MTH 330 MODERN GEOMETRIES Summer, 1999

HOMEWORK ¾ CHAPTER 1

 

Note: Homework should always be written out neatly, clearly, and in a well-organized manner.

Homework is always due at the beginning of the next class period after it is assigned.

 

Try these on your own: To be turned in:

 

Section 1.1 (p. 6- 7) A) #5, p. 6

#1- 15

 

Section 1.2 (p. 11- 12) B) #7, p. 12

#1- 13

 

Section 1.3 (p. 16- 17) C) #16, p. 16 [Write the proof in a step-by-step

#2- 18, 20 fashion, with a valid reason for each step.]

 

Section 1.4 (p. 20- 21) D) #12, p. 20

#1- 2, 4- 7, 8 (sides can be E) #24, p. 21

"portions" of lines), 9- 12, [Write proofs for D) and E) in a step-by-step

14- 25, 28 fashion, with a valid reason for each step.]

 

Section 1.5 (p. 24- 25) F) #17, p. 25 [Write proof in a step-by-step

#1- 11, 12 (must divide by 3, fashion, with a valid reason for each step.

why?), 13- 21, 22 (should If you use additional facts about Fano’s

read: "Write the plane dual Geometry as reasons in your proof besides

for each axiom…"), 23 the axioms and Theorems 1.7 and 1.8, you

must justify them first!]

G) #18, p. 25 [Instead of a picture, just make a

chart like Table 1.1 on page 20, using A, B,

C, D, E, etc. for points. This may take you a

while! Be sure your answer satisfies all 5

axioms for Young’s Geometry.]

H) #20, p. 25 [Write the proof in a step-by-step

fashion, with a valid reason for each step.]

 

(continued)