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
Tensions Between the
Romans and Jews
Romans
The Roman rulers thought
of Jesus as a threat to the
government and religion.
The Romans were very
furious because the Jews
refused to pray and honor
the statue of the roman
emperor .
Jews
Some people within
Poem
By Derek Adrian
At some point in time things in your life are going to finally be set and where
they're intended to be.
There are point in your life that come into play to fit snug side by side until
the final puzzle is completed.
Whether that be bec
The properties of integers
Associative Properties
It states that you can
change where the
grouping symbols are
(moving the
parenthesis) in an
addition or
multiplication problem
and the result will be
the same.
(6+7)+8=9+(7+6)
Commutative Property
It all
Expressions, Equations &
Inequalities
Writing Expressions
I can translate between algebraic
expressions, equations, inequalities,
and words.
Simplifying Expressions
I can simplify and expand algebraic
expressions by combining like terms and using
the Dis