About his "holy geometry book", Albert Einstein
wrote:
'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
wrote:
'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.'
Albert Einstein:
PhilosopherScientist, by Paul Arthur Schilpp, 1951.
Unlocking the Genius of Einstein: How His Act of Kindness Helped a Student Master Geometry
In 1943, Johanna Mankiewicz, a young Polish girl,
sent a letter to Einstein asking for his help in solving
a mathematical problem. Specifically, she was struggling
with a proof in Euclidean geometry.
Einstein responded to her letter, providing her with
detailed explanations and diagrams to help her better
understand the problem. He also encouraged her to
continue pursuing her studies in mathematics and
science, and expressed his admiration for her
perseverance and dedication.
The original letter from Einstein to Mankiewicz,
along with her original letter and subsequent
correspondence, are now housed in the Einstein Archives
at the Hebrew University of Jerusalem.
This incident is a testament to Einstein's
willingness to help others and his belief in the
importance of education and intellectual pursuit. It
also highlights his own expertise and deep understanding
of mathematics, particularly in the field of geometry.
Einstein'Proof
Proving Pythagorean theorem on the basis of the
similarity of triangles BCA, BHC, and CHA:
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