Math 130
Problem Set 8
Spring, 2012
Professor Hopkins
This problem set is due on Wednesday, April 25th Please make your answers as complete and clear
as possible. You are allowed to discuss these problems with others in the class, but your writing should
Math 130
Problem Set 4
Spring, 2012
Professor Hopkins
This problem set is due on Wednesday, Feb. 20th Please make your answers as complete and clear
as possible. You are allowed to discuss these problems with others in the class, but your writing should b
Math 130
Problem Set 7
Spring, 2012
Professor Hopkins
This problem set is due on Monday, April 9th Please make your answers as complete and clear as
possible. You are allowed to discuss these problems with others in the class, but your writing should be y
Math 130
Problem Set 3
Spring, 2012
Professor Hopkins
This problem set is due on Monday, Feb. 13th Please make your answers as complete and clear as
possible. You are allowed to discuss these problems with others in the class, but your writing should be y
Math 130Y, Homework
3
Problem 1
Suppose that 1 and 2 are distinct lines. A and B are two
points on 1 and A and B are two points on 2 . ConP
struct a perspectivity 1 (A, B) 2 (A , B ). Under what
circumstances is there more than one perspectivity with
this
MATH 130
SPRING, 2012
AFFINE AND PROJECTIVE GEOMETRY
M. J. HOPKINS
1. Affine geometry
Much of this material is taken from Hartshorne [1].
Denition 1.1. An Ane plane is a set A whose elements are called points and
a collection of subsets of A called lines
Math 130
Problem Set 1
Spring, 2012
Professor Hopkins
This problem set is due on Monday, Jan. 30th Please make your answers as complete and clear as
possible. You are allowed to discuss these problems with others in the class, but your writing should be y
Math 130Y Solution Set 2
1
Ane Geometry
1.1
Recall a,b,c is the locus of points (t1 , t2 ) such that at2 +bt2 +c = 0, which naturally contains
the point (x, y) by the relation it satises. To show a,b,c is parallel to a,b,c , it suces to
show they have no
Math 130: Solution Set 1
The following is a sample solution set for the types of responses I am looking for in this
class. I have also added in blue some general observations from the responses I received.
Please let me know if you nd any errors below.
1.
Studyguide, Exam 1
Study homework assignments, lecture notes. Be prepared to give examples, and answer true/false questions. There will also be some proofs on
the exam. I tried to indicate what you should know how to prove in this
studyguide.
Axioms: ind
Math 130
Problem Set 5
March 26, 2012
Azalea Vo
8. Let 0 < t < 1, X = (1 t)P + tQ.
d(P, X)
|P X|
=
d(X, Q)
|X Q|
|P (1 t)P tQ|
=
|(1 t)P + tQ Q|
|tP tQ|
=
|(1 t)P (1 t)Q|
t|P Q|
=
(1 t)|P Q|
Example, ratio r : s = 2:3 and P = (3, 5), Q = (8, 4). Then t =