Area in Neutral, Euclidean and
Hyperbolic Geometry
8.1 Introduction
Up to this time we have not yet dened area. It is a measurement, like distance and angle
measure, so it is a function that assigns a real number to a geometric object. We want to
see what
5.2 Geodesic Equations and Clairaut Relation
Now that we know what geodesics are, how can we do the calculations? Lets consider an
orthogonal patch x(u, u), (i.e., F : xu 'xv : 0). Let 0 be a geodesic in the patch x. Then,
we know that we can write C(15)
problem and mark your answers clearly. You must show all appropriate work in order to receive credit for an answer. Good luck!
INSTRUCTIONS: Write your name, section number, and ID number on this test sheet and each of the answer sheets. Number the
N0 CAL
Dr. Neal, Spring 2009
MATH 117 Right Triangle Word Problems
Here we shall consider various word problems that provide some physical applications
of the rightitriangle trig formulas.
RightiTriangle Formulas
x2+y2=z2 z="x2+y2 x: 22y2 y=\zzx2
Ad' 0 O
cosB=J:
_. (8 pts) Find parametric equations for the line through P = (-2, 0, 3) and Q = (3, 5, -2 .
3. (8 pts) Find the equation of the plane through (1, 1, -1), (2, 0, 2), and (0, 2, 1)
i. (8 pts) Sketch a rough graph for: (a) x2 +4z2 =16 (b) 2: = 8 x2 y2
1
/1_
NAME
10.
11.
INSTRUCTOR
. You must use a 35:52 pencil on the markisense sheet (answer sheet).
. If the cover of your question booklet is GREEN, write 01 in the TEST/QUIZ NUMBER
boxes and blacken in the appropriate spaces below. If the cover is ORANGE,
You will be graded on how well and fully you support your work! Use only methods from class.
F05)
l 2 3 4 5 6
1. [24] a) Let f(x) be defined by the graph given above. Mar-k each statement true or' false.
f(x)is continuous lirn f(x) exists lirn f(x) = l
For the following problems, the points A = (37 2), B : (47 7), C : (27 5), D = (O, 3).
1. The vector A33 2
b <\ ) 75>
(a) <1g5>
(b) <7,9>
(c) <1,5>
(d) <12,14> \
2 The length of BE: (/(91 13
(a) x/éngm MK.
(10} Mx/E
0) \f8
m
+ A i 1"
3.1fAE~< 1,2>, thenE~