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The Pythagorean Theorem (Making it real) " They know not, neither will they understand :
" Other
discoveries often attributed to
him (e.g., the
incommensurability
of the side and diagonal of a square, and the Pythagorean theorem for
right
triangles) were probably developed only later by the Pythagorean
school."
Encyclopedia Britannica 2002 cd"
(iv) The discovery of
irrationals. This is certainly
attributed to the Pythagoreans but it does seem unlikely to have been
due to Pythagoras himself This went against Pythagoras's philosophy the
all things are numbers,
since
by a number he meant the ratio of two whole numbers. However, because
of
his belief that all things are numbers it would be a natural task to
try
to prove that the hypotenuse of an isosceles right angled triangle had
a
length corresponding to a number."
School of Mathematics and Statistics University of St Andrews, Scotland
Introduction
The
purpose of this short
message is
to make it clear that the side and the diagonal of a square are
commensurable.This
means that we can use
a square to show that:
AB sq + BC sq = AC sq There is
no need to skew a triangle in order to put numerical values to
the three sides. More important is that it shows there is no need for
irrational numbers. The length of the side of a square is 12/17.
Rational numbers can
fill in all the gaps fabricated by irrational man.
The
diagrams are self
explanatory, the
addition of one after each side is squared, is to give substance to the
surface
area. Without this addition the surface areas will only be two
dimensional, a meaningless abstraction in thin air.(irrational) (ABsq+1) + (BCsq+1)
= (ACsq+1) Without any practical value, mathematics becomes a senseless exercise in futility.
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