Assignment 1

Assignment 1 - MATH 348: Assignment 1 (final version)...

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Unformatted text preview: MATH 348: Assignment 1 (final version) Leonid Chindelevitch July 11, 2008 1. Choose a geometer you are interested in and write a brief biography explaining their contribution to the geometry of their time. Thales Pythagoras Euclid Khayyam Archimedes Liu Hui Some possibilities to get you started: Desargues Descartes Fermat Hypatia Lobachevski Gauss Comment: I expect roughly 1 double-sided handwritten page or 1.5 single-sided double-spaced typewritten pages. Please use at least three different references (books, articles, webpages); provide a list of the references you have used. 2. Prove (Euclid-style) or disprove (by providing a counterexample) the following criteria for equality of triangles: 1) 2) 3) 4) a = a ,b = b ,α = α ; a = a ,b = b ,c = c ; α = α ,β = β ,γ = γ ; α = α ,β = β ,c = c . Comment: For statements which are true, make sure to clearly state what assumptions you are using in your proofs. A single counterexample is sufficient to prove that a statement is false. 3. Prove the following statements: a. if α = b. if α = √ 32 π 2 3 , then S = 4 [a − (b − c) ]; √ 32 2π 2 3 , then S = 12 [a − (b − c) ]. Comment: This exercise uses our conventional notation for triangles (see notes for Lecture 3). BONUS. Given a circle C with center O, divide its circumference into four equal parts using only a compass; justify your construction. Comment: Recall that the compass we are using only allows us to draw circles, not to measure distances (it magically closes on itself as soon as you are finished drawing a circle with it). 1 ...
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This note was uploaded on 12/10/2011 for the course MATH 348 taught by Professor Karigiannis during the Summer '06 term at McGill.

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