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Homework 1
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due Wednesday, April 10
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Reading:
chapter 6, chapter 7
Writing:
6A, 6B, 7A, 7B, 7C
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Homework 2
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due Wednesday, April 17
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Reading:
Chapter 7
Writing:
7D, 7F, 7H
Problem 1.
Let A, B be two points on one side of a line l. Construct a point P on the line l such that the quantity |AP| + |PB| is
minimal, and prove that such point is unique.
Problem 2.
Answer the following question with convincing justification: Which one of
the Postulates 1-9 of Neutral geometry is inconsistent with the Elliptic
parallel Postulate.
Bonus
(worth 2 points): reformulate problem 1 so that it can be given to smart 6th
graders, (assume they have some knowledge of geometry); that is, put a fun
story problem behind the “dry” geometric formulation.
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Special assignment, do by 11:59pm Wednesday, April
17
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Make a discussion board
post in the thread
on E.O.Wilson’s Op-Ed in the WSJ
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Homework 3
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due Wednesday, April 24
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Reading and writing: Carefully read
the proof of Th. 7.23 in the book and then put it in your notes in your own
words.
Reading:
Chapter 9
Writing: 9B,
9C, 9D, 9E, 9G
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Homework 4
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due Wednesday, May 1
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Reading:
Ch. 10
Writing:
10A, 10B, 10C, 10E, 10F, 10G
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Homework 5
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due Wednesday, May 8
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Reading:
Ch. 10
Start working on your
group projects
No written homework
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Homework 6
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due Wednesday, May 15
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Reading:
Ch. 11
Writing: 10M,
11A, 11D, 11G, Problem 5
Bonus:
11H
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Homework 7
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due Wednesday, May 22
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Special homework (by Wednesday, 5/15): try to come up with your own proof of 12.9
Reading:
chapter 12
Writing:
12A, 12D,
Problem 3:
Let ΔABC be a triangle, let B’ be a
point on the interior of the side AC and let D be a point on the interior
of the cevian BB’. Prove that S(ΔABD)/S(ΔCBD)=AB’/CB’.
12H (Hint: Use Problem 3 for the “if”
direction; the “only if” direction is proved by contradiction).
Problem 5: Prove
that the three angle bisectors of a triangle are concurrent.
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Homework 8
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Due Wednesday, May 29
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Reading:
Finish chapter 12.
Chapter 13 (most of the
chapter, including the trigonometry section, is an independent study –
we will not cover this material in class but you’ll be responsible
for learning it for the final and homework)
Reading and Writing: write down theorems 12.16-12.20 in your notes and
sketch the proofs (12.17 is a homework problem)
Writing:
Homework 8
An interactive page
where you experiment with different locations of the circumcenter:
http://www.mathopenref.com/trianglecircumcenter.html
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Homework 9
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Due Wednesday, June 5
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Reading:
Chapter 16, up to “Constructible Points etc.” (pp.295-308)
Writing:
Homework 9
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