Pythagoras
Pythagoras of Samos lived from 570 to 495 BC. The Pythagorean theorem applies in any vector space
with inner product assigning to two vectors a number.
The theorem is the relation a
2+b
2=c
2,
where a=|v|, b=|w| and c=|v-w| are lengths of a right angle triangle formed by the points A, B=A+v,
C=A+w where AB=v, AC=w, CB=v-w are the vectors connecting the points. The right angle assumption is written
mathematically in the form v.w=0. The length is defined as |v| = (v.v)
1/2. The theorem then follows
as c
2 = (v-w).(v-w) = v.v - 2 v.w + w.w = a
2 + b
2.
This theorem is so important that it can be considered the ``fundamental theorem of geometry".
Pythagoras teaching: From "The story of the greatest nations", (1910) From
Archiv
The Pythagoreans: Fyodor Bronnikov, (1827-1902)
