quantum well, and therefore the area under the probability density function is one:

 * $$\int\limits_{ - \infty }^\infty {\left| {\psi \left( x \right)} \right|^2 dx}  = \int\limits_0^L {\psi \left( x \right)^*\psi \left( x \right)}  dx  = 1$$

So, for our wavefunction, $$\psi _{n_x } \left( x \right) = \psi _0 \sin \left( {{{n_x \pi } \over L} }x \right)$$,

 * $$ \int\limits_0^L {\psi_0^2 \sin^2 \left(\frac{n_x \pi}{L}x \right) dx} = 1$$

 * $$ \psi_0^2 \int\limits_0^L {\frac{1}{2} \left(1-\cos \left(\frac{2 n_x \pi}{L} \right)x \right) dx} = 1$$

 * $$\psi_0^2 \left[ \int\limits_0^L {\frac{1}{2} dx} - \frac{1}{2}\int\limits_0^L {\cos \left(\frac{ 2 n_x \pi}{L} x \right) dx} \right] = 1$$

 * $$\psi_0^2 \left[\frac{L}{2} - \frac{L}{4 n_x \pi}\left[\sin \left(\frac{ 2 n_x \pi}{L} x\right) \right]_0^L \right]= 1$$

Because the area under the sine curve over a whole number of periods in zero, we have

 * $$\psi_0^2 \frac{L}{2} = 1$$

 * $$\psi_0 = \sqrt{\frac{2}{L}}$$

It turns out that this is independent of the wavenumber, so our normalised wavefunction for an electron in a 1-D infinite potential well is zero outside the well and given by the equation:

 * {|style=" border: solid 2px #D6D6FF; padding: 1em;" valign="top"

 * align="left"|$$\psi _{n_x } \left( x \right) = \sqrt{\frac{2}{L}} \sin \left( x \right), \quad n_x  = \left\{ {1,2,3, \ldots } \right\}$$
 * }

Inside it, the associated energies are given by:

 * {|style=" border: solid 2px #D6D6FF; padding: 1em;" valign="top"

 * align="left"|$$E_{n_x} = {{\hbar ^2 \pi ^2 } \over {2mL^2 }}n_x^2, \quad n_x = \left\{ {1,2,3, \ldots } \right\}$$
 * }


text:
User:Carl Turner

Hello!
Erm... yeah, see my Wikipedia page.

title: User:Carl Turner


text:
Talk:Scratch

Keep it simple
Please keep this page clean and simple. This is the "front page" that has links to other parts of this Wikibook, and should only have major sections listed. Individual chapters/modules and other parts of this book ought to be listed in the table of contents and as needed in other modules.

If there are ideas on how to improve this page, please feel free to add comments and suggestions below. --Rob Horning 23:45, 26 May 2007 (UTC)

Central Discussion
If you are making a comment about the general organization of this Wikibook, I would encourage you to use Scratch/Planning instead of this page for those discussion. This talk page should be limited to the appearance of this "title page" and any general organization thoughts to help improve this first impression people may have about this book. --Rob Horning 15:21, 27 May 2007 (UTC)

title: Talk:Scratch


text:
Scratch

An introduction to

imagine • program • share

/Introduction/ • /Authors/ • /Content License/ • /Planning/

Initial Setup

 * What is Scratch?
 * Online and Offline Editors

Getting Started

 * Finding and Downloading Scratch
 * Resources available to use in Scratch
 * Sharing Scratch projects
 * Introducing Scratch

Interface

 * Introduction
 * Top Bar
 * Code Area
 * Costume Editor
 * Sound
 * Project
 * Sprite and Background
 * Backpack

Tutorials

 * Making Sprites
 * Stage Design
 * Custom Image Design
 * Event Triggers and Blocks
 * Basic Animation
 * Movement
 * Scene and Stage Changes

title: Scratch


text:
Scratch/Authors

If you have made some major contributions to this Wikibook and wish to be credited as an author or contributor for the purposes of the GFDL and for citing this book, please add your name to the list below:

You do not need to use your full name, and for many people they will just use their user account name. For full copyright protection, you may wish to disclose you full legal name and where you live, although these legal requirements will vary from country to country.

 * Robert Scott Horning, Logan, Utah, USA
 * Tanderson11, USA

title: Scratch/Authors


text:
Cookbook:Æbleskiver (Danish Spherical Pancakes)

Æbleskiver or ebleskiver (literally "apple slices") are traditional Danish cakes, somewhat similar in texture to American pancakes. Æbleskiver are cooked in a special æbleskive pan, a cast-iron pan with several hemispherical indentations in the bottom of the pan.

Ingredients

 * 2 egg whites
 * 2 cups (480 ml) all-purpose flour
 * 2 teaspoons (10 ml) baking powder
 * 1 tablespoon (15 ml) white sugar
 * ½ teaspoon (5 ml) baking soda
 * ½ teaspoon (5 ml) salt
 * 4 tablespoons (60 ml) butter, melted
 * 2 cups (480 ml) buttermilk
 * 1 cup (240 ml) vegetable oil, for frying

Procedure

 * 1) Beat the whites until stiff.
 * 2) Mix together the flour, baking powder, salt, baking soda, sugar, melted butter and buttermilk at one time and beat until smooth. Gently fold in the egg whites last.
 * 3) Put about 1 tablespoon (15 ml) of vegetable oil in the bottom of each æbleskiver pan cup and heat until hot. Pour in about 2 tablespoons (30 ml) of the batter into each cup.
 * 4) As soon as they get bubbly around the edge, turn them quickly. Alternatively, you can turn them halfway first, so that the baked crusts protruding from the pan will look like the Sydney Opera House. And after a while you turn them the remaining 90°. This will give them a perfect ball-shape. Danish cooks use a long knitting needle, but a fork will work.
 * 5) Continue cooking, turning the ball to keep it from burning.

Notes, tips, and variations

 * An æbleskiver pan is required to cook these properly.
 * They were traditionally cooked with bits of apple or applesauce inside but these ingredients are not normally included in modern Danish forms of the dish.
 * Æbleskiver are not sweet themselves but are traditionally sprinkled with powdered sugar, accompanied with raspberry or sometimes strawberry jam, and served with gløgg.


text:
Abstract Algebra/Quaternions

The algebra of Quaternions is a structure first studied by the Irish mathematician William Rowan Hamilton which extends the two-dimensional complex numbers to four dimensions. Multiplication is non-commutative in quaternions, a feature which enables its representation of three-dimensional rotation. Hamilton's provocative discovery of quaternions founded the field of hypercomplex numbers. Suggestive methods like dot products and cross products implicit in quaternion products enabled algebraic description of geometry now widely applied in science and engineering.

Definitions
[[File:Inscription on Broom Bridge (Dublin) regarding the discovery of Quaternions multiplication by Sir William Rowan Hamilton.jpg|right|thumb|Quaternion plaque on Broom Bridge, Dublin, which says:

Here as he walked by on the 16th of October 1843 Sir William Rowan Hamilton in a flash of genius discovered the fundamental formula for quaternion multiplication $i^{2} = j^{2} = k^{2} = ijk = −1$ & cut it on a stone of this bridge

]]

A Quaternion corresponds to an ordered 4-tuple $$q=(a,b,c,d)$$, where $$a,b,c,d\in\mathbb{R}$$. A quaternion is denoted $$q=a + b i + c j + d k$$. The sum $$ b i + c j + d k$$ is called the vector part of q, and a is the real part. Hamiltion coined the term vector in this context. Subsequent developments have extended the usage of the term vector to any element of a linear space. The vectors in H form a 3-dimensional subspace V.

The set of all quaternions is denoted by $$\mathbb{H}$$. It is straightforward to define component-wise addition and scalar multiplication on $$\mathbb{H}$$, making it a real vector space.

Multiplication follows the rules of the "quaternion group" Q8 = {1, -1, i, -i, j, -j, k, -k} that Hamilton carved into a stone of Broom Bridge, Dublin:

 * $$i^2 = j^2 = k^2 = ijk = -1$$

The rules for the pairwise multiplication of $$i$$, $$j$$, and $$k$$ are:

 * $$ ij=k,\ \ jk=i,\ \ ki=j $$ (positive cyclic products)

 * $$ji=-k,\ \ kj=-i,\ \ ik=-j$$ (negative cyclic products).

Using these, one can define a general rule for multiplication of quaternions. Because quaternion multiplication is not commutative, $$\mathbb{H}$$ is a not a field. However, every nonzero quaternion has a multiplicative inverse (see below), so the quaternions are an example of a division ring. It is important to note that the non-commutative nature of quaternion multiplication makes it impossible to define the quotient $$p/q$$ of two quaternions p and q unambiguously, as the quantities $$pq^{-1}$$ and $$q^{-1}p$$ are generally different.

Like the more familiar complex numbers, the quaternions have a conjugation, often denoted by a superscript star: $$q^*$$. The conjugate of the quaternion $$q=a+bi+cj+dk$$ is $$q^*=a-bi-cj-dk$$. As is the case for the complex numbers, the product $$qq^*$$ is always a positive real number equal to the sum of the squares of the quaternion's components. The norm  of a quaternion is the square root of $$qq^*$$.

If pq is the product of two quaternions, then $$(pq)(pq)^* = (p p^*)(q q^*),$$ implying that $$\mathbb{H}$$ forms a composition algebra.

The multiplicative inverse of a non-zero quaternion $$q$$ is given by
 * $$q^{-1}=\frac{q^*}{qq^*}$$ where division is defined since $$qq^* \ne 0.$$

Unlike in the complex case, the conjugate $$q^*$$ of a quaternion $$q$$ can be computed algebraically:

 * $$q^*=-\frac{1}{2}(q+iqi+jqj+kqk)$$.

Versors and elliptic space
William Kingdon Clifford used Hamilton’s quaternions to explicate rotation geometry as an elliptic space with its own variety of lines, parallels, and surfaces. The ideas were reviewed in 1948 by Lemaitre and Coxeter and that sketch has these definitions:

A versor is a quaternion of norm one, thus it lies on a 3-dimensional sphere found in the 4-space of quaternions. The versors are given by Euler's formula for complex numbers where the imaginary unit is taken from the unit sphere in the 3-space of vector quaternions:
 * $$v = \cos c + s \sin c = e^{cs}, \ \ s^2 = -1 .$$

The distance between two versors u and v is $$d(u,v) = \arccos (u v^* + v u^*)/2 .$$

A right parataxy on elliptic space is effected by multiplying on the right by a versor $$v = e^{cs} .$$ Similarly a left parataxy arises from left multiplication. In recognition of his contribution to elliptic geometry, a parataxy is called a Clifford translation.

The general displacement of elliptic space is a combination of two parataxies, one left, one right:$$x \mapsto u x v .$$ Note that if $$u = v^* ,$$ then the real line in the quaternions is fixed and the displacement is a rotation of the 3-space of quaternion vectors.

The term line is appropriated for elliptic geometry. These lines are not straight, but they are parametrized by real numbers. Each line is associated with a right versor like s when c = π/2 in v. Then $$L = \{ e^{cs} : c \in R \}$$ is a typical elliptic line. It corresponds to the axis of the rotation
 * $$x \mapsto e^{cs} x e^{-cx} .$$

Now for u not on L, there are two Clifford parallels to L through u:
 * $$\{u e^{cs} : c \in R \}, \quad \{e^{cs} u : c \in R \} .$$

For fixed right versors r and s, a Clifford surface can be formed as a union of Clifford parallels or as
 * $$\{ e^{cs} e^{dr} : b, c \in R \} .$$

To form elliptic space from versors, two versors u and v are equivalent if u + v = 0. Modulo this equivalence, the versors, their algebra and geometry, represent elliptic space.

Linear viewpoint
Quaternions may be represented by 2×2 matrices with complex number entries: the place of $$i, j, k $$ is taken by these arrays:
 * $$\begin{pmatrix} i & 0 \\ 0 & -i \end{pmatrix}, \quad \begin{pmatrix} 0 & 1 \\ -1 & 0 \end{pmatrix}, \quad \begin{pmatrix} 0 & i \\ i & 0 \end{pmatrix}.$$

One uses matrix multiplication to verify that these expressions obey the rules of presentation of Q8.

M(2,C) denotes the full algebra of 2×2 complex matrices, which has eight real dimensions, and sustains a representation of $$\mathbb{H}$$ as a four-dimensional subalgebra. The linear properties of $$\mathbb{H}$$ and M(2,C) assure the fidelity of the representation once the copy of Q8 has been identified.

Quaternions, like other associative hypercomplex systems of the 19th century, eventually were viewed as matrix algebras in the 20th century. However, in 1853 Hamilton included biquaternions in his book of Lectures on Quaternions.

Biquaternions are quaternions with complex number coefficients, sometimes called complex quaternions. Biquaternions form an algebra isomorphic to M(2,C). If the rows or columns of a matrix are proportional, then the determinant is zero, and there is no inverse. Nevertheless, such matrices have been used in physical science to represent events on a light-path from the origin. Authors Silberstein and Lanczos refer to this algebra as the biquaternions, but other writers have abandoned the label: Elie Cartan used M(2,C) extensively in The Theory of Spinors (1938), and Wolfgang Pauli, in his matrix mechanics of the atom, caused himself to be associated with M(2,C).

Pauli Spin Matrices
Quaternions are closely related to the Pauli spin matrices of Quantum Mechanics. The Pauli matrices are often denoted as

 * $$\sigma_1=\begin{pmatrix}0 & 1 \\ 1 & 0\end{pmatrix}$$, $$\sigma_2=\begin{pmatrix}0 & -i \\ i & 0\end{pmatrix}$$ , $$\sigma_3=\begin{pmatrix}1 & 0 \\ 0 & -1\end{pmatrix}$$

(Where $$i$$ is the well known quantity $$\sqrt{-1}$$ of complex numbers)

The 2×2 identity matrix is sometimes taken as $$\sigma_0$$.

Thus $$S$$, the real linear span of the matrices $$\sigma_0$$, $$i\sigma_1$$, $$i\sigma_2$$ and $$i\sigma_3$$, is isomorphic to $$\mathbb{H}$$. For example, take this matrix product:

 * $$\begin{pmatrix}i & 0 \\ 0 & -i\end{pmatrix} \begin{pmatrix}0 & 1 \\ -1 & 0\end{pmatrix} = \begin{pmatrix}0 & i \\ i & 0\end{pmatrix}$$

Or, equivalently,  $$i\sigma_3 \ i\sigma_2 = i\sigma_1 .$$

All three of these matrices square to the negative of the identity matrix. If we take $$ 1=\sigma_0$$, $$i=i\sigma_3$$, $$j=i\sigma_2$$, and $$k=i\sigma_1$$, it is easy to see that the span of the these four matrices is "the same as" (that is, isomorphic to) the set of quaternions $$\mathbb{H}$$.

Exercises

 * 1) Using the presentation equations of Q8, write out the full product of two quaternions. In other words, given $$q_1=a_1+b_1i+c_1j+d_1k$$ and $$q_2=a_2+b_2i+c_2j+d_2k$$, find the components of their product $$q=q_1q_2 .$$
 * 2) Show the composition algebra property $$(pq)(pq)^* = (p p^*) (q q^*) .$$ Hint: use  Euler's four-square identity.

Axial pencils
Hamilton's quaternions provide a picture of a pencil of complex number planes that fill out his hyperspace. Another pair of pencils provide alternative descriptions of 4-space as made up of planar algebras: The hyperspace is $$\reals^4$$ with the first coordinate taken as the real line, and as the axis of the various pencils. The Hamilton case uses the sphere of imaginary units
 * $$S^2 = \{q \in H : q^2 = -1 \} = \{xi + yj + zk : x^2 + y^2 + z^2 = 1 \} .$$

Any pair of antipodal points on this sphere generates a plane isomorphic to the ordinary complex plane $$\Complex .$$

The second and third pencils derive from the findings of James Cockle and Arthur Cayley. Cayley set up an arithmetic of matrix multiplication which has expedited modern science. For instance, the so-called imaginary units are represented by $$\begin{pmatrix}0 & -1 \\ 1 & 0 \end{pmatrix}$$ which has multiplicative square equal to the negative of the identity matrix. But then there is also by $$\begin{pmatrix}0 & 1 \\ 1 & 0 \end{pmatrix}$$ which generates an algebraic plane distinct from ordinary complex numbers. This algebra split-binarions, has inverse proportion included as a structural feature, such as found in economics or spacetime. In fact, the Lorentz boost is exhibited by a split-binarion multiplication. The inherent relation was recognized in the 19th century by J. Cockle, W.K. Clifford, and A. Macfarlane in the English world and by some Serbians.

The second pencil is an imaginary one without linear representation. As Hamilton had a sphere of imaginary units, Macfarlane would have a sphere of hyperbolic units u with u2 = +1. The full algebra of split-binarions is $$A = \{ q = x + y u : x, y \in \reals \}$$ Any pair of elements that are polar opposite on this sphere generate a plane isomorphic to the split-binarions A. The 4-algebra containing this pencil is the hyperbolic quaternion algebra. As Oliver Heaviside and Willard Gibbs advocated a positive dot product for vectors, they have been associated with hyperbolic quaternions. When this algebra drew attention in the 1890s a "great vector debate" ensued in various publications including Nature. When the failure of the algebra to satisfy the associative law of multiplication was noted, it was realized that no matrix representation would be found.

Each plane of the pencil can represent a Lorentz boost. However, rotations of the vector subspace, an operation within the reach of Hamilton's structure, is beyond the means of hyperbolic quaternions, hence the Lorentz group cannot be represented with Macfarlane's algebra.

The third pencil arises from both imaginary units and hyperbolic units as found in the ring of 2x2 real matrices. In this figure there must be noted nilpotent matrices such as by $$\begin{pmatrix}0 & 1 \\ 0 & 0 \end{pmatrix}$$ which correspond to dual numbers in the matrix algebra. Such planes separate the complex and split-binarion planes, and are included in the pencil. The axis of the pencil is the line of matrices that are real multiples of the identity matrix. Over an alternate basis this ring is known as split-quaternions, and the pencil has three types of planar subrings.

title: Abstract Algebra/Quaternions


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User:Rcamp004

Richard Campanha

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User talk:Barak4wiki

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title: User talk:Barak4wiki


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General Astronomy/First Steps into Space

The first man-made object to be launched into space was the Soviet unmanned satellite named Sputnik I. This began the "Space Race" between the United States and the Soviet Union. The Soviets won almost every aspect (1st object, 1st man in space, 1st woman in space, etc.), except for the United States' 1st man on the moon.


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General Astronomy/Extrasolar Planets

Exoplanets are planets that orbit other stars.

Brief History of Detecting Exoplanets
Speculations about the existence of exoplanets have been ongoing since the time of Isaac Newton’s General Scholium (1713). Newton hinted that other stars had planets orbiting them just as our sun. The first claims of a detection of an exoplanet were centered on 70 Ophiuchi. In 1855 Capt. W. S. Jacob claimed that the orbit of the binary system exhibited an anomaly. A third body, an exoplanet, was held responsible. In the 1890’s, Thomas Jefferson Jackson See supported these claims based on orbital movement as well. In 1899, those claims were disproved by Forest Moulton who analyzed the triple system and demonstrated that such a system would be unstable under the orbital parameters put forth by Jackson.

In the 1960’s Peter Van de Kamp claimed that Barnard's Star had an exoplanet. He based this claim on an apparent wobble in the star’s motion. Kamp spent 40 years studying the Barnard star. Observations made by other telescopes were never able to replicate the date of the wobble. It is believed that the wobble was an anomaly of equipment at Sproul Observatory. There is still no conclusive evidences for or against a planet existing around Barnard’s Star.

The first detection to be later confirmed of an exoplanet was made in 1988 by Bruce Campbell, G.A.H. Walker and S. Yang. The star Gamma Cephei was tentatively proposed to have an exoplanet based on radial velocity observations. It was given a tentative status because the observations were made at the very limit of the capability of the instruments at the time. The claim was mistakenly retracted, for in 2002 Artie Hatzes and his collaborators were able to confirm the existence of the exoplanet.

In 1992 Wolszczan and Frail proved there were two planets of 3.9 and 4.3 Earth masses orbiting the pulsar PSR B1257+12 at .46 and .36 AU respectively. A third planet was discovered later of .025 Earth masses orbiting at .19 AU. This discovery is considered to be the first definitive detection of an exoplanet, because the Cambell, Walker, and Yang discovery was not confirmed until 2003. This was a rather strange discovery because it was revolving around a pulsar rather than a main sequence star like our sun. It is believed that the planets are the remains of a solar system after the star died.

The first discovery of an exoplanet orbiting a main sequence star, 51 Pegasi, was announced October 6, 1995 by Michel Mayor and Didier Queloz. When the distance and mass of the planet were determined they were found to be incompatible with theories of planetary formation at the time. They used the radial velocity method to detect the planet. This ushered in the modern era of exoplanet study. After their discovery numerous exoplanets have been detected as a result of improved telescopes with higher resolutions and more powerful computers.

As of August 19, 2012, 777 exoplanets have been detected. The rate of discovery has steadily increased due to improved technology and a greater interest in exoplanets, with 61 planets detected in 2007. Using the Spitzer Space Telescope, studies of the evolution of gas and dust around main sequence stars indicate that at least 20 percent, and possibly as many as 60 percent, of main sequence stars are candidates for forming rocky planets. The actual percentage is likely between these two extremes.

Most exoplanets detected have been massive Jupiter-like planets. Most likely this is due to the ease of detecting such in comparison to smaller terrestrial planets; this is known as a selection effect. Planets, labeled Super-Earths, have also been detected. They are about 5 to 10 Earth masses. One Earth mass would be the mass of the earth.

Detection Methods
There are six methods currently used to detect exoplanets: Astrometry, Radial Velocity, Pulsar timing, Transit method, Gravitational micro-lensing, Direct imaging. Three methods detect a dynamical perturbation of the star, or wobble of the star due to the planet’s gravitational force. Since the planet and the star revolve around a common center of mass the star will appear to wobble with the same period as the planet’s orbital period. From our point of view the wobble will be from side to side, towards and away, or some combination of the two.

The degree of a star’s wobble is determined by the mass of the star and the planet, and by the distance between them. The more massive a planet is in comparison to that of its star, the greater the wobble. The closer the planet’s orbit to the star the greater the degree of the wobble observed of the star. Any method that detects an exoplanet this way can give information about the planet’s mass, though a combination of methods is needed to find the true mass of a planet.

The three ways we detect this wobble are by radial velocity, astrometry, and pulsar timing. Radial velocity measurements detect the blue and red shifts of a star as it moves toward and away from Earth, respectively. As the star moves toward Earth, the light shifts to blue. As the star moves away from Earth the light shifts to red. The radial velocity can be deduced by studying the red and blue shifts in the spectroscopy of the star’s emission. Most exoplanets have been discovered by the radial velocity method.

The velocity of the star around the barycenter is much smaller than the planet’s velocity because the planet’s orbital distance from the center of mass is greater than the star’s. Current spectrometers can detect a velocity variation down to 1 m/s. The larger the velocity differences in the star, the easier it is to detect. Thus the radial velocity method can more easily detect exoplanets that have a larger mass and are closer to their stars.

The Astrometry Method is the oldest search method though it wasn’t the method used to discover the first exoplanet. The astrometry method looks for angular change in the position of a star. The more a star moves, the easier it is to detect. Since this method relies on the orbit around a center of mass it is dependent on the mass ratio of the planet and star.

However, unlike the radial velocity, the angular change in position increases with greater distance between the star and the exoplanet. The further the planet is from the star, the further they are from their mutual center of mass. The greater a star’s distance from the center of mass, the greater the angle change between the star’s opposite ends of its orbit.

In the Pulsar Timing Method, a pulsar emits radio waves in extremely regular time intervals as it rotates. Any anomalies in the time between radio waves are an indication that the pulsar is orbiting a center of mass. This method is very sensitive. Planets that are one-tenth Earth masses can be detected this way.

The Transit Method detects changes in the brightness of star as a planet moves across the star's face. The dimmer the star becomes, the larger the planet, thus the volume of a planet can be determined by this method. This method requires that the planet’s orbit passes directly between the star and earth, which is a rare alignment.

The Gravitational Lensing Method measures an amplification of a star’s brightness. As light from a background star passes the planetary system, the light is bent towards a planet due to its gravity. The light is focused into a smaller area thus increasing its brightness. This method is capable of detecting low mass planets around dim stars at a great distance. The final method currently used to detect planets is to directly observe them. Usually a parent star's shine obscures a planet's emission. However, in certain cases the reflected light of a planet can be seen. Such a method works best when the planet is more massive than Jupiter, less than a tenth the age of our solar system, more distant from its parent star than Jupiter and orbits a star less luminous than our sun. It is also possible to detect a planet’s light if we restrict ourselves to infrared radiation, which is the dominant emission wavelength of a planet. This is very difficult and few planets have been detected this way.

Extrasolar Jovians
Many gas giants have been discovered orbiting distant stars, many of larger than Jupiter. That is because big planets are massive enough to gravitationally affect the movement of their star sufficiently that the perturbation is detectable. Therefore the biggest extrasolar planets are the easiest and earliest to be found.

The First Discovery
The first extrasolar planet discovered was Gamma Cephei Ab, a planet orbiting Gamma Cephei A with an orbital period of around 900 days at a distance of around 1.7 - 2.5 AU from its parent. Its existence was suspected as early as in 1989, and evidence of it strengthened considerably in 2002 from observations at the McDonald Observatory. It is a Jovian-sized planet with a mass estimated to be above 1.59 times that of Jupiter's. The star it orbits is an orange sub-giant star part of the Gamma Cephei binary star system, with its companion Gamma Cephei B a red dwarf.

Spectra of Hot Jupiters
Astrophysicists have recently observed spectra from hot Jupiter sized planets in planetary systems many light years away. Since these planets are so distant, it’s not as simple as just looking at the planet and collecting data about the direct light from the planet. The planets are too distant for such techniques and they are too close to their parent stars (sometimes closer than Mercury is to our sun). Instead astrophysicists collect data from the star and planet during different parts of the planets’ orbit and separate the light from just the planet.

First the spectrum from the planet and star is collected. This is done when, as seen from earth, both planet and star are at their greatest separation. Then the spectrum of just the star is obtained. This is done when the planet is either directly in front of the parent star (primary eclipse) or directly behind its parent star (secondary eclipse). By subtracting the light of the star from the light of the star plus planet, the spectrum of the planet can be found.

Spectroscopic Techniques: Primary and Secondary Eclipses
The brightness of the parent stars of these planets is too high in comparison to the planets themselves in the optical range. Because of this, infrared light is detected to better differentiate the planet from the star. The planet itself reflects very little optical light because the cloud layers prevent much of it from escaping. The cloud layers emit much of the absorbed energy from its star as infrared light however, and so most it can be detected by the spectrometers of our telescopes (Spitzer and Hubble). Because the planet emits so much more radiation in the infrared range as compared to the reflected optical part of the spectrum, the differences in the two spectra are more exaggerated and the infrared part of the spectra is easier to use.

A secondary eclipse occurs when the hot Jupiter being observed passes behind its parent star, as viewed from Earth. A primary eclipse, also known as a transit, happens when the planet passes in front of the star as viewed from Earth. These eclipses are very rare because the planet, star and earth have to line up so that the planet completely eclipses. Only 54 of the 333 confirmed planets are transiting planets when viewed from Earth.

Spectroscopic results
Spectra are used to identify molecules in the planetary atmospheres, and to determine relative abundances. If you know at what wavelengths an atom or molecule will emit or absorb light, you can examine the spectrum of light from a planet and determine if that molecule is present. By looking at the full spectrum, scientists can decide which atoms or molecules specifically make up the planet and noting how much of that wavelength is emitted, the relative abundance of that atom or molecule can also be determined. Many attempts are focusing on identifying water vapor on other planets. The two planets, HD 209458b and HD 189733b are the first two planets observed. Originally, they both seemed to be void of water vapor. It is believed that the observational techniques weren’t sensitive enough to detect water vapor. By using new techniques, the evidence for these planets containing water vapor is growing. The first tests were done using a secondary eclipse of the star. Because of the atmospheric composition of the planets, this technique could not see through the clouds on the planets. The heat of the planet due to its closeness to the star also plays a part in the differences in results. Because the planet is so close to the star, the side closest to the star will have less water than the side away from the star. During a primary eclipse, the cooler and therefore wetter side will be facing towards earth. During a secondary eclipse, the dryer hotter side will be facing towards earth. By using a primary eclipse, a team of scientists in France has found peaks in the light curve at 3.6 microns, 5.8 microns and 8 microns in such a pattern that they believe only water vapor could produce.

Example Spectra

=References=

title: General Astronomy/Extrasolar Planets


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Iranian History/The Medes and the Early Achaemenids

The Aryan Migration Theory
During the second millennium BC, there were widespread migrations into Iran in waves from the north. These people, who had been commonly designated as Aryans, are believed to be the ancestors of the Iranians of today. Most historians feel that a majority of the Iranians of today are descended from nomadic pasture-dwellers from the north. However, recent discoveries and genetic studies have cast serious doubts on the Aryan theory. Even prominent historians like Sir Richard Frye have limited the use of the word "Aryan" while referring to Iran's ancient period. Recent genetic researches have revealed that the Aryans were actually a Middle-Eastern tribe closely related to the other peoples of the fertile crescent and were the descendants of the people who migrated to the Iranian plateau around 10,000 years ago, forming civilizations like the Elamite one.

The acceptance of the concept of an Aryan race has been more widespread and greater in Iran than in other countries with an "Aryan" heritage as the United Kingdom, India or other modern Western European countries. This is because the very name "Iran" is derived from the name of a mythical land called "Airyanem Vaego" mentioned in the Avesta as one of the sixteen lands created by Ahura Mazda.

The Medes
The Medes were an ancient Indo-Aryan people. In the third millennium BC, they migrated from the North-west of Iran to the south and occupied the highlands of the Zagros chain. Starting with the 7th century BC, they organized a powerful Empire that fought against the Assyrians with considerable success and heralded the downfall of the Imperial Assyrian Empire of Mesapotamia. They exercised their power over much of modern-day Iran for a brief span of around 150 years. But their contributions, especially to Zoroastrian religion and philosophy and the modern Persian language have been immense.The Medes are closely related to the modern Kurds.

Origin
The origin of the Medes is shrouded in obscurity. They are believed by some to be the people of Madai mentioned in the Old Testament of the Bible. Modern scholars hold the universal opinion that they are the people of the Avesta.

It is widely presumed that their presence in Iran must date at least as far back as 1500BC. The Gathas, the sacred hymns of Zoroastrianism are believed to have been composed during this period. However, the first mention of Medes does not go beyond 835BC when they appear in the records of the Assyrian king Shalmenesser II. However, the Iranologist George Rawlinson gives evidence to the contrary. He says that the historian Kanosys of Carthion mentions the conquest of Babylon by Medes as far back as 2000BC.

Rawlinson also says that the presence of Aryan influence amongst the "seven Chaldean talons" indicates Median presence in Northern Mesapotamia. He also says that the Medes were known to the Greeks and were referred to under the eponyms Medea and Andromeda. But most of these sources are uncertain and unreliable. We begin to get clear picture of the Medes only when they settle down in the country which is subsequently named after them and establish the Median Empire.

Kings
We first hear of Media during the time of Shalmanessar II of Assyria who speaks of having led an expedition to Media in the year 835BC. His son, Shamas-Vul boasts of having worsted the Medes in battle and ravaged their country. Following this invasion, the Medes appear to have become tributaries of Assyria and paid them regular tribute. However, a hundred years later, the Assyrians launched another invasion of Media and annexed the country of the Medes. Assyrian Emperors Sennacherib and Esar-haddon boast of having reduced Media into total submission.

Diyako or Deioces who united the seven Mede tribes is generally recognized as the first king of Media. However, both Herodotus and Ctesias claim that there were six Median "monarchs" prior to the rise of Deioces and gives their names as Arbaces, Maudaces, Sosarmus, Artycas, Arbianes and Artseus

Diyako (Deioces) 701 -665 BC
Deioces was the son of one Phraates and was a renowned judge in his part of Media. In 701BC, with dacoitry and lawlessness proving to be a headache, the seven tribes of Media came together and formed a kingdom. Deioces was the unanimous choice to be the king of Media. He ruled the state with an iron hand until his death in 665 BC. His rise to power is described in detail in Herodotus' Histories. He is credited with having built a palace in the capital city,Ecbatana.

Kshatrita (Phraates) 665 - 633 BC
Fravartish or Phraates ''Old Pers. Kshatrita'' succeeded his father Deioces and ruled Media from 665BC to 633BC.

Herodotus, in Line No.102 of his Historiestells that Phraates was an extremely ambitious ruler and credits him with the subjugation of the Persians. In 634BC, with the assistance of his son, Cyaxares, Phraates launched an invasion of Assyria. However, the invasion was an utter failure and in the battle fought at Adiabene, the Medes were worsted and their army, cut to pieces and Phraates, himself, killed.

Hvakshatra (Cyaxares) 633 - 585 BC
Following the death of his father Phraates in 633BC, Cyaxares retreated to Media and reorganized his army, till then under tribal chieftains, on a purely regimental basis. He then led a large army into Assyria and having defeated the Assyrians, pursued them to the gates of the Assyrian capital Nineveh. But Cyaxares did not launch a siege of Nineveh. Instead he was content to retreat with his soldiers back to Media. However, on his return to Media, the Median troops were confronted by bands of Scythians under their leader Madyes who inflicted a crushing defeat on them. Cyaxares surrendered and was compelled to pay a heavy tribute.

The Scythian hegemony lasted eight years during which they earned a reputation for avarice through their repeated exactions. However, Scythians rarely interfered in the affairs of the inhabitants. Finally, in 625BC, eager to throw off the Scythian yoke, Cyaxares invited the Scythian chiefs to a traditional banquet and had them treacherously murdered. There were simultaneous eruptions all over Media resulting in a large scale destruction of the Scythians such that barely a semblance of their eight-year rule survived.

Having emerged victorious from his battle with the Scyths, Cyaxatres now desired to expand his dominions. He concluded a marriage alliance with Nabopolassar of Babylon by giving his daughter Amytis in marriage to Nabopolassar's son Nebuchadnezzar. He then launched a second invasion of Assyria in 612BC and put an end to the Assyrian Empire. This event is believed to have occurred during the reign of the third Achaemenid king Cyrus I and hence signifies a shift of power from the Assyrians to the Medes.

Ctesias while describing the battle narrates how the combined forces of the Persians, the Arabs, the Medes and the Babylonians numbering four hundred thousand individuals were defeated in two pitched battles by the Assyrians and how they rallied at the arrival of reinforcements from Bactira and surprising the Assyrian camp at night inflicted a crushing defeat upon them. Cyaxares proceeded to sack Nineveh and pulled it to the ground.

During the latter part of his reign, Cyaxares also invaded and conquered Armenia, Northern Mespotamia and Lydia. In 585BC, the Battle of Halys was fought between the Medians and the Lydians. The battle ended in a truce between the Medes and the Lydians. Cyaxares died soon after the battle.

Ishtovigu (Astyages) 585 - 549 BC
Astyages succeeded Cyaxares in 585BC. He is described by Herodotus as a vain incapable monarch given to luxury and comfort. Tradition says that he was remarkably handsome, cautious, and of an easy and generous temper. His reign is regarded as one of peace and few battles were fought.

But Herodotus accuses him of excessive vanity. According to Greek accounts, he was always surrounded by eunuchs and women. Lavish feasts were held at the Great Palace of Ecbatana. The courtiers wore long flowing robes of many different colors, amongst which red and purple predominated, and adorned their necks with chains or collars of gold, and their wrists with bracelets of the same precious metal. Even the horses on which they rode had sometimes golden bits to their bridles. Astyages' chief pastime was hunting. The capital was surrounded by a park where the king hunted wild animals.

However, this period is especially remembered for the ascendancy of the Zoroastrian priestly class called the Magi.

All through this reign, there was one issue which bothered Astyages. His marriage with the principal queen, the Lydian princess Aryenis produced no male offspring nor did his affairs with any of his concubines. Legend says that he, however had a daughter Mandane who was married to Cambyses I of Persia. Their son Cyrus II would later wrest control of the state from his grandfather and become one of the greatest monarchs in history.

Though historians barely assign any important wars to this period, it is widely believed that Astyages and not Cyaxares could have been the king who had actually fought the Lydians. At the fag end of his reign, the Armeians rose into revolt and were subdued by Astyages with an iron hand.

In 559BC, Astyages had to face the revolt of his own grandson, Cyrus of Persia. A battle was fought in which Cambyses I was killed. But Cyrus rallied the forces together and inflicted a crushing defeat on the Medes. The fleeing Median soldiers were pursued deep into their territory along with their king and commander Astyages. There were a couple of engagements between the Medes and the Persians. On conclusion of the first, the Medes had to flee as their camp was taken over and their royal insignia fell into the hands of the Persians. In the second engagement, Astyages was captured by the Persians. This brought an end to the war. Ecbatana surrendered and Media became a province of the fledgling Persian Empire.

Zoroaster and the Birth of Zoroastrianism
Zoroaster also known as Zarathusra or Zardosht was born around this time. The religion which he founded, called Zoroastrianism originated from an older polytheistic faith called Magism. This was the religion of the Medes and the Persians prior to the birth of Zoroastrianism and was the official state religion during the sovereignty of Media.

Media and Magism are closely related, so much so that the high priests of Magism, the Magi who give the religion its name were exclusively chosen from a Median tribe of the same name. The actual Persian name of the Magi seems to have been Magupat which gradually changed into Mobed with the passage of time. These Magi were the most supreme spiritual authority in the Empire. However, with the passage of time, the Dastur was elevated to a position higher than that of the Magupat and the Magi themselves weren't picked ur from the Mede tribe.

The Iranians, prior to the birth of Zoroaster, worshipped natural forces. They were mostly Vedic divinites like Mithra, Varuna, Vayu, Agni, etc. One of the principal deities Yima Kshaeta (Jamshed in modern Persian) is believed to have originated from the Hindu Yama. Their pantheon also comprised other divinities like Anahita, Spenta Armaiti,Vohu-mano and Asha Vahishta.

As Zoroastrianism expanded to every nook and corner of Persia, these divinities were incorporated into Zoroastrianism as angels and good spirits. For example, Vohu-mano, Asha Vahishta, Spenta Armaiti, Kshatra Vairya, Haurvatat and Ameretat became the six Amesha Spentas(arch-angels) of Zoroastrianism. Apart from the Amesha Spentas, there were the Fravashis (angels) and the Yazatas (Adorable ones) who were worshipped.

Zoroaster: His Life and Philosophy
Zoroaster is believed to have born between 1400 and 1000BC in Northern Iran close to the Caspian coast. This is the land, which some people believe to be the paradise, Airyanem Vaego. His family name was Spitama, a cognate of the Sanskreit Swetha meaning "whiteness". His father was named Pourashaspa and his mother was Dugdhova. Little is known about his childhood except that he was an extremely pious boy. M.N.Dhalla in his History of Zoroastrianism (1938) describes Zoroaster's life in detail. However, this is an extremely biased account which gives credibility to legends and myths. Nevertheless, this is one among a few biographies of Zoroaster in existence.

Like the founder of each and every other religion, tales of Zoroaster's early life are often spiced and flavored with miracles. His birth had been prophesized prior to his arrival and was pre-destined to happen. Legend has it that Pourashaspa had longed for a child for a long, long time and prayed to Haoma to this effect. His prayers bore fruit with the birth of the Prophet. The Zarathusht-namah tells us that the angel Vohumanah entered the child's mind soon after his birth and the child laughed aloud immediately upon his birth which startled the people around. Tales also abound on how Porushaspa came under the influence of a wicked magician called Duasrobo and tried to kill the young child Zarathushtra on his insistence. However, the young Zoroaster escaped miraculously each and every time in the end, killing Duasrobo himself. These tales bear a striking resemblance to the stories of Kamsa's attempts on the life of the young Krishna and those of Herod on the young Jesus.

M.N.Dhalla says that Zoroaster was disillusioned with his religion at a very early age. He questioned the need of sacrifices and elaborate rituals. He stressed upon piety and goodness and was a sworn enemy of the Magian priests whom M.N.Dhalla calls Daivayasnians. However, the term Daivayasnians never existed and is purely an invention of the writer. Dhalla says that Zoroaster wanted to have a glimpse of the Great Lord Ahura Mazda but couldn't. However, he was suitably rewarded when his good thoughts, actions and conduct pleased Vohumanah who blessed him with a vision of the Great Lord Ahura Mazda Himself. This is one of the most important events in the history of Zoroastrianism. Ahura Mazda dictated the holy scripture unto Zoroaster which he later revealed to the Iranian people. This has since been written down in the form of the various books of the Avesta. This was the Zoroastrian revelation.

After his conversation with Ahura Mazda, Zoroaster was sure that he was the chosen One of the Lord and went from place to place preaching his new religion. (His first convert was his cousin Maidhyoimangha). In some places, he provoked the open enmity of the Magian priests. Dhalla mentions two Magian priests Bendva and Grehma who were his sworn enemies. However, Zoroaster had the last laugh when he travelled to the Iranian court and converted the Shah of Iran to his new religion. Zoroastrianism was subsequently made the state religion and the people were ordered to convert to the new faith. It is believed that Zoroaster lived up to the age of seventy-seven.

Zoroaster stressed upon three main principles: Humata (good thoughts), Huktha (Good words) and Huvarashta (Good deed). This has been adopted by the present Islamic regime and has been incorporated as the motto of the Islamic Republic of Iran: pendar-i-nik, goftar-i-nik, kerdar-i-nik. At the focal point of the Zoroastrian pantheon lay Ahura Mazda or the Supreme Lord. Below him lay the six Amesha Spentas about whom we had already seen. These were the forces of goodness. However, later fire gained prominence and gradually displaced all others as the principle object of worship. Like Hindus, the early Zoroastrians considered cows to be holy and a recipe made of cow's urine was considered to be an instant purifier which could absolve a man of any kind of sin.

The forces of evil were led by Ahrimaan (the Old Persian Angra Mainyos) who was assisted by an army of demons (daevas). Chief amongst them was Indra who was the Avestan counterpart of Vedic God Indra.

Zoroaster's marriage was arranged at a very early age. However, fables indicate, Zoroaster refused to marry the girl when she declined to remove her veil. Later, Zorosaster married three three times. His first wife bore him a son Isadvastra (whose son Ururvija was a prominent Zoroastrian missionary of later times) and three daughters—Freni, Thriti and Pouruschita. His second wife was, allegedly, a widow and she bore him two sons—Hvarechitra and Urvatnara.His third wife was Hvovi, daughter of Frashaoshtra, an important official in the court of Iran.

The name Zardosht is believed to have originated from either Zarat-ustra or Zarant-ustra.There are different theories with regard to the origin of his name:

Following *zarat-uštra- are:  "moving camels" or "driving camels," and related to Avestan zarš- "to drag" (Bailey, 1953:40-42) "desiring camels" or "longing for camels" and related to Vedic har- "to like" and perhaps (though ambiguous) also to Avestan zara-. (Mayrhofer, 42–43)  Following *zarant-uštra- are:  "with old/aging camels," related to Vedic járant- and similar to Ossetic zœrond. (Schlerath) "with yellow camels" with a parallel to Younger Avestan zairi- (Werba, 1982:184ff) "with angry camels," from Avestan *zarant- "angry, furious" (Mayrhofer, 42–43)

The Avesta
The Avesta is believed to have been compiled by the Prophet himself who dictated the 21 Nasks to his son-in-law Jamasp who inscribed the scripture in golden letters on cow hides. However, the cow hides have been lost to time. The Nasks themselves haven't survived in their entirety, except for one, the Vendidad which has been translated into English and most European languages.

The Avesta, in its modern form, was written down between 78 and 300AD. Today, it is regarded as the most holy book of Zoroastrianism and like the holy books of other religions is believed to have been revealed by Ahura Mazda Himself.They comprise the Vendidad which is made of 22 Fargards, the Yasna comprising 72 sections, the Visperad comprising 23 Kord (or sections), the Yashts, the Khorda Avesta (Small Avesta) and the Gathas. The oldest of these books are the Gathas believed to have been composed around 1300BC. The language of the Gathas closely resembles Vedic Sanskrit and form one of the earliest extant works in the language called Old Avestan.

The Avesta, often prefixed by the word "Zend" and called Zend Avesta is derived from the Old Persian word "A-vi-stak", the root word "vi" same as the root "vi" of the Vedas meaning "knowledge". The word "Zend" is derived from "Zainti"

The teachings of the Avesta appear highly-conservative even as per Zoroaster's standards. Ironically, for a man who spent a lifetime fighting superstition and rituals, the Avesta is filled with invocations to innumerable angels, black-magic, and prayers for the expiation of sins previously committed.These sins include introduction of any dead or impure matter into the holy fire, cremating or burying a corpse,etc. The Vendidad or Vi-daevodatem which means anti-demoniac law prescribes ways or purification of the impure. Pregnant women were regarded impure in Ancient Iran as they bore a grave in their wombs (in the form of a still-born child) and were to be confined to a corner of the house for nine-consecutive days and nights (known as Barashnum) far away from the holy fire. Similarly, a menstruating woman, corpse of a human being, etc. were all regarded as impure as they acted as carriers of the druj Nasu.Purity and chastity of an extreme kind were recommended. People who did not adhere to these rules were either whipped in public or were asked to pay a huge sum as penalty. These were the laws as prescribed by the Avesta. However, it remains to be seen to which extent these laws were implemented.

Apart from being a treasure in the eyes of a theologian, the Avestan books were also of immense historical interest. They were recited in a dialect of Old Persian which wasn't understood by the time they were written down (duri9ng the early Sassanian period). The Zand or the Zainti is believed to be a commentary in the Avesta which was essential for the religious text to be understood. The Avesta also gives a vivid description of the home of the Avestan people. Based on the Avesta, historians place the Avestan country in Northern Iran, roughly in the land known as Khorasan.

The Achaemenid Dynasty
The Achaemenids were princes of the Persian race, who were an Indo-European people who migrated from the north of Iran. With the Median highlands being people by the tough and powerful Medes, the Persians were obliged to settle in a comparatively quiet and less occupied province of Pars in Southern Iran. During the 7th century BC, one Hakhamanisha rose to power and crowned himself the first King of Persia. His descendants overthrew the Medes and established the Achaemenid Dynasty. They ruled Persia for around 225 years until the fall of their last king Darius III in 331BC. During this period, they waged highly successful wars against Egypt, the Levant and the Greeks and expanded their kingdom to distant parts of the globe.

Origin
The first supposed mention of the Persians is in an inscription of the Assyrian king Shalmanesser II in   in which references are made to the Parsu of south-western Armenia. In the seventh century BC, a semi-mythical personality called Hakhamanish established a kingdom in Persia and ruled as a feudatory of the Assyrian monarch. He is known as Achaemenes to the Greek writers. He was succeeded by Teispes (Cispi), Cyrus I and Cambyses I. However, no evidence exists regarding the existence of these monarchs and stories of them are regarded as purely fictitious and concocted. In 612BC, however, the Mede Cyaxares inflicted a crushing defeat upon the Assyrians and occupied Nineveh. This resulted in a shift of balance of power as the Medes emerged as overlords of the Middle East and most of the known world. Cyrus I is believed to be the Persian monarch who immediately submitted to the emerging power. Median overlordship lasted until 559BC when Astyages was overthrown by Cyrus II or Cyrus the Great with whose reign Persia enters historical times.

Cyrus II (Cyrus the Great) 549 - 529 BC
Cyrus ascended the throne of Persia in   His actual name in Old Persian happens to be Kurush. In his inscriptions, he extensively uses his royal title "Vazraka" which means "the Great". In modern times, Cyrus referred to as "Kurush-i-bozorg" has become a symbol of Persian revival and is regarded as a hero by monarchists and right-wing nationalists alike.

Early Life and Rise to Power
Cyrus II was born in 590 or 576 BC as per different versions, the son of the Persian Emperor Cambyses I and the daughter of Astyages of Media, Princess Mandane. There are a number of fantastical tales woven around the early life of Cyrus II including that he was brought up among a family of herdsmen. However, evidences of such an upbringing if at they are factual are yet to be found.

However, all the sources agree to the fact that Cyrus II was sent to the court of the Median ruler Astyages at Ecbatana at a very early age. The fact that Cyrus was a grandson of the Median ruler must be one possible reason. However, eyebrows are raised over the veracity of this claim. While Xenophon is the one who tells us that Cyrus was a grandson of Astyages, Nicolas and Ctesias say that Cyrus was in no way related to Astyages and his confinement at the court of Astyages was due to a strange personal attachment Astyages had towards him. However, Cyrus detested Ecbatana and the company of the vain old monarch who spent more of his time in merriment and conducting lavish feasts. He secretly desired to escape to his own country and lead a rebellion against Median yoke. But the royal priests and the Median astrologers had advised the monarch to keep Cyrus captive in Ecbatana for they said that if he ever allowed Cyrus to go back to Persia he would lose his kingdom forever. So, willing to preserve his kingdon, Astyages kept Cyrus under heavy-guard. But Cyrus managed to escape to Persia. The story of this escape is narrated in vivid detail by Rawlinson.

Desiring to leave for Persia, Cyrus petitioned Astyages requesting a leave of absence for five months reasoning that his father in Persia was ill. The first application was rejected. However, the second, made through the king's favorite eunuch was more successful. Astyages agreed and Cyrus set forth for Persia. But the next evening, as Astyages was enjoying a royal feast, one of the dancing-girls sang of "a lion which had let a wild boar escape". Immediately, Astyages realized his folly and bade his soldiers set forth for the frontier and capture Cyrus either alive or dead. They caught up with Cyurus before he reached the border but the latter fooled the soldiers by inviting them for a drink and made good his escape taking advantage of their intoxication. By the time they caught up with Cyrus again, he had crossed into Persia and at the head of a Persian contingent now, he repulsed the soldiers who returned empty-handed to Ecbatana. Furious, Astyages led a huge army into Persia. The contingent consisted of a hundred chariots, fifty thousand horsemen, and three hundred thousand light-armed foot, who were drawn up in in front of a fortified town near the frontier. The battle lasted two days during which Cambyses I was killed and the Persians defeated. Astyages and his soldiers pursued the fleeing Persians to the hills where a second battle was fought. The Persians, taking advantage of their high-ground, charged furiously at the Medes and slew sixty thousand of them. Astyages immediately withdrew and later attacked the Persians at Pasargadae.A battle was fought which brought about an overwhelming victory to the Persians. All the insignia of Median royalty along with their treasures fell into the hands of the Persians. Cyrus followed Astyages into Media where a sixth battle was fought. The Medians were completely defeated and Astyages captured as a prisoner. Following the capture of Astyages, the whole of Media surrendered without the slightest resistance and Cyrus emerged as the absolute sovereign of the First Persian Empire.

The end of the Median dynasty came with the conquest of Ecbatana by Cyrus in the year 549BC. This was also the year when Cyrus conquered Media and made himself the master of Iran. Almost immediately after his victory over the Medes, Cyrus launched an invasion of Bactria (modern-day Afghanistan). The north-west was another region which had successfully resisted attempts at conquest. Cyrus led a large expedition to the north-western frontier and after occupying the outlying provinces with ease came to a face-to-face encounter with the kingdom of Lydia.

Conquest of Lydia
The Emperor of Lydia Croesus was a brother of the Mede Astyages and was greatly affected by his dethronement and the annexation of Media by Persia.He had a built a powerful Empire in Asia Minor conquering all the smaller states and this sudden rise was made possible mainly by the friendly relations he had with Media and non-interference by neighbouring countries. During this period, Croesus earned perpetual fame for himself for the magnificent gold coins he minted. So, when Astyages was dethroned and his empire annexed by Cyrus he was worried about his own fate. This prompted him to ally with Greece and Babylonia. Cyrus, at once took an aggressive posture and invaded Asia Minor taking Diabekr, Malatiyah and Gurun. Croesus, at once declared war on Persia and crossing the Halys river attacked the city of Pteria in 547BC. This attack on Pteria has been immortalized by the famous legend involving the Oracle at Delphi. According to the legend, Croesus contacted the Oracle before his attack on Pteria. The Oracle suggested vaguely that, "if King Croesus should cross the Halys River, a great empire would be destroyed." Croesus took these words with delight, instigating a war that would ironically and eventually end not the Persian Empire but terminate his own.

The Lydian advance was checked by Persian troops within the gates of Pteria and a terrible battle ensued. Initially, the Lydians had the upper hand mainly due to the strength of their excellent cavalry. But Cyrus formed an advance brigade made of camelmen and charged at the Lydians forcing them to flee. However, soon, Cyrus gave up the charge allowing them to reach Lydia unmolested. When Croesus had reached his own palace and all fears of a Persian attack of Lydia had subsided, Cyrus saw his moment and gathered his army and attacked the Lydian capital taking Croesus by surprise. Croesus appealed to his allies for aid as the Lydian troops successfully defended the city for fourteen days. But on the fifteenth day, a Persian soldier discovered a secret passage into the city through its walls. The Persian soldiers capitalized on this discovery and enjacted a breach. Lydia was taken and absorbed into the Persian Empire. Croesus was captured and imprisoned but was later pardoned and ruled Lydia as a vassal of Persia.

Soon afterwards, Sardis became the scene of an insurrection. Pactyas, a Lydian, who had been entrusted with the duty of conveying the treasures of Croesus and his more wealthy subjects to Ecbatana, revolted against Tabalus, the Persian commandant of the town, and being joined by the native population and numerous mercenaries, principally Greeks, whom he hired with the treasure that was in his hands, made himself master of Sardis, and besieged Tabalus in the citadel. The news reached Cyrus while he was upon his march; but, estimating the degree of its importance aright, he did not suffer it to interfere with his plans. He judged it enough to send a general with a strong body of troops to put down the revolt, and continued his own journey eastward. Mazares, a Mede, was the officer selected for the service. On arriving before Sardis, he found that Pactyas had relinquished his enterprise and fled to the coast, and that the revolt was consequently at an end. It only remained to exact vengeance. The rebellious Lydians were disarmed. Pactyas was pursued with unrelenting hostility, and demanded, in succession, of the Cymaeans, the Mytilenseans, and the Chians, of whom the last-mentioned surrendered him.

Campaign Against the Greeks
Following the defeat of Pactyas, Cyrus dispatched Mazares to attack his Greek allies. The Greek cities of Priene and Magnesia in Asia Minor were attacked and subdued. Mazares was renowned for his cruelty and barbarism and on the conquest of Priene, he captured its entire populace and sold them as slaves. However, Mazares' successor Hapages was more lenient. The aggressive policy of Mazares was retained and more Greek cities were conquered. However, the inhabitants of these cities were treated well and retained a fair degree of independence. Miletus the most powerful and important of the Greek city-states made a determined resistance but was ultimately subdued and conquered. With this ended Cyrus' war in Asia Minor and when the last Greek city fell, he emerged as the undisputed master of West Asia stretching from Bactria to the Bosporus. This was the largest Empire till then to have ruled over the region.

The First World Empire
Following the defeat of the Greeks, Hapages subdued the Carians, the Dorian Greeks, the Caunians, and the people of Lycia. One by one the cities fell into the hands of the Persians and Greek resistance was completely wiped out by 542BC. Next, Cyrus turned his attention to the east and attempted the conquest of Bactria. There are different versions as to how Cyrus conquered Bactria. Ctesias says that they submitted peacefully when Darius married a Median princess. However, this is seriously contested by historians who reject the possibility that this could have any effect on the Bactrians. Herodotus says that Cyrus subdued Bactria after a long drawn out war and this seems most probable.

Following the conquest of Bactria, Cyrus' next campaign was against the Sacae (probably the Sakas or Scythians) who resided in the east of Bactria. Herodotus and Ctesias do not record much on the eastern campaigns of Cyrus the Great. However, the historian Pliny relates that Cyrus destroyed the city of Kapisa in Afghanistan. He was assisted in his campaigns by the Ariaspse, a people of Drangiana (near Lake Hamun in modern-day Sistan). Cyrus then marched against the Indians and conquered Gedrosia (the district of Makran in the Baluchistan province of Pakistan; its memory has been preserved by the presence of a city called Gwadar close to the Pakistan-Iran frontier). Among other countries subdued by Cyrus in this neighborhood, are Hyrcania, Parthia, Chorasmia, Sogdiana, Aria (or Herat), Drangiana, Arachosia, Sattagydia, and Gandaria.

Conquest of Babylonia
In 539 BC, towards the end of September, Cyrus' armies, under the command of Gubaru, the governor of Gutium, attacked Opis on the Tigris river and defeated the Babylonians after a minor uprising. When Opis was occupied, the Persians took hold of the vast canal system of Babylonia.

On October 10, the city of Sippar was seized without a battle. Nabonidus, the ruler of Babylonia, who was staying in the city at the time, fled to the capital, Babylon.

On October 12, Gubaru's troops entered Babylon, without facing any resistance from the Babylonians. Herodotus explains that to accomplish this feat, the Persians diverted the Euphrates river into a canal so that the water level dropped "to the height of the middle of a man's thigh," which allowed the invading forces to march directly through the river bed to enter at night.[20] On October 29, Cyrus himself entered the city of Babylon and arrested Nabonidus. He then assumed the titles of "king of Babylon, king of Sumer and Akkad, king of the four sides of the world."

Prior to Cyrus' invasion of Babylon, the Neo-Babylonian Empire had conquered many kingdoms. In addition to Babylonia itself, Cyrus incorporated its subnational entities into his Empire, including Syria and Palestine.

Before leaving Babylon, Cyrus also freed the Israelites by allowing them to return to their native land, effectively ending the Babylonian captivity. The return of the exiles reinforced the Jewish population in their homeland, which had been waning since the start of the Babylonian rule.

According to the Behistun Inscription of Darius the Great, Cyrus' dominions must have comprised the largest empire the world had ever seen. At the end of Cyrus' rule, the Achaemenid Empire stretched from Asia Minor and Judah in the west to the Indus River in the east.

Death
From cuneiform sources, it has now become clear that Cyrus' reign came to an end in the summer of 530. Authors like Ctesias and Xenophon give different accounts of his death. According to Rawlinson, who uses Herodotus' version, Cyrus was engaged in subduing the Massagatse who inhabited the desert of Khwarezm. In the first battle against the Massagatse, Cyrus inflicted a crushing defeat on the Massagatse killing its ruler Spargapises. But in the second battle against the Massagatse, Cyrus was killed by Sparagapises' mother Queen Tornyris who dipped his head in blood and reportedly used his skull as a vessel to drink fine wine for a long time afterwards. However, the Persians won the battle and Cyrus' body was found and carried to Persia where it was buried in the city of Pasargadae.

According to Plutarch, his epitaph says,

"O man, whoever you are and wherever you come from, for I know you will come, I am Cyrus who won the Persians their empire. Do not therefore grudge me this little earth that covers my body."

Cyrus was succeeded by son Khambujiya (Cambyses II).

Legacy
Cyrus was an excellent statesman and soldier and was the creator of the first world empire in history. His legacy remains alive and is greatly respected in modern Persia. He is also held favorably by the Jews and is the only Gentile to be designated as a messiah in the Tanakh (Isaiah 45:1-6). Some scholars believe that there are references to him in the Quran. Many believe that the Quranic figure of Zulqarnain is none other than Cyrus the Great though it has been seriously challenged by some.

One of his great legacies had to be the inscription of the Cyrus Cylinder described below.

A section of the Cyrus cylinder.

The Cyrus Cylinder
The Cyrus Cylinder, also known as the ‘Cyrus the Great Cylinder’, is an artifact of the Persian Empire, consisting of a declaration issued by the emperor Cyrus the Great inscribed in Babylonian (Akkadian) cuneiform on a clay cylinder.

It was discovered in 1879 by the Assyro-British archaeologist Hormuzd Rassam in the foundations of the Esagila (i.e., the Marduk temple of Babylon). This cylinder which composed of two broken pieces, now united in the British Museum, and comprises an account of Cyrus' capture of Babylon, a reference to the return of the captured statues of Mesopotamian gods, several topical remarks about the abolishment of unjust corvees, and a description of repairs to old buildings in Babylon. It was regarded as the Oldest Charter of Human Rights in the world by the government of Shah Mohamed Reza, a claim that has been subject to criticism from scholars, who point at the topical character of the document.

Cambyses II 529 - 522 BC
On the death of Cyrus II in 529BC, his son Cambyses II took hold the reins of power and continued his father's policy of conquest. His original Persian name might have been Kambujiya, which is of pure Indo-European origin and is synonymous with Kamboja. Cambyses II is represented as one of the most ambitious conquerors of the mould of Alexander and Khusro Parviz for like his Macedonian and Sassanian successors he aspired to expand his Empire into hitherto unexplored and unconquered parts of the globe.

Cambyses ascended the throne in the year 530 or 529BC and immediately after his accession murdered his brother Smerdis.

Campaign Against Egypt
The ambitious Cyrus had always willed to take his armies into Egypt but died before he could realize his dream. Now with the successful conquest of Mesapotamia and the Middle East, the gates were open for an invasion of Egypt.

In 529BC, soon after Cambyses had established himself on the throne, he demanded of Amasis, the Pharaoh of Egypt to send his daughter to him as a secondary wife. However, Amasis deceived Cambyses by sending a damsel named Nitesis instead of his own daughter. When he was acquainted of the fraud, Cambyses swore revenge. However, he waited for four years until the death of Amasis before launching an invasion of Egypt.

In 525BC, Amasis' son Psammetichus III became the Pharaoh of Egypt. Sensing an opportunity, Cambyses led an army of Persian soldiers and Arab mercenaries into Egypt. Amasis had always hoped that the Greeks would come to their aid in the case of a Persian invasion but the Greek Cypriots preferred to join with Cambyses. So assisted by the formidable Cypriot navy, Cambyses conquered Egypt.

Soon after the conquest of Egypt, the rulers of Libya and the Greeks of Barca and Cyrene sent rich tributes to the Persian Emperor. However, Cambyses intended to expand his empire further to the south and conquer the kingdom of Ammon in the North African desert. He sent an army fifty thousand strong which perished in the middle of the African desert. An invasion of the Phoenician colony of Carthage was planned but the plan was abandoned when the Phoenicians in his navy refused to fight against their countrymen. Another force led by Cambyses to conquer Ethiopia had to return when faced with defeat and loss of supplies.

Almost Immediately after his return to Egypt, Cambyses had to tackle the rebellion of Psammetichus III. The priests declared him an incarnation of the sacred bull of Egyptian mythology Apis and the whole country rose into revolt in support of the disinherited king. Cambyses reacted by crushing this insurrection with an iron hand and killing Psammetichus III and the priests who supported him. He then retaliated by stabbing the sacred calf regarded as an incarnation of the sacred bull Apis, killed its priests and prohibited the festivals dedicated to Apis. He ordered the desecration of the tombs of long dead Egyptian monarchs and showed blunt disregard and disrespect for the customs of the people.

At this juncture, there appeared disturbing news from Persia. A messenger informed him that an impostor had captured the thrown of Persia and claims to be Smerdis the deceased son of Cyrus the Great.

Death
Cambyses, the sources tell us, did not live long after the appearance of this new claimant to the throne. But died in an extremely suspicious circumstances. Some say that he committed suicide. However, this appears highly improbable. Nevertheless, while the truth is being investigated, it would be enough for us to bluntly conclude that Cambyses did die in the year 522BC and was succeeded by the impostor Smerdis.


text: Template:Scratch/License

title: Template:Scratch/License


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Scratch/Introduction

Welcome to the study of Scratch, a computer language that was developed by the MIT Media Lab to help provide a computer programming language that was easy enough for children to learn but complex enough to design some more elaborate computer programs.

The purpose of this textbook is to provide learning tools, lesson plans, and instructional material that would be useful in the study of this programming language. This book is provided free of charge and the development of this content is hosted on Wikibooks, one of the various sister projects of the Wikimedia Foundation.

One of the other goals of this project is to help provide some materials that can be used simultaneously with those learning resources offered by the Scratch development team. There are videos, quick help sheets, "Scratch Cards", and other resources available on other websites, and this textbook should be available under the same copyright terms. To achieve this goal, this content is dual licensed under the terms of the GFDL and Creative Commons - Attribute - Share Alike licenses. Please see Scratch/Content License for more details.

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title: Scratch/Introduction


text:
HSC Physics

Preliminary
The preliminary HSC Physics course consists of four core modules that make up 120 indicative hours in total.

The modules studied are:

 * The World Communicates (30 indicative hours);
 * Electrical Energy in the Home (30 indicative hours);
 * Moving About (30 indicative hours);
 * The Cosmic Engine (30 indicative hours).

All four core modules must be completed in order to complete the preliminary physics course. The preliminary physics course is a prerequisite to the HSC physics course.

HSC
The HSC Physics course consists of three core modules that make up 90 indicative hours in total, and ONE option chosen by the student that makes up 30 indicative hours.

The core modules studied are:

 * Space (30 indicative hours);
 * Motors and Generators (30 indicative hours);
 * From Ideas to Implementation (30 indicative hours).

The options available are:

 * Geophysics;
 * Medical Physics;
 * Astrophysics;
 * From Quanta to Quarks;
 * The Age of Silicon.

title: HSC Physics


text:
HSC Physics/Core/Space

Chapters

 * /The Earth's Gravitational Field/ [[File:00%.svg]]
 * /A Successful Rocket Launch/ [[File:00%.svg]]
 * /Gravity in the Solar System/ [[File:00%.svg]]
 * /Special Relativity/ [[File:00%.svg]]

title: HSC Physics/Core/Space