Abraham Kaestner and Euclid's Fifth (Parallel) Postulate
Date: 12/02/96 at 16:53:11 From: Anonymous Subject: MATH QUESTION I am a seventh grade student doing a research paper on a mathematician named Abraham Kaestner. I cannot find any information on him and was wondering if you could help me. Thanks, Kris
Date: 12/02/96 at 17:35:13 From: Doctor Sarah Subject: Re: MATH QUESTION Hi Kris - There's not a whole lot of information about Kaestner on the Web, but I did find some in the St. Andrews history archive: http://www-groups.dcs.st-and.ac.uk/~history/Indexes/K.html Abraham Gotthelf Kaestner Born: 27 Sept 1719 in Leipzig, Germany Died: 20 June 1800 in Gottingen, Germany Kaestner taught at Leipzig, then from 1746 at Gottingen where he was to succeed to Segner's chair. He was an excellent expositor of mathematics, although it is reported that Gauss didn't bother to go to his lectures as they were too elementary. However, he did influence Gauss, in particular with his interest in Euclid's parallel postulate. In fact, Kaestner's interest in the parallel postulate indirectly influenced Bolyai and Lobachevsky too (Kaestner taught Bolyai's father and Bartels, one of Kaestner's students, taught Lobachevsky). References: 1. _Dictionary of Scientific Biography_. 2. G Goe, Kaestner, Forerunner of Gauss, Pash, Hilbert, _Proceedings 10th International Congress of the History of Science II_ (Paris, 1964), 659-661. http://aleph0.clarku.edu/~djoyce/mathhist/math_history.books Here's the name of a 4-volume book by Kaestner: Kaestner, Abraham Gotthelf (1719-1800). _Geschichte der Mathematik seif der Wiederherstellung der Wissenschaften bis an das Ende des achtzehnten Jahrhunderts_. Four volumes. Rosenbusch, Gottingen, 1796-1800. This isn't really enough for a research paper, but you could follow the leads from the St. Andrews archive to Bolyai and Lobachevsky and also talk about Euclid's Parallel Postulate. There's a nice paper about it with illustrations at http://sunset.backbone.olemiss.edu/~rpagejr/euclid.html It begins "On Euclid's Fifth Postulate: al-Haytham's Innovative "Proof" and Omar Khayyam's Response": One of the most fascinating aspects of mathematics is that there exist statements that are both true and false. Perhaps the most famous of these is Euclid's controversial fifth postulate. Throughout history, almost from the postulate's conception, mathematicians have tried, in vain, to prove or disprove it. It seems that Euclid himself did not entirely trust the postulate, for he avoided using it as long as he could in his great work, _The Elements_, by proving his first 28 propositions without it. This paper will present a brief history of the postulate, a particularly inventive proof by al-Haytham, and the great Persian mathematician Omar Khayamm's comments upon its validity. From the beginning, Euclid's fifth postulate, also called the parallel postulate, stood out from among its brethren. The first four postulates are short, brief, and to the point, whereas the fifth is longer and rather strange sounding. The postulates are listed in _The Elements_ as such: 1. To draw a straight line from any point to another. 2. To produce a finite straight line continuosly in a straight line. 3. To describe a circle with any centre and distance. 4. That all right angles are equal to each other. 5. That, if a straight line falling on two straight lines make the interior angles on the same side less than two right angles, if produced infinitely, meet on that side on which are the angles less than the two right angles (Rosenfield 35). ________ The paper goes on from there. If you follow the arguments laid out in it, it's really pretty interesting. -Doctor Sarah, The Math Forum Check out our web site! http://mathforum.org/dr.math/
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