Traces the evolution of mathematics and explores the relationship of numbers to musical harmony, early astronomy, and perspective in painting. It follows the spread of Greek ideas through the courts and bazaars of the Islamic Empire, to Moorish Spain and Renaissance Europe.
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Pythagoras's theorem was proven many times before humans were doing algebra.
Pythagoroas Without Words
("The Ascent of Man", p 159)
Using this photo, and starting with the white triangle at top left, can you convince yourself that a square the size of the hypotenuse (the slanted side) of the triangle has the same area as the total area of squares the size of the other two sides? You only need to know that the area of a square is the length of one side multiplied by itself.
Hint: The first figure in the third row is a square whose sides are the length of the hypotenuse. The rod in the last sort-of L-shaped figure divides it into two squares, whose sides are the lengths of the "other two sides". Both the third row and fourth row figures are all made from the same tiles, so they must have the same area.
Look at me, Mom and Dad! No algebra!
Still mystified?
We'll walk through this in class.
© 1974, British Broadcasting Company
