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For our ancestors who didn’t have the benefit of a world map...

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For our ancestors who didn’t have the benefit of a world map...

Rizom - April,2018
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For our ancestors who didn’t have the benefit of a world map...

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In a New Way -Pythagorean Theorem Proof by Piyush Goel

Pythagorean Theorem from “a new angle”


unnamedLets see the legacy theorem “The Pythagoras Theorem” from a totally new angle, I hope you understood (wink).

Proof-

Distance CD = (AB+AE)/10……………..(Piyush Theorem)
10CD = (a-d) +a
5CD + 5CD = 2a-d
5(BD-BC) + 5(CE-DE) = 2a-d
5BD – 5BC + 5CE – 5DE = 2a-d
5CE – 5BC = 2a-d—– (BD=DE)
5(CE-BC) = 2a-d————————eqn.1

Now,

CE^2 = AE^2 – AC^2
BC^2 = AB^2 – AC^2
CE^2- BC^2 = AE^2 – AB^2
(CE+BC)(CE-BC) = (AE +AB) (AE – AB)
(a +d)(CE – BC) = (a +a –d) (a-a +d)
(a +d)(CE-BC) = (2a-d) d
CE – BC = (2a-d) d/ (a +d) , put  value from eqn.1
5(2a –d) d/ (a +d) = (2a-d)
5d/ (a +d) = 1
5d = a +d
5d – d = a
a = 4d
If it is a Right Angle Triangle,
(a +d)^2 = a^2 + (a-d) ^2
(a +d)^2 – (a-d) ^2 = a^2
(a + d + a – d)(a + d –a +d) = a^2
(2a)(2d) = a^2
a = 4d QED.

 Copyrighted © Piyush Goel (1987)



written by

written by

PK

 

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