Math 411: Geometry

Dr Langford
Contact me:
My schedule
My office location: 206E NH
My office phone number:

Grading policies, etc

Useful Links:
Euclid's Elements

List of Axioms and Theorems 2015

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Sept 2 NH 16
Euclid's Elements: the first axiomatic system for geometry.
Handout of part of the first book of Euclid's elements.
Assignment: write explanations in more modern wording for 2 of Euclid's Propositions of your choice (due Friday)
Ppt slides from class

Axiomatic systems
Axioms of Euclidean Geometry
(read chapter 1 on spherical and hyperbolic geometry)

Sept 7 Labor day

Exploring and understanding spherical and hyperbolic geometry
Figure out these facts
More about understanding the wording of propositions. Assn. Rewrite #23 and 24

More with spherical and hyperbolic geometry

Sept 14 Finish spherical and hyperbolic geometry. Axioms for the different systems. (Brief discussion of elliptical geometry)

Understanding postulates and axioms for Euclidan geometry. New handout
Draw what the parts of axioms 3 and 4 on the new handout mean.
Quiz (spherical and hyperbolic geometry)
Homework: Transformations
Sept 21 In the list of List of Axioms and Theorems 2015 prove the second bullet property in the congruence definition. Example in class (includes statement of what to prove for this assignment)

In class we discussed the assigned proof. Here are some notes:

In class we discussed theorem 2, Notes
Sept 28 Quiz (understanding wording of postulates and theorems)
Assignment (learn some constructions)
Watch this
Do this
Discussion of angle duplication and SAS. Assn: finish SAS Discussion of constructions. Assn: figure out 1. how to construct a square given a side, to construct a square in a circle, given the circle (and center) 3. how to construct a regular octagon

Oct 5: New version of the Axioms and Theorems 2015! Assignment (do problems 1-4 and 6) More comments and hints on #6 (proof of the new theorem 8)--video

Page 3 of the theorems list passed out.
Assignment: do #7 from the previous assignment.
Prove for 7b, that the triangles ABC and DEF are congruent.
Oct 12: Write ups of theorems 1-7
Quiz: Constructions and theorems 1-7
Make sure you know the constructions of a perpendicular bisector, perpendicular to a line through a point, duplicating and angle, and bisecting an angle.
Oct 19: 
Oct 26: Proofs of theorem 17. I suggest you first write up Pappus' proof, because it's short. I also suggest that if you did not get full credit on ASA that you try writing up the isometry proof too so you can get feedback to help you on next week's quiz.

Practice problems for the quiz.
(know how to prove theorem 19).

Nov 2: Solutions to practice problems Quiz  
Nov. 9  

 No class.
On the theorems list, please write up a proof that in theorem 24, if condition d holds,then condition b holds. Look up a proof that the sum of angles in a triangle is 180 °.  Work through the circle exploration sheet. For the circle problems, you can use all of the significant geometry theorems, not just the ones we've proven (so you can use that the sum of angles in a triangle is  180 ° and you can use the Pythagorean theorem, etc.).

Nov. 16: Homework: Prove theorems 26, 27  


Nov 23. Quiz Parallel theorems proofs to study
Construction write-ups to study.
Happy Thanksgiving
Nov 30: First things to do: More circle investigations.
Prove or disprove the quadrilateral conjectures on page 5 of the theorems list.



Dec 7: Quiz


Final exam is Thursday, December 17 @ 10:15 a.m. - 12:15 p.m.