Fibonacci numbers and golden ratio
Meetings: April 17 and
24, 2010
What determines the shape of a rectangle? Is there
a rectangle which is composed of a square and another rectangle of the
same shape as the original? Surprisingly, this question leads to a
discussion of Fibonacci numbers and their asymptotic behavior!
Friends and enemies
Meetings: March 6,
2010
Given a group of alliances and enemies (say between nations)
what does it mean for this system to be stable?
Once this is
decided, how can you tell if a system will be stable by looking at it?
A river crosses a road
Meetings: February 20,
2010
How many ways can a river cross a road? That is,
if n is any number, then how many ways can it loop back
on itself to cross the road exactly n times?
Geometry of the Earth
Meetings: November 7,
2009
What does it mean to be a straight line
on the Earth?
Geometry of the plane
Meetings: September Oct 31,
2009
Two points determine a line. But do two points
determine anything else interesting?
Logic and circuits Meetings: September 26,
2009
If a wire carrying current represents a 1, and a wire
carrying no current represents a 0, then we can perform binary
computation with a circuit. But how do we actually do it?
The size of infinite sets
Meetings: September 12, September 19, 2009
The discussion focused on the following argument:
Bill says that there are more numbers than even numbers, since every
even number is a number but not vice versa.
Jane says that there are the same number of numbers as even
numbers, since both collections are infinite.
Adding infinitely many numbers
Meetings: August 22, August 29, September 5, 2009
The discussion focused on the following questions:
Suppose I climb a ladder with infinitely many rungs, always climbing the next rung twice as fast as the previous. Will I climb the ladder? In how long?
What does it mean to add infinitely many numbers together?
Is there a number between .99999... and 1?
What is the relationship between lengths and numbers?
Meetings: August 15, 2009
The discussion will begin something like this:
Samuel: How can I measure the length of a line segment?
Avital: Use a unit measure!
Samuel: And what if the line segment isn't an even number of units?
How can we prove things about numbers?
Meetings: Saturdays March 14, March 21, 2009
The discussion will begin something like this:
Avital: How could we explain to an alien that 2 x 4 is equal to 4 x 2?
Ayal: They are both equal to 8!
Avital: What about 3 x 4 and 4 x 3?
Ayal: Those are both equal to 12!
Avital: What about 342 x 563 and 563 x 342?
Logic
Meetings: Saturdays February 7, February 14, February 21, 2009
The discussion will begin something like this:
Sam: What is an odd number?
Moe: It's one more than an even number.
Joe: Then what is an even number?
Moe: It's one more than an odd number.
Sam: Did you answer my question??
What is area?
Meetings: Saturdays January 10, January 17, January 24, 2009
This workshop is vaguely formed around our introduction to
area. Some questions we might talk
about:

What does it mean for two shapes to have the same area?

How would you go upon measing the area of a certain shapes?

Why are the formulas for the are of a rectangle, triangle, circle
correct? (or: more accurately, how could someone have come up with
them?)
Patterns in multiples of 9
Meetings: Wednesdays, December 17, January 7, January 14, 20089
The discussion began something like this:
Avital: Let's write down the first few multiples of 9. Each row will be 9
more than the previous one.
9
18
27
36
45
54
63
72
81
Samuel: That looks nice.
Avital: Do we notice some pattern?
< Back