Roots and Radicals 1: The Pythagorean Theorem

The Pythagorean theorem is the oldest theorem in mathematics. Do you know that there is a connection between the Pythagoreans and music?

Roots and Radicals 2: The Spiral of Roots

We can use the Pythogorean theorem to get a visual representation of lots of irrational numbers.

Roots and Radicals 3: Pythagoras and Shakespeare

The Pythagorean theorem is the oldest theorem in mathematics. Do you know that there is a connection between the Pythagoreans and music?

Roots and Radicals 4:  The Golden Rectangle

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

Roots and Radicals 5: Constructing a Golden Rectangle from a Square of Side 4

No matter how large or small a golden rectangle is, the ratio of length to width is always the same.

Roots and Radicals 6: More Golden Rectangles within Our Orginal

How many Golden Rectangles are contained in any Golden Rectangel?  An infinite number.

Roots and Radicals 7:  The Fibonacci Sequence and the Golden Ratio

Another surprising relationship between two things that initially seem unrelated.

Roots and Radicals 8: The Golden Ratio in Bagdad in 1150.

Here is one problem that has almost everything we know about roots and radicals contained within it.