Euclid and his modern rivals – wikipedia
Euclid and his Modern Rivals (English for Euclid and its modern rivals ) is a book by Charles Lutwidge Dodgson, better known as Lewis Carroll, which was first published by MacMillan Publishers in 1879. In the form of a drama, the work of Euclid defends elements Against modern geometry textbooks, especially in the treatment of parallels.
Act 1, Szene 1 [ Edit | Edit the source text ]
Minos corrects student exercises. In a monologue, he excites himself about a student who follows a textbook in Legrez, Euclid’s sentence 19 from sentence 20, but has shown sentence 20 from sentence 19 in the previous exercise and thus used a circle closure. Rhadamanthus occurs. He also has problems with tasks that he has to correct.
Act 1, Szene 2 [ Edit | Edit the source text ]
While Minos is sleeping, Euclid’s spirit occurs and asks Minos what is most important in a textbook on geometry. Minos is surprised, but the answer is that clear definitions and logical conclusions are more important than a complete presentation. Euclid asks Minos to comments about the points in which points a textbook could better represent the geometry than its elements And calls a series of textbooks that should compare minos with his own work. So that he does not have to read the books himself, Euclid’s spirit offers to get the spirit of a German professor who has read all of these books and defends it on behalf of her authors, called “Lord Nobody”.
The main points that should pay attention to the minos are:
- The order of the sentences should be maintained if possible.
- Construction tasks and sentences should not be separated.
- Definition and treatment of straight and angle
- Treatment of the parallel axiom
Before Minos examines the individual works, he and Euclid discuss them and some other points in general. Euclid also represents its elements before, first the sentences that can be proven without parallel postulate, then those in which this axiom is used. It adds a number of equivalent formulations of the axiom that were proposed by other authors. Euclid proves part of the sentences presented, the remaining evidence can be found in an appendix.
Act 2, Szene 1 [ Edit | Edit the source text ]
Nobody appears and starts to discuss the works of Euclid’s rivals.
Act 2, Szene 2 [ Edit | Edit the source text ]
Nobody starts with legendres Elements of geometry . It presents the definitions and evidence that differ greatly from Euclid’s approach. Minos comes to the conclusion that the work is elegant for advanced readers, but unsuitable for beginners.
Act 2, Szene 3 [ Edit | Edit the source text ]
The next work is Cooleys The Elements of Geometry, simplified and explained . Minos finds that a much stronger definition of parallel is used in the evidence than was defined and rejects the work.
Act 2, Szene 4 [ Edit | Edit the source text ]
Cuthbertsons follows Euclidian Geometry . This work tries to close some gaps that are available at Euclid by providing evidence of some explicit or implicit axioms. But in all of these evidence, minos find gaps or axioms that are not more obvious than the demonstrated statements. He comes to the conclusion that the work is not of Euclids very much Elements differentiates and has a clear style that Elements but is not superior.
Act 2, Szene 5 [ Edit | Edit the source text ]
The next work (only from the second edition) is Elementary Geometry: Congruent Figures by Olaus Henrici. Nobody has big problems finding the definitions that Minos wants to hear. Minos finds a number of contradictions in the various definitions to curve, straight and angle. Through Henrici’s attempt to justify the parallel postulate, minos and Lord nobody get into a discussion about non -tax geometries. Finally, Minos leads a number of places in which Henrici argues uncleans. He finally states that he considers Henrici’s book to be absolutely unsuitable.
Act 2, Szene 6 [ Edit | Edit the source text ]
This scene is divided into three sections in which Minos and Lord nobody discuss the following books that use similar approaches:
As a result, Minos in turn rejects all books as unsuitable textbooks.
Act 3, Szene 1 [ Edit | Edit the source text ]
In this scene, too, Minos and Lord discuss several works that all Euklid’s elements have as a model:
Minos is the first two works as good, albeit the Elements Do not consider, but refuse the three of the others due to different problems.
Act 3, Szene 2 [ Edit | Edit the source text ]
Then Minos and Lord will discuss the curriculum of the Association for the Improvement of Geometrical Teaching And Wilson’s textbook that follows this curriculum. Nobody claims to be a member of this association, because nobody was admitted the day before. In this role he accepts the name Nostradamus to appear Nero (to illuminate and warm up with a plan), Guy Fawkes (to improve the position of members of the parliament), Marie-Madeleine de Brinvilliers (with digestive alternatives) and f . Gustrell (the Shakespeare’s mulberry tree felled to improve literary taste). Finally, Newton’s dog Diamond appears with a half -burned manuscript.
In the discussion with Mr. Nobody (or Nostradamus), Minos first rejects the curriculum, then also Wilson’s Elementary Geometry, following the Syllabus prepared by the Geometrical Association ab.
Nobody and the other spirits disappear.
Akt 4 [ Edit | Edit the source text ]
Euclid appears again, with him Archimedes, Pythagoras, Aristotle, Plato and others. Minos reports that he has not found a textbook that is better than Euclids. However, he discusses some weaknesses of the elements , for example, that the use of a collapsing circle is cumbersome, whereas Euclid replies that – after the equivalence has been shown – an ordinary circle may also be used. Euclid also has good response against other objections. Euclid urges minos to maintain his work as a textbook and disappear with the other ghosts.
The first publication of Euclid and his Modern Rivals It took place in March 1879. Essays from Augustus de Morgan and Isaac are gratinized in two attachments. In 1885 a supplement was published that contained the book by Henrici and eight reviews of the first edition. In the same year, a second revised edition appeared, which also took over the new scene to Henrici’s book from the addition. In addition to these editions during Dodgson’s lifetime, there are a number of modern new editions, such as the 1973 with a foreword by H. S. M. Coxeter. [first]
In the UK, Euclids were elements At Dodgson’s time the standard textbook in school and university. It not only served as a textbook for geometry, but also for logical closing as well as – if it was used in the original – as a Greek exercise text. The first reform proposals arose in the 1860s, such as Thomas Hewitt Key or Thomas Archer Hirst. To the mathematicians who elements Defended as a textbook, in addition to Dodgson, the Morgan and Todhunter belonged. Dodgson is based on 25 years of experience that he had in teaching geometry.
In order to bundle the measures of an improvement in geometry lessons, the Association for the Improvement of Geometric Teaching was founded in 1871, the forerunner of today’s British Mathematical Association. The British Association also set up a similar committee. The first curriculum of 1877 competing with Euclid met with broad rejection at the universities. Despite the revisions, only two British universities (London and Edinburgh) allowed any textbooks for geometry, while all other universities continued to insist on the fact that the axioms and order of teaching rates largely Euclids Elements would have to follow. It was only with the beginning of the 20th century elements slowly abandoned as a binding textbook. [2]
Dodgson himself published a number of books on the Elements that follow his own suggestions, i.e. only present slightly modified editions of Euclid. With Curiosa Mathematica, Part I: A New Theory of Parallels In 1888 he also presented his own approach to treating parallels that differ significantly from Euclid. Instead of the usual axiom, he presupposes the statement that the area of an equilateral triangle (in the first editions of a hexagon) is larger than the area of each of the three circular segments.
Contemporary reviews were largely agreed on two criticisms: On the one hand, Dodgson used a difficult to understand symbol language in the first edition (he waived it for the second edition). On the other hand, criticism affects the one -sidedness of the work. Only arguments for the elements are named, nobody acts as a straw man. [3] It was also criticized that Dodgson has long revised editions, with the criticisms mentioned in the current editions. Some objections are just linguistic pointedness. [4] Nevertheless, most reviewers recommended the book to be worth reading because it is humorous.
Stuart Dodgson Collingwood reports that Euclid and his Modern Rivals was also used as a textbook. [5]
Today’s reviewers see the book on the one hand a valuable source of the history of mathematics didactics, on the other hand, it provides an interesting alternative view of the author, which is primarily known through books like Alice in Wonderland. [first]
In addition to the content -related discussion, the work was also received artistically: the first logo of Wikipedia that Bjørn Smestad had designed for the predecessor project Nupedia and was used until the end of 2001 shows an extract from the foreword in a fishy eye projection of Euclid and his Modern Rivals . [6]
- Euclid and his Modern Rivals. Macmillan, 1879.
- Supplement to Euclid and his Modern Rivals. Macmillan, 1885. ( Full text In the Google book search deer )
- Euclid and his Modern Rivals. Macmillan, 1885. ( online )
- Euclid and his Modern Rivals. Dover Phoenix Editions, 2004. ISBN 0-486-49566-3.
- ↑ a b Amirouche Moktefi: Review: Euclid and his modern rivals, by Charles L. Dodgson. In: The Mathematical Gazette. Vol. 89, No. 516 (November 2005), S. 556–558. (JSTOR: 3621985 )
- ↑ W. H. Brock: Geometry and the Universities: Euclid and his Modern Rivals 1860–1901. In: Journal of the History of Education Society. 1975, vol. 4, No. 2. S. 21-35. (( doi:10.1080/0046760750040203 )
- ↑ Reviews in English Mechanic and World of Science We will 2. May 1879, Saturday Review We will 10. May 1879, Journal of Science from July 1879, Nature from July 10, 1879, The Examiner from October 25, 1879, reprinted in Supplement to Euclid and his Modern Rivals. Macmillan, 1885.
- ↑ Review in Nature. Juli 1879, Volume 20, Number 506, S. 240–241 ( online, PDF )
- ↑ Stuart Dodgson Collingwood: The Life and Letters of Lewis Carroll. 1899. Chapter V. ( The Life and Letters of Lewis Carroll im Project Gutenberg )
- ↑ Logo history on meta.wikimedia.org, accessed on December 22, 2014.
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