Math 411: Geometry 

Dr Langford
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My office location: 206E NH
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General syllabus

Useful Links:
Euclid's Elements


Tuesday Thursday
Sept 7:
Exploration assn, due Tuesday Sept 12
HS review assn. due Sept 21 (do marked problems)
Check out this spherical circle
Sept 12 Properties of spheres
More sphere problems and properties (especially measurment properties) of transformations. Assignment
Discussion of transformations and of the proof on assignment 2. New topic: function properties and functions on the plane (and similar geometric objects)
Assignment: Do FT2, FT4 and FT5 from the function properties sheet.  Here is a version of FT4 and FT5 that I wrote up for a discrete math course a while back.
Sept 19 Solve FT6, with this revised version of the definitions. In /class notes
Work on these questions about rotations
Do some more rotations and reflections
Sept 26 Study for quiz. Make sure you understand the answers to this worksheet.  Here's some ways of proving the spherical triangle theorem from the homework (study that too) Quiz Homework:
Read pgs 34-45.
Do problems 2 and 3 on page 45.
Do  problems 2, 3, 4, 6 in 3.1 and problems 2, 3 on 3.2 from this sheet
Oct 3 Bring textbook and laptop to class
A link:
Finish 3.1 and 3.2 sheet with the addition of 3.2 # 8
check out these axioms and theorems and do these proofs
Oct 10 New and improved axioms and theorems. Notes on the proof of  theorem 9.
Do first page of these HS problems (Ch 2)
For the quiz Thursday: study how to show a rotation and reflection (compass, straight edge, etc), and the proofs we did from the function page (now theorems 6-8)
Continue working on the HS Ch 2 problems--do through 2.3 for Tuesday.
Class notes for SAS--finish the proof.
Oct 17 Prove ASA (theorem 11) and do the HS Ch 2.4 problems. Here is a video outlining the proof of ASA Prove theorem 12 for Monday (outline) (turn in Tuesday)
Work on the 8.1 HS problems.
Study the proofs of theorems 1-5 for next Thursday's quiz.  Here are the proofs. Here are some things to look for in the proofs.
Oct 24 Work on this practice sheet  (not collected) Quiz Work on 8.2  HS problems. Watch these videos on the proof of Thm 14, and choose one to write up and learn. Proof 1 (isometries); Proof 2 (Pappus); Proof 3 (Euclid). Due next Thursday.
Oct 31 Notes. Homework: review ASA proof, beginning of SSS proof, and write proofs for Thm 14 and 15. New and improved theorems list! Work on theorem 17 (perpendicular bisectors): hint through
Make sure you understand the proof of  SSS hint through
Review the application theorem by pasting these pieces into the right order to complete the proof.. 
More hints for theorem 17 (hopefully un-needed?)
Nov 7 Some versions of the application theorem proof.
Outlines of all 3 proofs
Quiz on Theorems: Application, SAS, ASA
Work on the Chapter 6 HS exercises.
Nov 14 Today's proofs (pictures).
To do:
Due Thursday: Write up the proofs of theorems 22 and 24.  I did thm 22 last Thursday and it is also in the textbook.  The proof of thm 24 should be short and should use Axiom 5: the parallel postulate. Hint: consider the sum of the interior angles on one side of the transversal. That sum can be =180 or <180 or >180.
Due next Tuesday: Proofs of theorems 17-19, and HS 6.1-6.3 problems.

Nov 21 Quiz on theorems 17-19,
Brainstorm a list of potential
Happy Thanksgiving
Nov 28
Dec 5 Quiz
Dec 12
Final Exam Thursday Dec 21 10:15-12:15