Math 411: Geometry

Dr Langford
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Euclid's Elements

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Sept 3 NH 16
Euclid's Elements: the first axiomatic system for geometry.
Assignment: Explain what propositions 1-5 mean. Handout of part of the first book of Euclid's elements.

More decoding of axioms and theorems; order of several important theorems in Euclid; decoding a proof
* Explain propositions 6 and 10 on paper.
* Identify where these 7 theorems appear in Book 1 of Euclid's elements
* Watch this lecture about the parallel postulateYou can read more about Euclid's axioms in the textbook section 2.2
You can read more about the parallel postulate here and here.

Sept 8 The parallel postulate and axiom systems. Equivalent axiom systems. Euclid vs Hilbert vs the axioms we will be using for our class

Proofs by contradiction
Quiz 1

Sept. 15 SAS. Study Euclid's proof of I.5 online and read Pappus proof in the textbook.

Euclid's proof of I.5
Watch these videos and finish writing up Euclid's proof of I.5. Part 1, Part 2 (you might need to wait a minute for the pages to load)
SSS. Here are my notes on SSS. Over the weekend you should study a proof of SSS (my notes, your notes, the proof in the book, whatever...). Then try to write out the proof from memory. It doesn't need to be word perfect, but it does need to have all of the important steps and ideas.
Sept 22 ASA, Parallel lines exist? I can't find the file we made in class, so I've rewritten ASA and parallel lines exist. Hopefully it's not different in a confusing way. Quiz 2 (write out proofs of one of the famous theorems)
Sept 29 There's a new page in the theorems list, and you'll be proving these easier theorems and sharing your proofs over the next week/2-weeks. Start by proving parts of theorem 13 (if a then b, if b then c, etc.) In class we proved AAS Quiz 3 write out a proof of another famous theorem (ASA or parallel lines exist)
Over the weekend prove more of theorem 13, and prove theorem 14 and 15.
Oct 6:
Oct 13:    
Oct 20: 
  In the book, pg 71, 2.3N #7 and 8
Prop 2.3.24
Prop I.20, I.21 Hints for 8 and I.21
Oct 27:    
Nov 3:    
Nov. 10  


Nov. 17:  


Nov 24. Happy Thanksgiving



Dec 8:  


Final exam is Wednesday, Dec. 17 @ 1:00-3:00 pm