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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 doublesided handwritten page or 1.5
singlesided doublespaced typewritten pages. Please use at least three
diﬀerent references (books, articles, webpages); provide a list of the references you have used.
2. Prove (Euclidstyle) 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).
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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.
 Summer '06
 Karigiannis
 Geometry

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