About his "holy geometry book", Albert Einstein
'At the age of 12 I experienced a second wonder of a
totally different nature: in a little book dealing with Euclidean plane
geometry, which came into my hands at the beginning of a school year. Here were
assertions, as for example the intersection of the three altitudes of a triangle
in one point, which - though by no means evident - could nevertheless be proved
with such certainty that any doubt appeared to be out of the question. This
lucidity and certainty made an indescribable impression upon me. That the axioms
could not be proved did not annoy me. Actually I was completely satisfied when I
was able to rely on such theorems whose validity were not doubtful to me.'
About the Pythagorean theorem, Albert Einstein
'For example I remember that an uncle told me the
Pythagorean theorem before the holy geometry booklet had come into my hands.
After much effort I succeeded in "proving" this theorem on the basis of the
similarity of triangles ... for anyone who experiences [these feelings] for the
first time, it is marvelous enough that man is capable at all to reach such a
degree of certainty and purity in pure thinking as the Greeks showed us for the
first time to be possible in geometry.'
Philosopher-Scientist, by Paul Arthur Schilpp, 1951.
Proving Pythagorean theorem on the basis of the
similarity of triangles BCA, BHC, and CHA: