Math 130, Problem Set 2 Solutions
1
Finite Ane Coordinate Geometry
We are given that the kitchen committee is the line y = 0 and that the tenure committee is the line
x = 0. Furthermore, Nancy is the point (0, 0), James is the point (1, 0), and Emily is t
Math 130 Problem Set 5 Solutions
1
Determining an Ane Transformation
Let P = (1, 1), P = (4, 2), Q = (1, 1), Q = (2, 0), R = (1, 1), and R = (0, 6). Because
cfw_Q P, R P = cfw_(2, 0), (0, 2) and cfw_Q P , R P = cfw_(6, 2), (4, 8) are bases for E 2 ,
the
Math 130 Problem Set 1 Solutions
1
Practice with Axioms
(a) First we show that if p + q = p + r = s, then q = r. Given vectors p and s, Axiom A2 guarantees
the existence of a vector q such that p + q = s. Suppose there exists another vector r such that
p
Math 130 Problem Set 3 Solutions
1
Ryan, Problem 1.8
We have
d(P, X) (a) |P X| (b)
t|P Q|
t
=
=
=
,
d(X, Q)
|X Q|
(1 t)|P Q|
1t
where (a) follows by denition of the distance in E 2 ([1, p. 11]) and (b) follows from the fact
that X lies between P and Q, so
Math 130: Problem Set 9 Solutions
1
Spherical Geography
(a)
p = cos1 P, Q = cos1 (cos 1.38 cos 0.91) = 1.4541 radians.
(b)
mQ = cos1
cos q cos p cos l
sin p sin l
cos 0.91 cos 1.4541 cos 1.38
sin 1.4541 sin 1.38
= cos1
= 0.9189 radians
The plane should he
Homework 11 Solutions
Notation: projective geometry coordinates specify the one-dimensional subspace by a representative, so (2, 2, 1) = (4, 4, 2).
Problem 1:
a. The six spacelike committees can be found by joining two of the four lightlike points
(six wa
Math 130 Problem Set 10 Solutions
Notation: projective geometry coordinates specify the one-dimensional subspace by a representative, so (2, 2, 1) = (4, 4, 2).
Problem 1
a. Carl = (u, 0, 1). Lynn = (u + 1, u, 1). The committee s that contains both Carl an
Math 130 Problem Set 8 Solutions
All geometries in this problem set, excluding problem 5a, are to be Minkowskian by default.
Problem 1
a. The lengths are: a = 392 152 = 36, b = 642 02 = 64, and c = 252 152 = 20. The
3
5
5
angles are: sinh A = vA 2 = q 5 3
MATH 130 PROBLEM SET 4 SOLUTIONS
Problem 1
a) A reection in the x-axis followed by a reection in a line of slope 1 is a rotation twice the
3
counter-clockwise angle formed between the x-axis and the line, about the point where the line
intersects the x-ax
Math 130: Problem Set 7
1
Galilean Theorem of Menelaus
(a) The diagram below illustrates the theorem:
y
C
F
E
A
T1 t1
T2
B
t2
D
T
t
(b) The theorem is the Galilean version of the theorem of Menelaus. Applying the Galilean law of
sines to CF E, BDE, and DF