Primary Questons for Geometers

Thales by Donnie Maynard and Peter Merrick

  1. When and where did Thales live?
  2. Thales was the first person to do what?
  3. What mathematical discoveries is Thales famous for?
  4. What mathematical field was his specialty?
  5. What discoveries (theorems/postulates) of his do we use in mathematics on a day-to-day basis?

Pythagoras by James Bathe

  1. When and where did Pythagoras live? (Greece, 500 B.C.)
  2. Did he do his work alone? (no, he had a whole school of followers who attributed their work to him.)
  3. What great mathematical theory bears his name?
  4. Did he invent it? How is it useful?
  5. What did the Pythagoreans discover regarding sqrt(2)?

Desargues by Lexi Velez and Rebecca Cleveland

  1. What was Desargues's theorem? (Perspective Theorem)
  2. What polygon did Desargues's Theorem relate to? (Triangle)
  3. What type of geometry did Desargues invented? (Projective or Modern?)
  4. Name two contemporary mathematicians to Desargues who recognized his work. (Mersenne, Descartes, Pascal).
  5. How many new terms did Desargues introduce during the times of his writing? and what was the only one preserved? (70. involution.)
  6. What was Desargues's occupation and nationality (French architect and military engineer.)

Playfair by Anika Kasper and Cate Reed

  1. What is John Playfair known for? (John Playfair is known for his parallel postulate that was based on Euclidean's fifth postulate)
  2. How does Playfair's postulate based on non-Euclidean geometries relate to Euclid's fifth postulate?
  3. Can Playfairs Parallel Postulate be proved from other Euclids postulates? Why or why not?
  4. How is Playfair's Parallel Postulate different than Euclid's 5th Postulate?
  5. Is Playfair's postulate still used today? If so. when and how? If not, why not?

Legendre by Brandie Radde and Rick Storm

  1. What were his contributions towards Geometry?
  2. When and where did Legendre live.
  3. What important discovery did he publish in 1806 (which Gauss wrote about in 1802)?
  4. What other great mathemeticians influenced him? How?
  5. How did the French Revolution affect his life?

Gauss by Colin Smith and John Van Der Linden

  1. What were his major contributions to the mathematical community?
  2. Which of his works or studies is he best known for?
  3. Did Gauss devise or discover any axioms, postulates, theorems, etc.? If so, which one(s) is/are he credited for?
  4. Did Gauss work with any other people? Who? Why?
  5. How do Gauss' discoveries impact math today, and do they tie in at all with what we're learning in Geometry class?

Dedekind by Philip Patterson and Jordan Harris

  1. When and where did Dedekind live?
  2. What was his important contribution to defining the real numbers? (Dedekind Cut)
  3. What is a Dedekind Cut?
  4. Joint paper? Zeta functions??

Riemann by Steven Long and Miles Strebeck

  1. What other famous mathematician lectured Riemann? (Gauss)
  2. What General Theory of Riemann's formed the basis of some of his most important work? (General Theory Of Complex Variables)
  3. Euler's Zeta Function was examined by Riemann, who changed it to form Riemann's Hypothesis helps to describe what? (The Distribution of Prime Numbers)
  4. Riemann's work later influenced what person famous for his Theory of Relativity? (Einstein)
  5. When and where did Riemann live?
  6. Riemannian Geometry now means something different than it did. Explain.

Pasch by Eric Wolff and Andy Breslin

  1. How did Pasch `axiomate' Geometry?
  2. What was Pasch's Theorem, and why was it necessary?
  3. How did Peano and Hilbert refine parts of his work?
  4. How did his work affect other branches of mathematics (i.e. calculus)?
  5. What mathematical discoveries did he realize had been based on nothing from an axiomatic point of view?

Lobachevsky by Erin Weber and Bryan Green

  1. When and where did Lobachevsky live?
  2. What was Lobachevsky best known for? His work in the field of Non-Euclidean Geometry, sometimes called Lobachevkian Geometry of H?/E? Geometry)
  3. What 2 natural disasters struck the University of Kazan while Lobachevsky was the "rector of Kazan"? (A cholera epidemic in 1830 and a big fire in 1842.)
  4. Which Euclidean postulate did Lobachevsky show false in his own geometry? Euclid's fifth postulate
  5. What was his parallel postulate? (There exist more than one lines parallel to a given line through a given point not on the line.)

Bolyia by Grant Goodman and Jonathan Poole

  1. What geometry was he (co) founder of? (Hyperbolic)
  2. Who else discovered this geometry/when relative to him/independently or no?
  3. What assumption did he make?
  4. What famous mathimatician was he friends with? (Gauss)
  5. What axiom was he interested in? (Parallel Axiom)

Poincare by Joe Furner and Tyler Jedlicka

  1. When ard where did Poincare live?
  2. What mathematical area is Poincare the founder of?
  3. What mathematical contest did Poincare win even though he did not provide a complete solution?
  4. What did this contest question deal with? (Answer: Dynamic Stability of the Solar System.)

Klein by Mallorie Kettlehut and Kristen Lee

  1. When and where did Klein live?
  2. What important discoveries/contributions did Klein make to non-euclidean Geometry?
  3. Sketch/describe a Klein Bottle.

Hilbert by Will Loux and Dan Stanage

  1. What happened in 1900 to make Hilbert famous? (23 Problems speech in Paris)
  2. What area of mathematics did Hilbert make special contributions. (Geometry, Grundlagen, 1899?)
  3. How many axioms did Hilbert have? Why so many more than Euclid?
  4. What contribution he made to mathematics?
  5. Where he came from and how he grew up?

Birkhoff Nikki Martyniuk and Sarah Munchow

  1. Personal information - born in Michigan, died in Cambridge Massachusetts, lived 1884 to 1944, etc
  2. Where and how did he get his education? - He attended havard and the University of Chicago. In 1907 he got a PhD from Chicago.
  3. What were his contributions to geometry?
  4. How many axioms did he have and why/how does this compare to Hilbert.
  5. How was he honored? - The Grorge David Birkhoff Prize est 1967, awarded by SIAM and AMS for "outstanding contribution to applied mathematics in the highest and broadest sense."