Patterns and Connections 1:  Odds and Squares

We build the sequence of squares from the sequence of odd numbers and observe ourselves doing mathematics.

Patterns and Connections 2:  The Fibonacci Sequence

Fibonacci introduces us to an interesting sequence of numbers that has many applications in the world around us.

Patterns and Connections 3:  The Fibonacci Sequence and Pascals Triangle

Another unexpected connection.

Patterns and Connections 4:  The Golden Rectangle

Constructing the Golden Rectangle, finding the Golden Ratio, and then noticing other Golden Rectangles within the first Golden Rectangle

Patterns and Connections 5:  The Fibonacci Sequence and the Golden Ratio

Another surprising relationship between two things that initially seem unrelated.

Patterns and Connections 6:  The Sierpinski Triangle

The Sierpinski triangle is a simple, but interesting, fractal. We create it here to start our discussion of fractals. We will see it later with Pascal's triangle and the sequence of odd numbers.

Patterns and Connections 7: Pascal's Triangle and the Sierpinski Triangle

Another very surprising relationship between two triangles that seem completely unrelated. And we use the first sequence of numbers that we started with to uncover the relationship.

Patterns and Connections 8:  The Chaos Game

The Chaos Game gives us an intuitive idea of how chaotic functions behave.