Get Our Extension

The Number Devil

From Wikipedia, in a visual modern way
The Number Devil
NumberDevil.jpg
The Number Devil: A Mathematical Adventure cover
AuthorHans Magnus Enzensberger
TranslatorMichael Henry Heim
IllustratorRotraut Susanne Berner
Cover artistRotraut Susanne Berner
CountryGermany
LanguageGerman
GenreChildren's book
PublisherHenry Holt and Company
Publication date
1997
Published in English
1998
Media typePaperback/Hardcover
Pages261
ISBN0-8050-6299-8

The Number Devil: A Mathematical Adventure (German: Der Zahlenteufel. Ein Kopfkissenbuch für alle, die Angst vor der Mathematik haben) is a book for children and young adults that explores mathematics. It was originally written in 1997 in German by Hans Magnus Enzensberger and illustrated by Rotraut Susanne Berner. The book follows a young boy named Robert, who is taught mathematics by a sly "number devil" called Teplotaxl over the course of twelve dreams.

The book was met with mostly positive reviews from critics, approving its description of math while praising its simplicity. Its colorful use of fictional mathematical terms and its creative descriptions of concepts have made it a suggested book for both children and adults troubled with math. The Number Devil was a bestseller in Europe, and has been translated into English by Michael Henry Heim.

Discover more about The Number Devil related topics

German language

German language

German is a West Germanic language of the Indo-European language family, mainly spoken in Central Europe. It is the most widely spoken and official or co-official language in Germany, Austria, Switzerland, Liechtenstein, and the Italian province of South Tyrol. It is also a co-official language of Luxembourg and Belgium, as well as a national language in Namibia. Outside Germany, it is also spoken by German communities in France (Bas-Rhin), Czech Republic, Poland, Slovakia and Hungary (Sopron).

Mathematics

Mathematics

Mathematics is an area of knowledge that includes topics as numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively.

Hans Magnus Enzensberger

Hans Magnus Enzensberger

Hans Magnus Enzensberger was a German author, poet, translator and editor. He also wrote under the pseudonyms Andreas Thalmayr, Elisabeth Ambras, Linda Quilt and Giorgio Pellizzi. Enzensberger was regarded as one of the literary founding figures of the Federal Republic of Germany and wrote more than 70 books. He was one of the leading authors in the Group 47, and influenced the 1968 West German student movement. He was awarded the Georg Büchner Prize and the Pour le Mérite, among many others.

Rotraut Susanne Berner

Rotraut Susanne Berner

Rotraut Susanne Berner is a German graphic designer and illustrator. She illustrated The Number Devil by Hans Magnus Enzensberger.

Mathematical notation

Mathematical notation

Mathematical notation consists of using symbols for representing operations, unspecified numbers, relations and any other mathematical objects, and assembling them into expressions and formulas. Mathematical notation is widely used in mathematics, science, and engineering for representing complex concepts and properties in a concise, unambiguous and accurate way.

Bestseller

Bestseller

A bestseller is a book or other media noted for its top selling status, with bestseller lists published by newspapers, magazines, and book store chains. Some lists are broken down into classifications and specialties. An author may also be referred to as a bestseller if their work often appears in a list. Well-known bestseller lists in the U.S. are published by Publishers Weekly, USA Today, The New York Times and The Washington Post. Most of these lists track book sales from national and independent bookstores, as well as sales from major internet retailers such as Amazon.com and Barnes & Noble.

Michael Henry Heim

Michael Henry Heim

Michael Henry Heim was a professor of Slavic languages at the University of California at Los Angeles (UCLA). He was an active and prolific translator, and was fluent in Czech, Russian, Serbo-Croatian, Hungarian, Romanian, French, Italian, German, and Dutch. He died on September 29, 2012, of complications from melanoma.

Plot

Robert is a young boy who suffers from mathematical anxiety due to his boredom in school. His mother is Mrs. Wilson. He also experiences recurring dreams—including falling down an endless slide or being eaten by a giant fish—but is interrupted from this sleep habit one night by a small devil creature who introduces himself as the Number Devil. Although there are many Number Devils (from Number Heaven), Robert only knows him as the Number Devil before learning of his actual name, Teplotaxl, later in the story.

Over the course of twelve dreams, the Number Devil teaches Robert mathematical principles. On the first night, the Number Devil appears to Robert in an oversized world and introduces the number one. The next night, the Number Devil emerges in a forest of trees shaped like "ones" and explains the necessity of the number zero, negative numbers, and introduces hopping, a fictional term to describe exponentiation. On the third night, the Number Devil brings Robert to a cave and reveals how prima-donna numbers (prime numbers) can only be divided by themselves and one without a remainder. Later, on the fourth night, the Number Devil teaches Robert about rutabagas, another fictional term to depict square roots, at a beach.

An illustration by Rotraut Susanne Berner depicts the Number Devil showing a mathematical proof to Robert.
An illustration by Rotraut Susanne Berner depicts the Number Devil showing a mathematical proof to Robert.

For a time after the fourth night, Robert cannot find the Number Devil in his dreams; later, however, on the fifth night, Robert finds himself at a desert where the Number Devil teaches him about triangular numbers through the use of coconuts. On the sixth night, the Number Devil teaches Robert about the natural occurrence of Fibonacci numbers, which the Number Devil shortens to Bonacci numbers, by counting brown and white rabbits as they reproduce multiple times. By this dream, Robert's mother has noticed a visible change in Robert's mathematical interest, and Robert begins going to sleep earlier to encounter the Number Devil. The seventh night brings Robert to a bare, white room, where the Number Devil presents Pascal's triangle and the patterns that the triangular array displays. On the eighth night, Robert is brought to his classroom at school. The Number Devil arranges Robert's classmates in multiple ways, teaches him about permutations, and what the Number Devil calls vroom numbers (factorials).

On the ninth night, Robert dreams he is in bed, suffering from the flu, when the Number Devil appears next to him. The Number Devil teaches Robert about natural numbers, which the Number Devil calls garden-variety numbers, the unusual characteristics of infinite, and infinite series. Robert finds himself at the North Pole, where the Number Devil introduces irrational numbers (unreasonable numbers), as well as aspects of Euclidean geometry, such as vertices (dots) and edges (lines). By the eleventh night, Robert has shown considerable increased interest in mathematics, but questions its validity, to which the Number Devil introduces the concept of mathematical proofs, ending with the Number Devil showing Robert a complicated proof of basic arithmetic. On the twelfth night, Robert and the Number Devil receive an invitation (which names the Number Devil as Teplotaxl) to Number Heaven, as Robert's time with the Number Devil has finished. At Number Heaven, Robert learns of imaginary numbers, which Teplotaxl describes as imaginative numbers, as well as the Klein bottle. Walking through Number Heaven, Teplotaxl introduces Robert to various famous mathematicians, such as Fibonacci, whom Teplotaxl calls Bonacci, and George Cantor, or Professor Singer. The book ends with Robert in class using his newfound mathematical knowledge.

Discover more about Plot related topics

Mathematical anxiety

Mathematical anxiety

Mathematical anxiety, also known as math phobia, is anxiety about one's ability to do mathematics.

Recurring dream

Recurring dream

A recurring dream is a dream which is experienced repeatedly over a long period. They can be pleasant or nightmarish and unique to the person and their experiences.

Devil

Devil

A devil is the personification of evil as it is conceived in various cultures and religious traditions. It is seen as the objectification of a hostile and destructive force. Jeffrey Burton Russell states that the different conceptions of the devil can be summed up as 1) a principle of evil independent from God, 2) an aspect of God, 3) a created being turning evil, and 4) a symbol of human evil.

Negative number

Negative number

In mathematics, a negative number represents an opposite. In the real number system, a negative number is a number that is less than zero. Negative numbers are often used to represent the magnitude of a loss or deficiency. A debt that is owed may be thought of as a negative asset. If a quantity, such as the charge on an electron, may have either of two opposite senses, then one may choose to distinguish between those senses—perhaps arbitrarily—as positive and negative. Negative numbers are used to describe values on a scale that goes below zero, such as the Celsius and Fahrenheit scales for temperature. The laws of arithmetic for negative numbers ensure that the common-sense idea of an opposite is reflected in arithmetic. For example, −(−3) = 3 because the opposite of an opposite is the original value.

Exponentiation

Exponentiation

Exponentiation is a mathematical operation, written as bn, involving two numbers, the base b and the exponent or power n, and pronounced as "b (raised) to the n". When n is a positive integer, exponentiation corresponds to repeated multiplication of the base: that is, bn is the product of multiplying n bases:

Prime number

Prime number

A prime number is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways of writing it as a product, 1 × 5 or 5 × 1, involve 5 itself. However, 4 is composite because it is a product (2 × 2) in which both numbers are smaller than 4. Primes are central in number theory because of the fundamental theorem of arithmetic: every natural number greater than 1 is either a prime itself or can be factorized as a product of primes that is unique up to their order.

Division (mathematics)

Division (mathematics)

Division is one of the four basic operations of arithmetic, the ways that numbers are combined to make new numbers. The other operations are addition, subtraction, and multiplication.

Remainder

Remainder

In mathematics, the remainder is the amount "left over" after performing some computation. In arithmetic, the remainder is the integer "left over" after dividing one integer by another to produce an integer quotient. In algebra of polynomials, the remainder is the polynomial "left over" after dividing one polynomial by another. The modulo operation is the operation that produces such a remainder when given a dividend and divisor.

Rutabaga

Rutabaga

Rutabaga or swede is a root vegetable, a form of Brassica napus. Other names include Swedish turnip, neep (Scots), and turnip. However, elsewhere the name "turnip" usually refers to the related white turnip. The species Brassica napus originated as a hybrid between the cabbage and the turnip. Rutabaga roots are eaten as human food in a variety of ways, and the leaves can be eaten as a leaf vegetable. The roots and tops are also used for livestock, either fed directly in the winter or foraged in the field during the other seasons. Scotland, Northern and Western England, Wales, the Isle of Man and Ireland had a tradition of carving the roots into lanterns at Halloween.

Pascal's triangle

Pascal's triangle

In mathematics, Pascal's triangle is a triangular array of the binomial coefficients that arises in probability theory, combinatorics, and algebra. In much of the Western world, it is named after the French mathematician Blaise Pascal, although other mathematicians studied it centuries before him in India, Persia, China, Germany, and Italy.

Permutation

Permutation

In mathematics, a permutation of a set is, loosely speaking, an arrangement of its members into a sequence or linear order, or if the set is already ordered, a rearrangement of its elements. The word "permutation" also refers to the act or process of changing the linear order of an ordered set.

Factorial

Factorial

In mathematics, the factorial of a non-negative integer , denoted by , is the product of all positive integers less than or equal to . The factorial of also equals the product of with the next smaller factorial:

History

Hans Magnus Enzensberger
Hans Magnus Enzensberger

Enzensberger fostered a passion for mathematics and numbers, although he was not a mathematician by trade. In 1998, he delivered a speech at the International Congress of Mathematicians criticizing the isolation of mathematics from popular culture.[1][2] The Number Devil was ultimately written on suggestion from Enzensberger's eleven-year-old daughter Theresia. Because he was displeased with the way mathematics was taught to students at school, the German author decided to pen a book that teaches mathematics in an innovative way.[3] German illustrator Rotraut Susanne Berner provided many full-page illustrations, as well as smaller drawings, for the book.[4] The Number Devil was first published in German in 1997.[5] The Number Devil has been noted for its unorthodox abandonment of standard notation; instead, Enzensberger created a variety of fictional terms to help describe mathematical concepts. For instance, exponentiation takes the term hopping, and the fictional term unreasonable numbers was coined for irrational numbers.[6] The UCLA Professor of Slavic Languages Michael Henry Heim translated the book from German to English. The translation was particularly difficult in that it required special attention to the numerical aspect of the book. He was also challenged by the necessity to use simple English words appropriate for the target audience of The Number Devil—that is, children aged eleven to fourteen.[7] The mathematics book was then published in English in 1998.[5]

The book was a hit across Europe, becoming a best seller in at least Spain, Germany,[8] the Netherlands,[9] and Italy.[10] The Number Devil also had considerable success in Japan.[11] After the success of The Number Devil, Enzensberger wrote a follow-up, called Where Were You, Robert?, a children's book focusing on history rather than math. The German author has since stated he will not write any more young adult's books, but instead direct his effort towards poetry.[3] Viva Media later published an educational computer game, similarly titled The Number Devil: A Mathematical Adventure, based on the book.[12] An audiobook was also released for The Number Devil.[13]

Discover more about History related topics

International Congress of Mathematicians

International Congress of Mathematicians

The International Congress of Mathematicians (ICM) is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union (IMU).

Rotraut Susanne Berner

Rotraut Susanne Berner

Rotraut Susanne Berner is a German graphic designer and illustrator. She illustrated The Number Devil by Hans Magnus Enzensberger.

Mathematical notation

Mathematical notation

Mathematical notation consists of using symbols for representing operations, unspecified numbers, relations and any other mathematical objects, and assembling them into expressions and formulas. Mathematical notation is widely used in mathematics, science, and engineering for representing complex concepts and properties in a concise, unambiguous and accurate way.

Exponentiation

Exponentiation

Exponentiation is a mathematical operation, written as bn, involving two numbers, the base b and the exponent or power n, and pronounced as "b (raised) to the n". When n is a positive integer, exponentiation corresponds to repeated multiplication of the base: that is, bn is the product of multiplying n bases:

Irrational number

Irrational number

In mathematics, the irrational numbers are all the real numbers that are not rational numbers. That is, irrational numbers cannot be expressed as the ratio of two integers. When the ratio of lengths of two line segments is an irrational number, the line segments are also described as being incommensurable, meaning that they share no "measure" in common, that is, there is no length, no matter how short, that could be used to express the lengths of both of the two given segments as integer multiples of itself.

University of California, Los Angeles

University of California, Los Angeles

The University of California, Los Angeles (UCLA) is a public land-grant research university in Los Angeles, California. UCLA's academic roots were established in 1881 as a teachers college then known as the southern branch of the California State Normal School. This school was absorbed with the official founding of UCLA as the Southern Branch of the University of California in 1919, making it the second-oldest of the 10-campus University of California system.

Michael Henry Heim

Michael Henry Heim

Michael Henry Heim was a professor of Slavic languages at the University of California at Los Angeles (UCLA). He was an active and prolific translator, and was fluent in Czech, Russian, Serbo-Croatian, Hungarian, Romanian, French, Italian, German, and Dutch. He died on September 29, 2012, of complications from melanoma.

Japan

Japan

Japan is an island country in East Asia. It is situated in the northwest Pacific Ocean, and is bordered on the west by the Sea of Japan, while extending from the Sea of Okhotsk in the north toward the East China Sea, Philippine Sea, and Taiwan in the south. Japan is a part of the Ring of Fire, and spans an archipelago of 6852 islands covering 377,975 square kilometers (145,937 sq mi); the five main islands are Hokkaido, Honshu, Shikoku, Kyushu, and Okinawa. Tokyo is the nation's capital and largest city, followed by Yokohama, Osaka, Nagoya, Sapporo, Fukuoka, Kobe, and Kyoto.

Poetry

Poetry

Poetry, also called verse, is a form of literature that uses aesthetic and often rhythmic qualities of language − such as phonaesthetics, sound symbolism, and metre − to evoke meanings in addition to, or in place of, a prosaic ostensible meaning. A poem is a literary composition, written by a poet, using this principle.

Educational game

Educational game

Educational games are games explicitly designed with educational purposes, or which have incidental or secondary educational value. All types of games may be used in an educational environment, however educational games are games that are designed to help people learn about certain subjects, expand concepts, reinforce development, understand a historical event or culture, or assist them in learning a skill as they play. Game types include board, card, and video games.

Audiobook

Audiobook

An audiobook is a recording of a book or other work being read out loud. A reading of the complete text is described as "unabridged", while readings of shorter versions are abridgements.

Reception

The Number Devil received mostly positive reviews from critics. Mathematics professor John Allen Paulos of Temple University wrote an article for The New York Review of Books, praising The Number Devil as a "charming numerical fairy tale for children."[14] Likewise, mathematics writer Martin Gardner of the Los Angeles Times applauded Enzensberger's introduction of mathematics "in such an entertaining way."[15] In a book review for The Baltimore Sun, Michael Pakenham approved of the book's simplicity, writing, "it's not incomprehensible. Not for a minute."[8]

Not all reviews were positive, however. The American Mathematical Society's Deborah Loewenberg Ball and Hyman Bass reviewed the book from a mathematical perspective. Although they praised its "attractive and imaginative fantasy," the two mathematicians found several issues. Ball and Bass were concerned with The Number Devil's negative characterization of math teachers, its apparent presentation of mathematics as magical rather than factual, and a number of other contentions.[2] Ted Dewan, writing for the Times Educational Supplement, believed it to be "far more compelling than a standard text," but found it less adventurous than he hoped for. He also criticized its use in mathematics education, stating "I suspect this is the sort of book that well-meaning adults will mistakenly thrust upon children because it will be good for them."[16]

Discover more about Reception related topics

John Allen Paulos

John Allen Paulos

John Allen Paulos is an American professor of mathematics at Temple University in Philadelphia, Pennsylvania. He has gained fame as a writer and speaker on mathematics and the importance of mathematical literacy. Paulos writes about many subjects, especially of the dangers of mathematical innumeracy; that is, the layperson's misconceptions about numbers, probability, and logic.

Temple University

Temple University

Temple University is a public state-related research university in Philadelphia, Pennsylvania. It was founded in 1884 by the Baptist minister Russell Conwell and his congregation Grace Baptist Church of Philadelphia then called Baptist Temple. On May 12, 1888, it was renamed the Temple College of Philadelphia. By 1907, the institution revised its institutional status and was incorporated as a research university.

Martin Gardner

Martin Gardner

Martin Gardner was an American popular mathematics and popular science writer with interests also encompassing scientific skepticism, micromagic, philosophy, religion, and literature – especially the writings of Lewis Carroll, L. Frank Baum, and G. K. Chesterton. He was also a leading authority on Lewis Carroll. The Annotated Alice, which incorporated the text of Carroll's two Alice books, was his most successful work and sold over a million copies. He had a lifelong interest in magic and illusion and in 1999, MAGIC magazine named him as one of the "100 Most Influential Magicians of the Twentieth Century". He was considered the doyen of American puzzlers. He was a prolific and versatile author, publishing more than 100 books.

Los Angeles Times

Los Angeles Times

The Los Angeles Times is a daily newspaper that started publishing in Los Angeles in 1881 and is now based in the adjacent suburb of El Segundo. It has the fifth-largest circulation in the U.S. and is the largest American newspaper not headquartered on the East Coast. The paper focuses its coverage of issues particularly salient to the West Coast, such as immigration trends and natural disasters. It has won more than 40 Pulitzer Prizes for its coverage of these and other issues. As of June 18, 2018, ownership of the paper is controlled by Patrick Soon-Shiong. It is considered a newspaper of record in the U.S.

The Baltimore Sun

The Baltimore Sun

The Baltimore Sun is the largest general-circulation daily newspaper based in the U.S. state of Maryland and provides coverage of local and regional news, events, issues, people, and industries.

American Mathematical Society

American Mathematical Society

The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, advocacy and other programs.

Deborah Loewenberg Ball

Deborah Loewenberg Ball

Deborah Loewenberg Ball is an educational researcher noted for her work in mathematics instruction and the mathematical preparation of teachers. From 2017 to 2018 she serves as president of the American Educational Research Association. She served as dean of the School of Education at the University of Michigan from 2005 to 2016, and she currently works as William H. Payne Collegiate Professor of education. Ball directs TeachingWorks, a major project at the University of Michigan to redesign the way that teachers are prepared for practice, and to build materials and tools that will serve the field of teacher education broadly. In a sometimes divisive field, Ball has a reputation of being respected by both mathematicians and educators. She is also an extremely well respected mentor to junior faculty members and to graduate students.

Hyman Bass

Hyman Bass

Hyman Bass is an American mathematician, known for work in algebra and in mathematics education. From 1959 to 1998 he was Professor in the Mathematics Department at Columbia University. He is currently the Samuel Eilenberg Distinguished University Professor of Mathematics and Professor of Mathematics Education at the University of Michigan.

Fantasy literature

Fantasy literature

Fantasy literature is literature set in an imaginary universe, often but not always without any locations, events, or people from the real world. Magic, the supernatural and magical creatures are common in many of these imaginary worlds. Fantasy literature may be directed at both children and adults.

Mathematics education

Mathematics education

In contemporary education, mathematics education – known on the European continent as the didactics or pedagogy of mathematics – is the practice of teaching, learning and carrying out scholarly research into subjects related to the transfer of mathematical knowledge.

Mathematical proof

Mathematical proof

A mathematical proof is an inferential argument for a mathematical statement, showing that the stated assumptions logically guarantee the conclusion. The argument may use other previously established statements, such as theorems; but every proof can, in principle, be constructed using only certain basic or original assumptions known as axioms, along with the accepted rules of inference. Proofs are examples of exhaustive deductive reasoning which establish logical certainty, to be distinguished from empirical arguments or non-exhaustive inductive reasoning which establish "reasonable expectation". Presenting many cases in which the statement holds is not enough for a proof, which must demonstrate that the statement is true in all possible cases. A proposition that has not been proved but is believed to be true is known as a conjecture, or a hypothesis if frequently used as an assumption for further mathematical work.

Ted Dewan

Ted Dewan

Ted Dewan is an American-born British writer and illustrator of children's books who resides in England. He is best known as the creator of the award-winning book series, Bing, now adapted into an animated television series.

Source: "The Number Devil", Wikipedia, Wikimedia Foundation, (2022, November 25th), https://en.wikipedia.org/wiki/The_Number_Devil.

Enjoying Wikiz?

Enjoying Wikiz?

Get our FREE extension now!

References
  1. ^ Enzensberger, Hans Magnus. "Zugbrücke außer Betrieb, oder die Mathematik im Jenseits der Kultur—eine Außenansicht" (in German). Deutsche Mathematiker Vereinigung. Retrieved 17 December 2011.
  2. ^ a b Deborah Loewenberg Ball and Hyman Bass (January 2000). "The Number Devil book review" (PDF). Notices of the AMS. 47 (1): 51–56. Retrieved 3 September 2011.
  3. ^ a b Karacs, Imre (29 July 2000). "From long division to multiplication". The Independent. Archived from the original on 2022-06-18. Retrieved 26 October 2011.
  4. ^ Auclaire-Meier, Sebastien. "Der Zahlenteufel. Ein Hörspiel in neun Nächten für alle, die Angst vor der Mathematik haben" (in German). Archived from the original on 26 April 2012. Retrieved 16 December 2011.
  5. ^ a b Enzensberger, Hans Magnus (1997). The Number Devil. New York: Henry Holt and Company. ISBN 0-8050-6299-8.
  6. ^ Thuy-Anh Mai, Angie. "Personal Reflections on The Number Devil". Math Horizons. Mathematical Association of America. Retrieved 16 December 2011.
  7. ^ Matsumoto, Valerie J. "Faculty Show Depth, Breadth of the Written Word". UCLA Today. University of California Press. Archived from the original on 4 April 2012. Retrieved 23 October 2011.
  8. ^ a b Pakenham, Michael (11 October 1998). "Does your head need exercise? Here's just the book for you". The Baltimore Sun. Retrieved 3 September 2011.
  9. ^ "from Amsterdam". New Scientist (2133). 9 May 1998. Retrieved 21 December 2011.
  10. ^ "Bestsellers: from Rome". New Scientist (2126). 21 March 1998. Retrieved 21 December 2011.
  11. ^ Cordsen, Knut (22 July 2010). "German children's books prove to be bestsellers abroad". Deutsche Welle. Retrieved 16 December 2011.
  12. ^ "The Number Devil - PC". IGN. Archived from the original on November 25, 2004. Retrieved 5 September 2011.
  13. ^ Eisenbichler, Ernst. "Der "Fliegende Robert" der Literaten". Bayerischer Rundfunk (in German). Retrieved 16 December 2011.
  14. ^ Paulos, John Allen (18 November 1999). "The Way to Numerical Heaven". The New York Review of Books. 46 (18). Retrieved 3 September 2011.
  15. ^ Gardner, Michael (8 November 1998). "It All Adds Up". Los Angeles Times. Retrieved 3 September 2011.
  16. ^ Dewan, Ted. "Book of the week". Times Educational Supplement. TSL Education Ltd. Archived from the original on 21 April 2013. Retrieved 7 December 2011.

The content of this page is based on the Wikipedia article written by contributors..
The text is available under the Creative Commons Attribution-ShareAlike Licence & the media files are available under their respective licenses; additional terms may apply.
By using this site, you agree to the Terms of Use & Privacy Policy.
Wikipedia® is a registered trademark of the Wikimedia Foundation, Inc., a non-profit organization & is not affiliated to WikiZ.com.