Quote:
Originally Posted by Robh
Nice rendition of the tale.
Excuse the digression but it reminds me of another story ...
Preliminary-
Pythagoras' theorem states that for a right triangle with sides a, b, c (the hypotenuse), then a^2+b^2=c^2. A Pythagorean triad is a set of 3 sides for a right triangle e.g. 3,4,5 where 3^2+4^2=5^2 or 9+16=25.
In those days, Liethagoras, who was jealous of Pythagoras' fame, noticed an interesting connection between Pythagorean triads and proposed a much simpler theorem for right-angled triangles: a^2=b+c.
3,4,5 ---> 3^2=4+5
5,12,13 ---> 5^2=12+13
7,24,25 ---> 7^2=24+25
However, his fame was short-lived when it was brought to Pythagoras' attention and he laughed off the proposition.
For anyone interested, under what condition is Liethagoras correct?
Regards, Rob.
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c^2=a^2+b^2
a^2=c^2-b^2
a^2=(c+b)(c-b)
Hence a^2=(b+c) if (c-b)=1.
Regards
Steven