Remembering trigonometric formulas
Autumn 2012
Math 1181H
Jim Fowler
Neo: What are you trying to tell me? That I can memorize all
trigonometric formulas?
Morpheus: No, Neo. Im trying to tell you that when youre ready,
you wont have to.
An approximation to
Log-Log graph paper
Math 1181H
Autumn 2012
Jim Fowler
Congratulations! Here is some log-log graph paper for you to plot the Dehn function.
Dehn function of Plane built from Unit Squares
40
35
30
25
20
15
enclosed area
10
5
1
1
5
10
curve length
15
20
25
3
Isoperimetric inequality
Math 1181H
Autumn 2012
Jim Fowler
How does perimeter compare to enclosed area? Here are familiar Euclidean examples.
k
r
s
k
s
k
perimeter = 4k
area = k 2
s
k
perimeter = 2r
area = r2
perimeter = 3s
area = 3s2 /4
For a given lengt
Dog on the beach
Math 1181H
September 2012
Jim Fowler
Yesterday, we talked about the following problem.
A beach runs perfectly eastwest; a perfectly spherical dog
is 5 m north of the edge of the
water, and a ball oats motionlessly 10 m south and 10 m
east
Sums of angles in a triangle
Math 1181H
Autumn 2012
Jim Fowler
What do the three angles of a triangle sum to? In the Euclidean case, you know the answer.
c
a + b + c = 180
b
a
What about in the ve-squares-to-a-vertex case? Cut out the following shapes, th