The Real Projective Plane (Mathematics 479)

Prepared by:

Joseph Malkevitch
Department of Mathematics
York College (CUNY)
Jamaica, New York 11451

email:

malkevitch@york.cuny.edu

web page:

http://york.cuny.edu/~malk/

1. Which point of the real projective plane is associated with the Euclidean point given:

a. (1, 1)

b, (2, -3)

c. (-5, -4)

d. (0, 5)

e. (-8, 0)

2. Which point of the Euclidean plane is associated (if any) with the point of the real projective plane given:

a. (2, 4, 8)

b. (-3, 4, -1)

c. (2, -3, 5)

d. (0, 0, 0)

e. (0, -2, 1)

f. (-4, 0, -2)

4. Find the line of the real projective plane which joins the two given points:

a. (1, 2, 3) and ( -1, 0, 4)

b. (2, 0, 0) and ((0 -3, 0)

c. (-2, 1, 1) and (2, 0, 1)

d. (0, 2, 4) and ( -1, 0, 1)

5. Find the point where the given lines of the real projective plane intersect:

a., 2x + y - z = 0 and x + y + z = 0

b. 2x - y + z = 0 and x = 0

c. x + y = 0 and x + 2z = 0

d. x + 3y = 0 and y + 2z = 0

6. Which line of the real projective plane corresponds to the Euclidean lines given below:

a. x - y = 3

b. x + 2y + 5 = 0

c. 3x - 2y = 7

d. x = 2

e. y = 0

f. y = -3x + 8

g. y = -3