Pythagoras and the Pythagoreans - Department of Mathematics

Pythagoras and the Pythagoreans 21
This diagram is identical to the original figure used in the Euclid’s
proof theorem. The figure was known to Islamic mathematicians as the
Figure of the Bride.
Sketch of Proof. Note that triangles 4ADC and 4ADE are congruent
and hence have equal area. Now slide the vertex C of 4ADC to B.
Slide also the vertex B of 4ADE to L. Each of these transformations
do not change the area. Therefore, by doubling, it follows that the area
of the rectangle ALME is equal to the area of the square upon the side
AB. Use a similar argument to show that the area of the square upon
the side BC equals the area of the rectangle LCNM.
This stamp was issued by Greece. It
depicts the Pythagorean theorem.
6.2 The Golden Section
From Kepler we have these words
“Geometry has two great treasures: one is the Theorem
of Pythagoras; the other, the division of a line into extreme
and mean ratio. The first we may compare to a measure of
gold; the second we may name a precious jewel.”