text:
Horticulture/Acer rubrum

Acer rubrum (Red Maple, also known as Swamp or Soft Maple) is one of the most common and widespread deciduous trees of eastern North America. It ranges from the Lake of the Woods on the border between Ontario and Minnesota, east to Newfoundland, south to near Miami, Florida, and southwest to east Texas. Many of its features, especially its leaves, are quite variable in form. At maturity it often attains a height of around 25 metres (82 feet). It is aptly named as its flowers, petioles, twigs and seeds are all red to varying degrees. Among these features, however, it is most well known for its brilliant deep scarlet foliage in autumn.

Over most of its range, red maple is adaptable to a very wide range of site conditions, perhaps more so than any other tree in eastern North America. It can be found growing in swamps, on poor dry soils, and most anywhere in between. Elevation is also not a limiting factor in its range, as it grows well from sea level to about 900 m (3,000 feet). Due to its attractive fall foliage and pleasing form, it is often used as a shade tree for landscapes. It is used commercially on a small scale for maple syrup production as well as for its medium to high quality lumber. It is also the State Tree of Rhode Island.

Description
Though A. rubrum is generally easy to identify, it is highly variable in morphological characteristics. It is a medium to large sized tree, reaching heights of 18 to 27 metres (60 to 90 feet) and exceptionally over 35 metres (115 feet). The diameter can range from 46 to 76 cm (18 to 30 inches), depending on the growing conditions. In forests, the bark will remain free of branches until some distance up the tree. Individuals grown in the open are shorter and thicker with a more rounded crown. Generally speaking, however, the crown is irregularly ovoid with ascending whip-like curved shoots. The bark is a pale grey and smooth when the individual is young. As the tree grows the bark becomes darker and cracks into slightly raised long plates. The largest known living red maple is located near Armada, Michigan, at a height of 38.1 metres (125 feet) and a bole circumference, at breast height, of 4.95 metres (16.25 feet).

The leaves of the red maple offer the easiest way to distinguish it from its relatives. As with all maples, they are deciduous and arranged oppositely on the twig. They are typically 5–10 cm (2-4 inches) long and wide with 3-5 palmate lobes with a serrated margin. The sinuses are typically narrow, but the leaves can exhibit considerable variation. When 5 lobes are present, the three at the terminal end are larger than the other two near the base. In contrast, the leaves of the related silver maple, A. saccharinum, are much more deeply lobed, more sharply toothed and characteristically have 5 lobes. The upper side of A. rubrum's leaf is light green and the underside is whitish and can be either glaucous or hairy. The leaf stalks are usually red and are up to 10 cm (4 inches) long. Furthermore, the leaves turn a brilliant red in autumn.

The twigs of the red maple are reddish in colour and somewhat shiny with small lenticels. Dwarf shoots are present on many branches. The buds are usually blunt and greenish to reddish in coulour, generally with several loose scales. The lateral buds are slightly stalked, and in addition there may be collateral buds present as well. The buds form in fall and winter and are often visible from a distance due to their reddish tint. The leaf scars on the twig are V-shaped and contain 3 bundle scars.

The flowers are generally unisexual, with male and female flowers appearing in separate sessile clusters, though they are sometimes also bisexual. They appear in spring from April to May, usually coming before the leaves. The tree itself is considered polygamo-diecious, meaning some individuals are male, some female, and some monoecious. The flowers are red with 5 small petals and a 5-lobed calyx borne in hanging clusters, usually at the twig tips. They are lineal to oblong in shape and are pubescent. The pistillate flowers have one pistil formed from two fused carpels with a glabrous superior ovary and two long styles that protrude beyond the perianth. The staminate flowers contain between 4 and 12 stamens, often with 8.

The fruit is a 15 to 25 milimeter (.5 to .75 inch) long double samara with somewhat divergent wings at an angle of 50 to 60 degrees. They are borne on long slender stems and are variable in colour from light brown to reddish. They ripen from April through early June, before even the leaf development is altogether complete. After they reach maturity, the seeds are dispersed for a 1 to 2 week period from April through July.

Ecology
Red maple seldom lives longer than 150 years, making it short to medium lived. It reaches maturity in 70 to 80 years. Its ability to thrive in a large number of habitats is largely due to its ability to produce roots to suit its site from a young age. In wet locations, red maple seedlings produce short taproots with long and developed lateral roots, while on dry sites, they develop long taproots with significantly shorter laterals. The roots are primarily horizontal, however, forming in the upper 25 cm (10 in) of the ground. Mature trees have woody roots up to 25 meters (80 ft) long. They are very tolerant of flooding, with one study showing that 60 days of flooding caused no leaf damage. At the same time, they are tolerant of drought due to their ability to stop growing under dry conditions by then producing a second growth flush when conditions later improve, even if growth has stopped for 2 weeks.

A. rubrum is one of the first plants to flower in spring. A crop of seeds is generally produced every year with a bumper crop often occurring every second year. A single tree between 5 and 20 cm (2 and 8 inches) in diameter can produce between 12,000 and 91,000 seeds in a season. A tree 30 cm (1 foot) in diameter was shown to produce nearly a million seeds. Fertilization has also been shown to significantly increase the seed yield for up to two years after application. The seeds are epigeal and tend to germinate in early Summer soon after they are released, assuming a small amount of light, moisture, and sufficient temperatures are present. If the seeds are densely shaded, then germination commonly does not occur until the next Spring. Most seedlings do not survive in closed forest canopy situations. However, one to four year old seedling are common under dense canopy and though they eventually die if no light reaches them, they serve as a reservoir, waiting to fill any open area of the canopy above.

Red maple is able to increase its numbers significantly when associate trees are damaged by disease, cutting, or fire. One study found that 6 years after clearcutting a 3.4 hectare (8.5 acre) Oak-Hickory forest containing no red maples, the plot contained more than 2,200 red maple seedlings per hectare (900 per acre) taller than 1.4 m (4.5 feet). One of its associates, the black cherry (../Prunus serotina/), contains benzoic acid, which has been shown to be a potential allelopathic inhibitor of red maple growth. Red maple is one of the first species to start stem elongation. In one study, stem elongation was one-half completed in 1 week, after which growth slowed and was 90% completed within only 54 days. In good light and moisture conditions, the seedlings can grow 30 cm (1 ft) in their first year and up to 60 cm (2 ft) each year for the next few years making it a fast grower.

The red maple is a used as a food source by several forms of wildlife. Elk and white-tailed deer in particular use the current season's growth of red maple as an important source of winter food. Several Lepidoptera (butterflies and moths) utilize the leaves as food; see List of Lepidoptera which feed on Maples. Due to A. rubrum's very wide range, there is significant variation in hardiness, size, form, time of flushing, onset of dormancy, and other traits. Generally speaking, individuals from the north flush the earliest, have the most reddish Fall color, set their buds the earliest and take the least winter injury. Seedlings are tallest in the north-central and east-central part of the range. The fruits also vary geographically with northern individuals in areas with brief frost free periods producing fruits that are shorter and heavier than their southern counterparts. As a result of the variation there is much genetic potential for breeding programs with a goal of producing red maples for cultivation. This is especially useful for making urban cultivars that require resistance from verticillium wilt, air pollution, and drought.

Red maple frequently hybridizes with Silver Maple; the hybrid, known as Freeman's Maple Acer x freemanii, is intermediate between the parents.

Varieties
Numerous cultivars have been selected, often for intensity of fall color, with 'October Glory' and 'Red Sunset' among the most popular. Toward its southern limit, 'Fireburst', 'Florida Flame', and 'Gulf Ember' are preferred. Many cultivars of Freeman's Maple are also grown widely. Below is a partial list of cultivars:
 * 'Armstrong' - Columnar to fastigate in shape with silvery bark and modest orange to red fall foliage
 * 'Autumn Blaze' - Rounded oval form with leaves that resemble the silver maple. The fall colour is orange red and persists longer than usual
 * 'Autumn Flame' - A fast grower with exceptional bright red fall color developing early. The leaves are also smaller than the species.
 * 'Autumn Radiance' - Dense oval crown with an orange-red fall colour
 * 'Autumn Spire' - Broad columnar crown; red fall colour; very hardy
 * 'Bowhall' - Conical to upright in form with a yellow-red fall colour
 * 'Burgundy Bell' - Compact rounded uniform shape with long lasting, burgundy fall leaves
 * 'Columnare' - An old cultivar growing to 20 metres (70 feet) with a narrow columnar to pyramidal form with dark green leaves turning orange and deep red in fall
 * 'Gerling' - A compact, slow growing selection, this individual only reaches 10 metres (30 feet) and has orange-red fall foliage
 * 'Northwood' - Branches are at a 45 degree angle to the trunk, forming a rounded oval crown. Though the foliage is deep green in summer, its orange-red fall colour is not as impressive as other cultivars.
 * 'October Brilliance' - This selection is slow to leaf in spring, but has a tight crown and deep red fall colour
 * 'October Glory' - Has a rounded oval crown with late developing intense red fall foliage. Along with 'Red Sunset', it is the most popular selection due to the dependable fall colour and vigorous growth.
 * 'Red Sunset' - The other very popular choice, this selection does well in heat due to its drought tolerance and has an upright habit. It has very attractive orange-red fall colour and is also a rapid and vigorous grower.
 * 'Scarlet Sentinel' - A columnar to oval selection with 5-lobed leaves resembling the silver maple. The fall colour is yellow-orange to orange-red and the tree is a fast grower.
 * 'Schlesingeri' - A tree with a broad crown and early, long lasting fall colour that a deep red to reddish purple. Growth is also quite rapid.
 * 'Shade King' - This fast growing cultivar has an upright-oval form with deep green summer leaves that turn red to orange in fall.
 * 'V.J. Drake' - This selection is notable due to the fact that the edges of the leaves first turn a deep red before the colour progresses into the center.

Uses
Red Maple is widely grown as an ornamental tree in parks and large gardens, except where soils are too alkaline or salty. In parts of the Pacific Northwest, it is one of the most common introduced trees. Its popularity in cultivation stems from its vigorous habit, its attractive and early red flowers, and most importantly, its flaming red fall foliage. The tree was introduced into the United Kingdom in 1656 and shortly thereafter entered cultivation. There it is frequently found in many parks and gardens, as well as occasionally in churchyards.

Red Maple is a good choice of a tree for urban areas when there is ample room for its root system. The red maple is excellent at withstanding harsh urban conditions, including tolerance of both dry and wet soils, and a higher tolerance of pollution than sugar maple. Like several other maples, its low root system can be invasive and it makes a poor choice for plantings in narrow strips between a sidewalk and a street. It attracts squirrels, who eat its buds in the early spring, although squirrels prefer the larger buds of the silver maple.

In the lumber industry A. rubrum is considered a soft maple. The wood is close grained and as such it is similar to that of A. saccharum, but its texture is softer, less dense, and has a poorer figure and machining qualities. High grades of wood from the red maple can nonetheless be substituted for hard maple, particularly when it comes to making furniture. As a soft maple, the wood tends to shrink more during the drying process than with the hard maples. Red maple is also used for the production of maple syrup, though the hard maples A. saccharum and A. nigrum, the black maple, are more commonly used. One study compared the sap and syrup from the Sugar Maple with those of the red maple, as well as those of the Silver Maple, boxelder (A. negundo), and Norway maple (A. platanoides), and all were found to be equal in sweetness, flavor, and quality. However, the buds of red maple and other soft maples emerge much earlier in the spring than the sugar maple, and after sprouting chemical makeup of the sap changes, imparting an undesirable flavor to the syrup. This being the case, red maple can only be tapped for syrup before the buds emerge, making the season very short.

Toxicity
The leaves of red maple, especially when dead or wilted, are highly toxic to horses. The toxin is currently unknown, but it is believed to be an oxidant due to its destruction of red blood cells and thus causing the blood to be unable to properly transport oxygen, a condition otherwise known as acute hemolysis. The ingestion of 700 grams (1.5 pounds) of leaves is considered toxic and 1.4 kilograms (3 pounds) is lethal. Symptoms occur within one or two days after ingestion and can include depression, lethargy, increased rate and depth of breathing, increased heart rate, jaundice, dark brown urine, coma, and death. Treatment is limited and can include the use of methylene blue or mineral oil and activated carbon in order to stop further absorption of the toxin into the stomach. About 50% to 75% of affected horses die or are euthanized as a result.

title: Horticulture/Acer rubrum


text: Talk:Macroeconomics/Inflation

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

title: Talk:Macroeconomics/Inflation


text:
User talk:82.201.192.198

I have nominated your recently created book REBECCA_OF_SUNNYBROOK_FARM for speedy deletion. Wikibooks is a project for creating text books and not for novels or works of fiction. I would suggest that this may be more suitable on another wiki site but I searched on Google and this book is on many different websites on the Internet so there's no need to duplicate it again.

Xania talk 12:44, 9 December 2007 (UTC)

title: User talk:82.201.192.198


text:
Horticulture/Veronica persica

Veronica persica (also Persian speedwell, Large Field Speedwell, or Bird's-eye) is an annual or winter annual native to Eurasia, but also widespread in the United States, and east Asia (including Japan).

Description
The seed leaves are broadly triangular cotyledons, with truncated base. The short-stalked leaves are broadly ovate, having coarsely serrated margins. V. persica has weak stems that form a dense, prostrate ground cover. Tips of stems are often ascending. Leaves on the lower stems are paired, but are alternate on the upper portion of the stem. The short-petioled leaves are longer than they are broad and coarsely toothed.

The flowers are sky-blue with dark stripes and a white center, and they are zygomorphic (they only have one plane of symmetry, which is vertical). They are solitary on long, slender, hairy stalks in the leaf axils. The fruits are heart-shaped and hairy.

title: Horticulture/Veronica persica


text: Horticulture/Alnus incana

title: Horticulture/Alnus incana


text: Horticulture/Cornus mas

title: Horticulture/Cornus mas


text:
User talk:Birds5

I've blocked you for 1 day because of your nonsensical edits, after Mike warned you. If you're going to add messages to Wikibooks, they must be on-topic. --Whiteknight (Page) (Talk) 02:08, 16 December 2007 (UTC)

title: User talk:Birds5


text:
Conlang/Intermediate

The Intermediate level of this book is for those familiar with the basic elements of conlangs (or of languages in general) who want to learn how to create a conlang with added depth. It aims to familiarize you with the internal structure of different elements of language, and basic terminology for discussing them. It assumes prior familiarity with technical terms only up to the minimal level explained by the Beginner level.

Theory and practice
The terminology explained in this level, and the analysis of language structure described by that terminology, are useful tools for conlanging. They give you a map with which to navigate the vast territory of language. However, as you study these useful tools, remember that the map is not the territory.

For one thing, they are tools of analysis, and that doesn't necessarily suit them for constructing languages. By breaking something into pieces you can describe it, and then try to figure out how it was put together in the first place; but the way you broke it down probably isn't the way it was put together, especially if it's something really complex. Language — as has been noted in the conlanging community — is the most complex thing humans do. Strange natlang features aren't random; if you use linguists' analysis as a menu of things to do, rather than working from why and how those features come about, there's a risk your conlang could acquire an oddly artificial feel.

Linguists' analysis of language may only sometimes work. There are languages that don't have syllables (or so some linguists figure). Sometimes it's hard to be sure when things are or aren't separate words. Words often don't classify neatly into standard parts of speech. Or, the analysis may be (or may be suspected to be) purely descriptive, with no causal structure behind it; some linguists have suggested that ergativity (a feature that has enjoyed some popularity amongst conlangers, and which we'll get to in the Advanced level) is just a superficial characteristic of language, the way "has blue feathers" is a superficial characteristic of some birds that doesn't really tell you anything important about bird biology.

The terminology and analysis offered here is useful; we need some way to talk about language. Just don't let it limit your understanding, or your creativity.

What's in this level?
Each section is designed to cover details of a different facet of languages, natural and constructed. The sections are:
 * Sound notation: Different languages — or even different dialects of the same language — may have different rules for how written words should be pronounced.  This section introduces an alphabet for representing just the sounds of human speech, no matter what language the sounds are being used in.
 * Phonetics and phonology: How the sounds of a language (phonetics) fit together to form a system (phonology).
 * Grammar: How words change and combine to determine meaning.
 * History: How languages change over time.
 * Writing systems: The many and varied written representations of language.
 * Tips for adding irregularities to your conlangs: Kinds and causes of irregularities in a language.
 * Exploring new realms: Some thoughts on deliberately leaving the beaten path.

title: Conlang/Intermediate


text: Wikibooks:Requests for deletion/Wikibooks:Instant messaging Wikibookians


text:
User:Nesnad

Knowledge is power. (Not sure why I never added something here before.)

title: User:Nesnad


text:
User talk:Brttnyrhea

Come introduce yourself at the new users page. If you have any questions, you can ask there or contact me personally. – Mike.lifeguard  | talk 16:22, 9 December 2007 (UTC)

title: User talk:Brttnyrhea


text:
User talk:Nesnad

Come introduce yourself at the new users page. If you have any questions, you can ask there or contact me personally. – Mike.lifeguard  | talk 16:23, 9 December 2007 (UTC)

HAHAHA Should I be offended since I'm not a new user? Don't copy and paste like mad! Thanks. Nesnad (talk) 17:16, 9 December 2007 (UTC)

My /sandbox is here for now.

Japanese Wikibook discussion
Hi Nesnad,

I just added a comment on Talk:Japanese which I wanted to draw your attention to as you've been involved in this book. --Swift (talk) 05:19, 10 June 2008 (UTC)

Quick Start Japanese
Hi Nesnad,

Just in case you drop in again, I wanted to ask you if you had any plans for the Quick Start Japanese you set up in a sub-page of your userpage. --Swift (talk) 10:50, 8 February 2009 (UTC)

Hey Swift, I guess I should put this on your page to since you maybe wont stop by here again soon. Yes, I plan to polish them up soon and publish them here. I have sounds and dialogs, I think it would be quite useful for the community. I have just been busy these days :) Nesnad (talk) 05:47, 6 April 2009 (UTC)

title: User talk:Nesnad


text:
User talk:Kalor~enwikibooks

Come introduce yourself at the new users page. If you have any questions, you can ask there or contact me personally. – Mike.lifeguard  | talk 16:24, 9 December 2007 (UTC)

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 Kalor. To make sure that both of you can use all Wikimedia projects in future, we have reserved the name Kalor~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 23:21, 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) 05:07, 19 April 2015 (UTC)

title: User talk:Kalor~enwikibooks


text:
User talk:Diberri

Come introduce yourself at the new users page. If you have any questions, you can ask there or contact me personally. – Mike.lifeguard  | talk 16:24, 9 December 2007 (UTC)

title: User talk:Diberri


text:
Real Analysis/Total Variation

Let f be a continuous function on an interval [a,b]. A partition of f on the interval [a,b] is a sequence xk such that a=x0< x1 <...< xk-1 < xk < ...xn=b. The total variation t of a function on the interval [a,b] is the supremum

t= sup{$$ \sum_{k=1}^{n} |f(x_k)-f(x_{k-1})| $$ : xk is a partition of [a,b]}.

If this supremum exists, then the function is of bounded variation on [a,b]. If a real function is of bounded variation over its whole domain, then it is called a function of bounded variation.

title: Real Analysis/Total Variation


text:
Real Analysis/Uniform Convergence

Definition: A sequence of real-valued functions $$f_n{(x)}$$ is uniformly convergent if there is a function f(x) such that for every $$\epsilon>0$$ there is an $$N > 0$$ such that when $$n > N$$ for every x in the domain of the functions f, then $$|f_n(x)-f(x)| < \epsilon$$

Theorem (Uniform Convergence Theorem))
Let $$f_n$$ be a series of continuous functions that uniformly converges to a function $$f$$. Then $$f$$ is continuous.

Proof
There exists an N such that for all n>N, $$|f_n(x) - f(x)|<\frac{\epsilon}{3}$$ for any x. Now let n>N, and consider the continuous function $$f_n$$. Since it is continuous, there exists a $$\delta$$ such that if $$|x'-x|<\delta$$, then $$|f_n(x)-f_n(x')|<\frac{\epsilon}{3}$$. Then $$|f(x')-f(x)|\le |f(x')-f_n(x')|+|f_n(x')-f_n(x)|+ |f_n(x)-f(x)| < \frac{\epsilon}{3}+\frac{\epsilon}{3}+\frac{\epsilon}{3} = \epsilon$$ so the function f(x) is continuous.

title: Real Analysis/Uniform Convergence


text:
User talk:Tmv9~enwikibooks

Come introduce yourself at the new users page. If you have any questions, you can ask there or contact me personally. – Mike.lifeguard  | talk 16:53, 9 December 2007 (UTC)

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 Tmv9. To make sure that both of you can use all Wikimedia projects in future, we have reserved the name Tmv9~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 23:50, 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) 05:36, 19 April 2015 (UTC)

title: User talk:Tmv9~enwikibooks


text: User talk:129.215.59.63

title: User talk:129.215.59.63


text:
Real Analysis/Pointwise Convergence

Let $$f_n(x)\,$$ be a sequence of functions defined on a common domain $$D\subseteq\mathbb{R}\,$$. Then we say that $$f_n(x)\,$$ converges pointwise to a function $$f(x)\,$$ if for each $$x\in D\,$$ the numerical sequence $$f_n(x)\,$$ converges to $$f(x)\,$$. More precisely speaking: For any $$x\in D\,$$ and for any $$\varepsilon>0\,$$, there exists an N such that for any n>N, $$\left|f_n(x)-f(x)\right|<\varepsilon$$

An example:

The function

$$f_n(x) = \frac{x^n}{1+x^n}$$ converges to the function

$$f(x) = \left\{ \begin{array}{ll} 1 & \text{if } |x| > 1\\ \frac{1}{2} & \text{if } x = 1\\ 0 & \text{if } |x| < 1 \\ \end{array} \right.$$

This shows that a sequence of continuous functions can pointwise converge to a discontinuous function.

Análise real/Índice/Convergência pontual

title: Real Analysis/Pointwise Convergence


text: User talk:99.228.130.147

title: User talk:99.228.130.147


text: User talk:220.224.117.218

title: User talk:220.224.117.218


text:
Linear Algebra/Cofactors and Minors

Cofactors
Consider any column, the kth one. Consider all terms that contain the element aik, and factor out aik. The sum of all such terms is called the cofactor of aik, do be denoted Co(aik).

Every term contains exactly one element from the kth column. A determinant D can thus be written as a1kCo(a1k)+a2kCo(a2k)+a3kCo(a3k)+...ankCo(ank).

If, in fact the cofactors of a column or row were to be multiplied by some different column and row, its sum would be zero because it would be the same as a determinant with repeat columns and rows.

title: Linear Algebra/Cofactors and Minors


text:
Linear Algebra/Linear Dependance of Columns

Let C1, C2, C3, ..., Cn be n columns of m numbers $$C_n = \begin{bmatrix} a_{1n} \\ a_{2n} \\ a_{3n} \\ \vdots \\ a_{mn} \\ \end{bmatrix}$$.

A linear combination of columns n1C1+n2C2+n3C3+...+nnCn is the column

$$C_n = \begin{bmatrix} c_1 \\ c_2 \\ c_3 \\ \vdots \\ c_n \\ \end{bmatrix}$$.

Where ck=n1ak1+n1ak1+n2ak2+n3ak3+...+nnakn.

Theorem
If there is a determinant of order n which is A=aij, and there are n columns of n elements such that the ith entry of the jth column is equal to aij, then if one of the columns is a linear combination of the other columns, then the determinant is equal to 0.

Proof
Suppose that the kth column is a linear combination of the other column,

$$\begin{bmatrix} a_{11} & a_{12} & a_{13} & \ldots & c_1a_{11}+c_2a_{12}+ c_3a_{13} + \ldots + c_na_1n & \ldots & a_{1n} \\ a_{21} & a_{22} & a_{23} & \ldots & c_1a_{21}+c_2a_{22}+ c_3a_{23} + \ldots + c_na_2n & \ldots & a_{2n} \\ a_{31} & a_{23} & a_{33} & \ldots & c_1a_{31}+c_2a_{32}+ c_3a_{33} + \ldots + c_na_3n & \ldots & a_{3n} \\ \vdots & \vdots & \vdots & \vdots & \vdots & \vdots & \vdots \\ a_{n1} & a_{n3} & a_{n3} & \ldots & c_1a_{n1}+c_2a_{n2}+ c_3a_{n3} + \ldots + c_na_nn & \ldots & a_{nn} \\ \end{bmatrix}$$.

Then by the linearity of determinants, the determinant is equal to

$$c_1\begin{bmatrix} a_{11} & a_{12} & a_{13} & \ldots & a_{11} & \ldots & a_{1n} \\ a_{21} & a_{22} & a_{23} & \ldots & a_{21} & \ldots & a_{2n} \\ a_{31} & a_{23} & a_{33} & \ldots & a_{31} & \ldots & a_{3n} \\ \vdots & \vdots & \vdots & \vdots & \vdots & \vdots & \vdots \\ a_{n1} & a_{n3} & a_{n3} & \ldots & a_{n1} & \ldots & a_{nn} \\ \end{bmatrix} + c_2\begin{bmatrix} a_{11} & a_{12} & a_{13} & \ldots & a_{12} & \ldots & a_{1n} \\ a_{21} & a_{22} & a_{23} & \ldots & a_{22} & \ldots & a_{2n} \\ a_{31} & a_{23} & a_{33} & \ldots & a_{32} & \ldots & a_{3n} \\ \vdots & \vdots & \vdots & \vdots & \vdots & \vdots & \vdots \\ a_{n1} & a_{n3} & a_{n3} & \ldots & a_{n2} & \ldots & a_{nn} \\ \end{bmatrix} + c_3\begin{bmatrix} a_{11} & a_{12} & a_{13} & \ldots & a_{13} & \ldots & a_{1n} \\ a_{21} & a_{22} & a_{23} & \ldots & a_{23} & \ldots & a_{2n} \\ a_{31} & a_{23} & a_{33} & \ldots & a_{33} & \ldots & a_{3n} \\ \vdots & \vdots & \vdots & \vdots & \vdots & \vdots & \vdots \\ a_{n1} & a_{n3} & a_{n3} & \ldots & a_{n3} & \ldots & a_{nn} \\ \end{bmatrix} + \ldots + c_n\begin{bmatrix} a_{11} & a_{12} & a_{13} & \ldots & a_{1n} & \ldots & a_{1n} \\ a_{21} & a_{22} & a_{23} & \ldots & a_{2n} & \ldots & a_{2n} \\ a_{31} & a_{23} & a_{33} & \ldots & a_{3n} & \ldots & a_{3n} \\ \vdots & \vdots & \vdots & \vdots & \vdots & \vdots & \vdots \\ a_{n1} & a_{n3} & a_{n3} & \ldots & a_{nn} & \ldots & a_{nn} \\ \end{bmatrix} $$.

Since all of those matrices have repeat columns, their determinants are 0, and so their sum is 0.

Rank of a Matrix
The rank of a matrix is the maximum order of a minor that does not equal 0. The minor of a matrix with the order of the rank of the matrix is called a basis minor of the matrix, and the columns that the minor includes are called the basis columns.


text:
User:Aeluwas

Aeluwas at wikipedia - created an account to do some edits as I go along and read.

title: User:Aeluwas


text: User talk:131.123.177.152

title: User talk:131.123.177.152


text:
Conlang/Advanced/Sounds/Clicks

/Soft Redirects

title: Conlang/Advanced/Sounds/Clicks


text: User talk:86.153.3.201

title: User talk:86.153.3.201


text:
User talk:AVRS

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Good luck! --Panic (talk) 21:11, 9 December 2007 (UTC)

title: User talk:AVRS


text:
User talk:Aeluwas

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Good luck! --Panic (talk) 21:11, 9 December 2007 (UTC)

title: User talk:Aeluwas


text:
User talk:Psychopath mind

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title: User talk:Psychopath mind


text:
User talk:Doublethink~enwikibooks

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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.

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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.

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 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) 04:54, 19 April 2015 (UTC)

title: User talk:Doublethink~enwikibooks


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Good luck! --Panic (talk) 21:11, 9 December 2007 (UTC)

title: User talk:Virtualsam


text:
User talk:Soul windsurfer

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Good luck! --Panic (talk) 21:11, 9 December 2007 (UTC)

Multibrot_sets
Hi, I was categorizing pages, and came across this page that you created. I was wondering if you had inteded it to be part of the fractals book, but at the moment this page is out there as its own book. Is this intentional? Thenub314 (talk) 11:07, 19 June 2009 (UTC)

Hi, You are right. I had intended to make it as a part of book about fractals. If you can change it please do it ( I only know how to create new page in proper position and nominate for deletion old one). --Adam majewski (talk) 17:53, 19 June 2009 (UTC)

WikiProject Mathematics
Hi, I have been trying to restart the Mathematics project here at Wikibooks. The aim is simply to provide some community for the editors interested in improving the mathematics coverage here. Give a place to discuss issues with wikibooks (such as "hey this won't TeX correctly" or "how do I make a nice picture"); or actual mathematics content. I know you've been around for a long time working on Fractals and thought you might be interested in joining. Thenub314 (talk) 15:17, 30 June 2010 (UTC)

Thx for invitation. I'm intresting, but I work in very chaotic way. (:-)).--Adam majewski (talk) 04:07, 7 July 2010 (UTC)

 * LOL. How very appropriate for someone who is editing a book on fractals.  I wonder if your daily edits are similar to your monthly or yearly edits, maybe after some appropriate translation in time?

 * Very good. Well keep up the good work! If you ever feel like you could use the help of some other mathy types don't hesitate to leave a note on the project talk page. Thenub314 (talk) 15:28, 7 July 2010 (UTC)

Request for comment
Hi Requesting your comment and guidance.

Reading_room/General

Thanks and regards Mahitgar (discuss • contribs) 03:13, 11 March 2017 (UTC)

Greetings
Greetings! Nice to meet another mathematical mind here. I note "1010 years" instead of "10 years" in your quote from Robert Israel; is it intended? Boris Tsirelson (discuss • contribs) 21:50, 25 December 2017 (UTC)

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A few doubts
Hi, seeing that you're a mathematician, I have a few math doubts which I would appreciate if I clarify them with you. Since posting them here could be awkward (but it's fine if you want it that way), is it possible to send them by email to you? Thanks in advance.

Leaderboard (discuss • contribs) 17:23, 18 August 2018 (UTC)

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Escaping functions in TeX
If you just use "cos" it is rendered as a product of three variables c, o and s. If you instead use "\cos" then it is correctly rendered as the cosine function. This also goes for pi, exp etc (all standard functions and variables).

Greetz from FractalForums,

lycium

Hi lycium. Thx for info. Where I have made it ? I would like to improve it. TIA --Adam majewski (discuss • contribs) 08:00, 29 March 2020 (UTC)

Information about images
Good morning, i'm an italian ingeneer with great interest in matematics and i note that the images in the paragraph User:Adam_majewski#Z_=_Z-m_+_C    and following is not visible.

Inside the box appares the text "Archivo:MANDEL Z2+C.jpg" but no image.

Is it possible to see the image or put a link where the images cames from ?

Best regards and congratulations for your works. --Ming mm (discuss • contribs) 08:37, 24 February 2022 (UTC)

p.s. Sorry if my english is not perfect.

I'm more present in wikipedia.it & correct errors... ITA: --Ming_mm (msg)

title: User talk:Soul windsurfer


text:
User talk:Slinker

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Good luck! --Panic (talk) 21:11, 9 December 2007 (UTC)

title: User talk:Slinker


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User talk:Citer

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title: User talk:Citer


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User talk:Dhokarena56

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 * There is a box at the top of the edit window (if javascript is enabled on your browser) that will insert it too (looks like part of a signature). This will let others know who left it, and make it easy to reply back to you.
 * Remember to conduct any editing experiments in the sandbox.
 * You can tell the community something about yourself in your userpage.
 * You can get to this page by clicking the tab at the top of the page labeled with your registered username.
 * Wikibooks is a collection of open-source textbooks. (What is Wikibooks).
 * If you are a Wikipedian, see Wikibooks for Wikipedians for a primer on how things work here (it's a little different).
 * If you want to base your work here on materials from Wikipedia, please use WB:RFI (requests for importation) to bring the material over in compliance with the GFDL.
 * If you're an instructor and plan on using Wikibooks for a class project, see Guidelines for class projects
 * Please say hello at the Reading Room with any questions or ideas.
 * Eventually, you might want to read the Manual of Style and Policies and Guidelines.
 * Help us by participating in policy and guideline creation.
 * Please take a look at Naming policy before starting a new book.
 * Remember to maintain a Neutral point of view.
 * Explore, be bold in editing pages, and have fun!

You will find more resources in Community Portal. If you want to ask a question, visit the Study help desk, the Reading Room, IRC channel or ask me personally on my talk page. For site news, see the Bulletin board. It might be a good idea to add that page to your "watchlist" so that you can see when any new information is posted there. You can do that by clicking the tab labeled "watch" at the top of the page.

Good luck! --Panic (talk) 21:13, 9 December 2007 (UTC)

title: User talk:Dhokarena56


text:
User talk:12.210.16.106

Welcome!
Welcome to Wikibooks, a 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
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 * The right to be heard in votes and elections
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We hope that you choose to become a Wikibookian and create an account. Feel free to ask me any questions you may have on my talk page. By the way, make sure to sign your posts and comments with four tildes (~~~~), which will let others know who left it.

– Mike.lifeguard  | talk 21:45, 9 December 2007 (UTC)

title: User talk:12.210.16.106


text:
User:Dhokarena56

Dhokarena56 is an avid conlanger and conworlder. He has an account of the same name on the ZBB, at www.spinnoff.com/zbb. He edits the Conlang wikibook.

title: User:Dhokarena56


text:
User talk:Redrocketboy

Come introduce yourself at the new users page. If you have any questions, you can ask there or contact me personally. – Mike.lifeguard  | talk 22:29, 9 December 2007 (UTC)

WB:VFD
Hello again,

If you haven't already, please review the deletion policy. This is not to say that your view expressed so far are invalid, but rather that out policies are not the same as at Wikipedia, though they are similar (many are simple common sense). Hope you're enjoying Wikibooks! If you ever need anything, don't hesitate to ask. Happy editing! – Mike.lifeguard  | talk 23:23, 9 December 2007 (UTC)

title: User talk:Redrocketboy


text:
User:Redrocketboy

I am Redrocketboy on Wikipedia.

title: User:Redrocketboy


text:
User talk:59.92.131.78

Welcome!
Welcome to Wikibooks, a 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 Wikibookian and create an account. Feel free to ask me any questions you may have on my talk page. By the way, make sure to sign your posts and comments with four tildes (~~~~), which will let others know who left it.

– Mike.lifeguard  | talk 22:49, 9 December 2007 (UTC)

title: User talk:59.92.131.78


text:
Cookbook:Azuki Bean

Azuki or adzuki beans are small, usually red beans that are very popular in East Asian cuisines as both a savoury and sweet food.

Characteristics
Azuki beans are small, red, and ovoid. Overall, they are considered mild in flavor.

Uses
Azuki beans can be cooked with sugar and processed into sweet red bean paste. This mixture is commonly used as a sweet filling for desserts. The beans can also be added to soups, stews, and salads.

title: Cookbook:Azuki Bean


text:
Linear Algebra/Invariant Subspaces

Given a field K and a linear operator A, a subspace S of that field K is invariant under A if for any A(S) is a subset of S.

title: Linear Algebra/Invariant Subspaces


text: User talk:71.64.111.224

title: User talk:71.64.111.224


text: User talk:129.49.7.137

title: User talk:129.49.7.137


text:
Differential Geometry/Tangent Line, Unit Tangent Vector, and Normal Plane

The arc length can be used as a derivative for the vector function f, which is denoted t(x):

$$t(x)=\frac{df(x)}{ds}$$.

Since

$$\frac{df(x)}{ds} = \frac{f'(x)}{s'(x)}= \frac{f'(x)}{|f'(x)|}$$

which confirms the fact that it is a unit vector since the dot product with itself is 1. This also verifies a useful formula for the unit tangent vector

$$t(x)= \frac{f'(x)}{|f'(x)|}$$.

The tangent line goes through f(x) and is spanned by the vector t(x). Thus, it is equal to the line spanned by

$$f(x)+a\frac{f'(x)}{|f'(x)|}$$

where a is any real number.

The normal plane at the point f(x) is the plane that is normal to the tangent line, and thus the unit tangent vector. Therefore, its equations is given by

$$|z-f(x)|\cdot t(x)=0$$

where z is any element of the surface, since it must be orthogonal.


text: User talk:71.12.97.225

title: User talk:71.12.97.225


text:
User talk:Zoris

Welcome message
Hello, and welcome to Wikibooks!

Here are some tips to help you get started:
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You will find more resources in Community Portal. If you want to ask a question, visit the Study help desk, the Reading Room, IRC channel or ask me personally on my talk page. For site news, see the Bulletin board. It might be a good idea to add that page to your "watchlist" so that you can see when any new information is posted there. You can do that by clicking the tab labeled "watch" at the top of the page.

Good luck! --Panic (talk) 01:04, 10 December 2007 (UTC)

title: User talk:Zoris


text: User talk:68.162.138.26

title: User talk:68.162.138.26


text:
User:Neskaya/Sandbox

--Neskayatalk 02:11, 10 December 2007 (UTC)

title: User:Neskaya/Sandbox


text:
Topology/Completion

The completion of a metric space is a very important construction of a complete metric space from a possibly non-complete metric space. In effect, it is the smallest extension of a metric space to a complete version of it.

Definition: Take equivalence classes of Cauchy sequences in a metric space X such that two Cauchy sequences are equivalent when they converge to each other i. e. their difference approaches a limit 0. This set of equivalence classes is called the closure of the metric space.

Theorem
The completion of a metric space is unique and complete, and forms a metric space under the metric d(xn,yn) is equal to the limit of their difference, where xn and yn are two Cauchy sequences, and this metric is well-defined. Moreover, the subset of the equivalence classes which converge to an element in the metric space X is homeomorphic to X, and any other complete extension of X must contain its completion.

Example
One way of constructing the Real numbers is by saying that it is the completion of the rational numbers.

title: Topology/Completion


text:
User talk:Daveparise

While you're welcome to have a userpage, we do require that it does not have a resume, advertisement or promotion, per policy. Further questions can be directed to my talk page, or the Reading Room. Happy editing! – Mike.lifeguard  | talk 02:45, 10 December 2007 (UTC)

Come introduce yourself at the new users page. If you have any questions, you can ask there or contact me personally.

title: User talk:Daveparise


text:
User talk:24.21.86.4

– Mike.lifeguard  | talk 02:50, 10 December 2007 (UTC)

 * Please do join. It does bring benefits. Webaware talk 23:12, 24 March 2008 (UTC)

title: User talk:24.21.86.4


text: Template:Goodbook/First Aid

title: Template:Goodbook/First Aid


text:
User talk:CAPete

Welcome message
Hello, and welcome to Wikibooks!

Here are some tips to help you get started:
 * To learn the wiki-markup-language syntax, see Help:Editing.
 * Make sure to sign your posts and comments with four tildes, like this: ~~~~
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 * Remember to conduct any editing experiments in the sandbox.
 * You can tell the community something about yourself in your userpage.
 * You can get to this page by clicking the tab at the top of the page labeled with your registered username.
 * Wikibooks is a collection of open-source textbooks. (What is Wikibooks).
 * If you are a Wikipedian, see Wikibooks for Wikipedians for a primer on how things work here (it's a little different).
 * If you want to base your work here on materials from Wikipedia, please use WB:RFI (requests for importation) to bring the material over in compliance with the GFDL.
 * If you're an instructor and plan on using Wikibooks for a class project, see Guidelines for class projects
 * Please say hello at the Reading Room with any questions or ideas.
 * Eventually, you might want to read the Manual of Style and Policies and Guidelines.
 * Help us by participating in policy and guideline creation.
 * Please take a look at Naming policy before starting a new book.
 * Remember to maintain a Neutral point of view.
 * Explore, be bold in editing pages, and have fun!

You will find more resources in Community Portal. If you want to ask a question, visit the Study help desk, the Reading Room, IRC channel or ask me personally on my talk page. For site news, see the Bulletin board. It might be a good idea to add that page to your "watchlist" so that you can see when any new information is posted there. You can do that by clicking the tab labeled "watch" at the top of the page.

Good luck! --Panic (talk) 03:11, 10 December 2007 (UTC)

title: User talk:CAPete


text:
User talk:Shade~enwikibooks

Welcome message
Hello, and welcome to Wikibooks!

Here are some tips to help you get started:
 * To learn the wiki-markup-language syntax, see Help:Editing.
 * Make sure to sign your posts and comments with four tildes, like this: ~~~~
 * There is a box at the top of the edit window (if javascript is enabled on your browser) that will insert it too (looks like part of a signature). This will let others know who left it, and make it easy to reply back to you.
 * Remember to conduct any editing experiments in the sandbox.
 * You can tell the community something about yourself in your userpage.
 * You can get to this page by clicking the tab at the top of the page labeled with your registered username.
 * Wikibooks is a collection of open-source textbooks. (What is Wikibooks).
 * If you are a Wikipedian, see Wikibooks for Wikipedians for a primer on how things work here (it's a little different).
 * If you want to base your work here on materials from Wikipedia, please use WB:RFI (requests for importation) to bring the material over in compliance with the GFDL.
 * If you're an instructor and plan on using Wikibooks for a class project, see Guidelines for class projects
 * Please say hello at the Reading Room with any questions or ideas.
 * Eventually, you might want to read the Manual of Style and Policies and Guidelines.
 * Help us by participating in policy and guideline creation.
 * Please take a look at Naming policy before starting a new book.
 * Remember to maintain a Neutral point of view.
 * Explore, be bold in editing pages, and have fun!

You will find more resources in Community Portal. If you want to ask a question, visit the Study help desk, the Reading Room, IRC channel or ask me personally on my talk page. For site news, see the Bulletin board. It might be a good idea to add that page to your "watchlist" so that you can see when any new information is posted there. You can do that by clicking the tab labeled "watch" at the top of the page.

Good luck! --Panic (talk) 03:11, 10 December 2007 (UTC)

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 Shade. To make sure that both of you can use all Wikimedia projects in future, we have reserved the name Shade~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 23:40, 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) 05:28, 19 April 2015 (UTC)

title: User talk:Shade~enwikibooks


text:
User talk:Panic2k4/CrossTalk

Meat puppets
Should address the subject of meat puppets and address historical problem that existed not only on Wikibooks but in sister projects. I'll try to hunt down all that I said on this subject of parallel or "back channels", I prefer the last definition as it indicates the secondary place on any off site forums. --Panic (talk) 03:17, 10 December 2007 (UTC)

Meta:Cabal, WP:CABAL and DefendAgainstParanoia say more than I ever could say about this proposal. I disagree with the intent of this proposal and suggestions of adding wording about "meat puppets" and/or "back channels". This proposal sounds like paranoia to me. --dark lama  03:57, 10 December 2007 (UTC)

 * To address an issue one must start by identifying it. All of the realities you mention do exist and are part of the human status, arising from our tribal orientation and social structure. I've yet to read the text as it stands but for me it will only be of importance that it states several warnings so to protect the privacy of parallel discussions, the value/relevance they may have on our local discussions and identify the problems of expecting Wikibookians to be aware of any information shared offsite this includes for instance discussions on Meta, Wikipedia that may have an impact on our community.
 * Also covering the fragility of such discussions as representative of the community and how they can harm it.
 * This has the ability to be a framework that addresses this issues and provide a common ground of understanding this problems, safeguarding future discussions from the implications.  --Panic (talk) 04:16, 10 December 2007 (UTC)

Other sources/locations
Any discussion of significance or facts can only become valid and constructive if they are reflected on Wikibooks, no expectation can be imparted only because a number of Wikibookians seem to be are aware of them, they must be part of the public record, here, as to validate any expectation of mutual understanding of the problems/subjects. This doesn't mean that providing a simplification/summary of the discussion and a link to a secondary location is problematic, advancing and promoting the Wikibooks project outside of the site should be promoted and providing information and enabling others to participate should be embraced but it must not be expect or consider an obligation. The primary public location to discuss Wikibooks with other Wikibookians is Wikibooks, that is what constitutes the community common basis of understanding and sharing of information any other channel should be seen as secondary and prone to not be accepted as a valid forum for the community interests (at best it will can only claim to represent part of the community) this also raises other problems verifiability of authenticity, completeness (may lack of intermediary logs) and can lead to the problem of promoting group think (ie: us vs they situations). --Panic (talk) 04:16, 10 December 2007 (UTC)

title: User talk:Panic2k4/CrossTalk


text:
User talk:76.103.80.207

Welcome!
Welcome to Wikibooks, a 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 Wikibookian and create an account. Feel free to ask me any questions you may have on my talk page. By the way, make sure to sign your posts and comments with four tildes (~~~~), which will let others know who left it. --Panic (talk) 05:44, 10 December 2007 (UTC)

title: User talk:76.103.80.207


text:
User talk:Chje0702

Welcome message
Hello, and welcome to Wikibooks!

Here are some tips to help you get started:
 * To learn the wiki-markup-language syntax, see Help:Editing.
 * Make sure to sign your posts and comments with four tildes, like this: ~~~~
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 * You can tell the community something about yourself in your userpage.
 * You can get to this page by clicking the tab at the top of the page labeled with your registered username.
 * Wikibooks is a collection of open-source textbooks. (What is Wikibooks).
 * If you are a Wikipedian, see Wikibooks for Wikipedians for a primer on how things work here (it's a little different).
 * If you want to base your work here on materials from Wikipedia, please use WB:RFI (requests for importation) to bring the material over in compliance with the GFDL.
 * If you're an instructor and plan on using Wikibooks for a class project, see Guidelines for class projects
 * Please say hello at the Reading Room with any questions or ideas.
 * Eventually, you might want to read the Manual of Style and Policies and Guidelines.
 * Help us by participating in policy and guideline creation.
 * Please take a look at Naming policy before starting a new book.
 * Remember to maintain a Neutral point of view.
 * Explore, be bold in editing pages, and have fun!

You will find more resources in Community Portal. If you want to ask a question, visit the Study help desk, the Reading Room, IRC channel or ask me personally on my talk page. For site news, see the Bulletin board. It might be a good idea to add that page to your "watchlist" so that you can see when any new information is posted there. You can do that by clicking the tab labeled "watch" at the top of the page.

Good luck! --Panic (talk) 05:48, 10 December 2007 (UTC)

Rhetoric and Composition
Looks like you've been doing some great work on this book. I hope you're sticking around for a while! If you ever need anything, I'm not usually far. – Mike.lifeguard  | talk 21:11, 12 December 2007 (UTC)

title: User talk:Chje0702


text:
User talk:TwistedWeasel

Welcome message
Hello, and welcome to Wikibooks!

Here are some tips to help you get started:
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 * Remember to conduct any editing experiments in the sandbox.
 * You can tell the community something about yourself in your userpage.
 * You can get to this page by clicking the tab at the top of the page labeled with your registered username.
 * Wikibooks is a collection of open-source textbooks. (What is Wikibooks).
 * If you are a Wikipedian, see Wikibooks for Wikipedians for a primer on how things work here (it's a little different).
 * If you want to base your work here on materials from Wikipedia, please use WB:RFI (requests for importation) to bring the material over in compliance with the GFDL.
 * If you're an instructor and plan on using Wikibooks for a class project, see Guidelines for class projects
 * Please say hello at the Reading Room with any questions or ideas.
 * Eventually, you might want to read the Manual of Style and Policies and Guidelines.
 * Help us by participating in policy and guideline creation.
 * Please take a look at Naming policy before starting a new book.
 * Remember to maintain a Neutral point of view.
 * Explore, be bold in editing pages, and have fun!

You will find more resources in Community Portal. If you want to ask a question, visit the Study help desk, the Reading Room, IRC channel or ask me personally on my talk page. For site news, see the Bulletin board. It might be a good idea to add that page to your "watchlist" so that you can see when any new information is posted there. You can do that by clicking the tab labeled "watch" at the top of the page.

Good luck! --Panic (talk) 05:48, 10 December 2007 (UTC)

title: User talk:TwistedWeasel


text:
User talk:Pearl~enwikibooks

Come introduce yourself at the new users page. If you have any questions, you can ask there or contact me personally. --Girdi (talk) 06:03, 10 December 2007 (UTC)

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 Pearl. To make sure that both of you can use all Wikimedia projects in future, we have reserved the name Pearl~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 23:36, 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) 05:21, 19 April 2015 (UTC)

title: User talk:Pearl~enwikibooks


text:
Rhetoric and Composition/Teacher's Handbook/Teaching Oral Presentations

Teaching Oral Presentations
It has been said that the greatest fear people have is that of public speaking. The comic, Jerry Seinfeld, once remarked on this phenomenon, saying: "Most people would rather be in the coffin than giving the eulogy." With this fear of public speaking so pervasive, it is no wonder that your students will need some guidance and support when you have them present material in front of the class. No matter what the material the students will be presenting, it is important that you provide them with specific ideas about how they should prepare in order for them to engage their audience in an effective presentation about their topic. Share the following strategies and information with your students.

Presentation Evaluation
In order to help students feel prepared, it is a good idea to have a rubric to give them before they are going to present so they know exactly what is expected of them and how this grading will be different from that of a paper. The following are all possible areas that you might consider when making up your rubric:
 * Delivery - Does the student make eye contact? Do they project their voice? Is their speech clear? Do they exhibit a presence before the class?
 * Visual Aids- Are the visuals presented successfully? Have they been creatively made and used?
 * Creativity- Does the student show an ability to solve the problems of the assignment in an original way? Do they try unique approaches in the presentation in order to get their information across?
 *  Knowledge- Does the student convey their knowledge of the issue fluently? Are they able to answer questions without stumbling? Do they give enough specific details to show a depth of understanding about their topic? Do their examples illustrate the topic in a clear and effective way?
 * Insight- Does the student offer the audience insights about their research/information? For instance, do they offer answers to why this topic is important or how it can affect their audience?
 * Preparation/Process- Does it look like the student has prepared materials and their speech well or does it look like they put it together in a slapdash manner?

What do Effective Speakers Do?
Offer your students some pointers and practice in the class a few weeks before they will have to give a major presentation. You might offer the following suggestions about how to speak in front of a class such as:

Compelling speakers do the following:

 * Get the audience's attention by using strategies such as a personal anecdote, a brief story, or humor.
 * Maintain eye contact with the audience as much as they can.
 * Enunciate the words well and project their voice so that everyone can hear them.
 * Provide an overview of the presentation at the beginning.
 * Give strong examples to help explain the main ideas.
 * Use transitions to show where one idea ends and another one begins.
 * Provide a summary of the main points at the end.
 * Anticipate questions that the audience might have and answer them effectively.

To give students the chance to see what it is like to be the center of attention and how they will physically or psychologically respond in such a situation, you can try assigning short speeches weeks or days before they are to give a longer presentation. Depending upon what you are teaching at the time, give students one minute impromptu topics that they can speak informally about in front of the class. Or, you could also assign students a topic a day ahead and then give them one minute to say something cohesive about it in front of the class. The more they practice being in front of a crowd, the better they might feel when called upon to present more material later.


text:
Web 2.0 and Emerging Learning Technologies/Facilitative Tools of PLE

Facilitative Tools
Different definitions of PLE reflect different perspectives. One is from the perspective of emerging technology and tools which can facilitate the learner to construct a personal learning environment. For example, Sean FitzGerald held the view, "A Personal Learning Environment (PLE) is a collection of free, distributed, web-based tools, usually centred around a blog, linked together and aggregating content using RSS feeds and simple HTML scripts". George Siemens held a similar stating, a PLE is "a collection of tools, brought together under the conceptual notion of openness, interoperability, and learner control".

Though people view PLEs from the perspective of emerging technology and tools, there are differences. The main difference is between the construction of a PLE from the learner's or the designer/developers point of view. For example, the PLE project at Bolton University has released the PLE software PLEX 2006.

The following is a list of emerging technology and tools from the view of the learner.

1. Tools to facilitate user created content.

Tools to facilitate user to created content can be divided into two categories. One is like Blog,Flickr,Yutube,etc., and the other is like a wiki or google docs a "mashup" such as, google maps or google earth, Panoramio.

Supporting the user to produce content is a common characteristic but the way of how to organize the content is very different. The former is according to the user identity, so every one has a unique website that accumulates personal content. The latter is according to the content logic itself.

One can make an extensive list of tools by media type, which the tool mainly supports. For example, here list some tools in China.
 * Video,Tudou http://www.tudou.com/
 * Audio,8box http://www.8box.cn/
 * picture,yupoo http://www.yupoo.com/

2. Tools to facilitate communication.

Apart from Email, as main online communication tool, some new forms of communication tools have appeared in recent years,such as Skype and Twitter (called microblog by some people). Similar products of Twitter are found in China such as jiwai,zuosha,fanfou,etc.

3. Tools to facilitate social networking.

There are services called social network sites(SNSs) which help users to develop a social network. Boyd, d. m., & Ellison, N. B. (2007) argues the public display of connections is a crucial component of SNSs. According to the report of 《Sharing Privacy and Trust in Our Networked》(OCLC 2007) SNSs are primarily designed to facilitate interaction between users who share interests,attitudes, and activities, such as Facebook,Mixi and MySpace.

4. Tools to facilitate effectiveness.

Tools like RSS Reader and Tag offer a new way for a user to manage information and knowledge effectively.

For each kind tool listed above, there are many tools and/or services the user can utilize. Here some examples:

 * David Delgado and his PLE,http://eduspaces.net/davidds/weblog/category/ple
 * Michele Martin and her PLE,http://michelemartin.typepad.com/thebambooprojectblog/2007/04/my_personal_lea.html
 * Ray Sims and his PLE,http://simslearningconnections.com/ple/ray_ple.html

Reference

[1]Sean FitzGerald, http://seanfitz.wikispaces.com/creatingyourple

[2]George Siemens,http://www.elearnspace.org/blog/archives/002884.html

[3]PLEX(2006),http://www.reload.ac.uk/plex/

[4]boyd, d. m., & Ellison, N. B. (2007). Social network sites: Definition, history, and scholarship. Journal of Computer-Mediated Communication, 13(1), article 11. http://jcmc.indiana.edu/vol13/issue1/boyd.ellison.html

[5]OCLC(2007),Sharing Privacy and Trust in Our Networked World,Retrieved December 9, 2007 from: http://www.oclc.org/reports/pdfs/sharing.pdf


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A-level Chemistry/AQA/Module 1/Periodicity

Ionisation Energy
Ionisation Energy is the energy needed to dislodge an electron from the attraction which holds it in an atom/ion/molecule. The first ionisation energy is the energy needed to dislodge the least powerfully held electron. Second ionization energy is the energy needed to dislodge the second least powerfully held electron etc.

The size of the ionisation energy for an electron is related to the size of the attraction between that electron and the nucleus to which it is bound. 4 factors effect the size of this attraction.

''' The number of protons in the nucleus. '''

The higher the number of protons in the nucleus the higher its total positive charge and the higher the electrostatic attraction between it and the negatively charged electron.

''' The distance between the electron and the nucleus it is bound to. '''

Attraction decreases with distance.

 The number of intervening electrons between the electron and the nucleus - 'Screening'

Intervening electrons have a negative charge which repulses other electrons and reduces the attraction between electron and nucleus. This is referred to as screening. Note that intervening electrons do not 'block' attraction as the name suggests rather they reduce attraction by providing an opposing repulsion.

 Whether or not the electron under consideration is alone in its orbital or paired with another electron

Paired electrons repulse each other and reduce attraction between the electron and the nucleus.

Changes in first Ionisation Energy within groups and periods
The First Ionisation Energy decreases down Group II. This is because each element has a new shell, increasing the amount of shielding and the atomic radius.

The First Ionisation Energy increases across Period III. This is because:
 * The effective nuclear charge increases, due to increase in the number of protons.
 * The radius of atom decreases with increasing atomic number, hence more energy is required to remove outer electrons.
 * The number of shells remains the same; leading to the same amount of shielding.

There is a drop from Mg to Al because there is a new subshell which is higher in energy (more energy is required to remove the outer electrons). There is another drop from P to S because both electrons are now filled in the 3p subshell, leading to some repulsion.

Changes in Atomic Radius
Across Period 3 (Na to Ar) as the number of protons in the nucleus increases, the effective nuclear charge increases but shielding by inner electrons is kept unchanged as new electrons enter the same shell as they are attracted by the protons. This in turn will decrease the atomic radius.


text:
User:Kiwi8

Hello! I'm Kiwi8!

title: User:Kiwi8


text:
User talk:Kiwi8

Hello! I'm Kiwi8!

title: User talk:Kiwi8


text: Template:Backlog

title: Template:Backlog


text:
User talk:Neskaya

Welcome message
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Good luck! --Panic (talk) 16:34, 10 December 2007 (UTC)

title: User talk:Neskaya