Best Answer:
It is easy to grasp and prove Pythogorous theorem by relating right angle triangles having "whole number sides lengths alone"!

3^2+4^2+5^2 is graphically explainable on computers.

(Rearrange it as 5^2-4^2= 3^2. Note that 3^2=9 and (5+4) = 9

Further, 5^2 is 25 and by a split of it as 13 and 12 we have (13^2-12^2) = 5^2

And so on, endless possibilities of (odd number)^2 split and relating to separate right angle triangles exists!

A circle of "radius 5" has 8 number of " x,y whole number points" (2 per 2D-quadrant) and another four points on x and y axes (where either a-'x' or a-'y' is zero). In all 12 points with "x and y as whole numbers".

Similarly a circle of "radius-13" too has 8 numbers x,y whole number points (2 per a- quadrants) and another four points on x and y axes (where either a -x or a- y is zero). In all 12 points exist with "x and y as whole numbers".

Above two triplets actually relates smaller near-zero number sets "3, 4, 5" and "5, 12, 13". And we have

3^2+4^2= 5^2.................(1) and "5" is a hypotanuse.

5^2+12^2= 13^2.............(2) 5 and 13 are hypotanuses.

We have 3 hypotanuses in above two formulae. '5' and '5,13'

"3, 4 and 12" are not hypotanuses in both formulae!

Now imagine a brick of size 3 units (height), 4 units (breadth) and 12 units (length). Said brick has volume 3* 4* 12 = 12^2 = 144 cubic units!

(3^2 +4^2 = 5^2 is not only an equality in between 'sum of square units of two sides' and 'a hypotanuse square unit' but also extends as a volume and surface area relations as stated herinafter!

We know that 12^2 cubic units is volume of brick!

Surface area of brick is 5*4*12 =240 sq units which is "5 multiplied by base area (48 sq units) /( 4 *12) " Said relations exist when said pair of triplets relate 'a brick size'!

Probably said relatins were knowingly fixed by first users of brick having 3 inches height, 4 anches wide and 12 inches long sizes! It reveals an ancient manner of proving utility of pythagorus theorem!

You may regard above facts as a practical application of pythogorus theorem. It also give an insight into "area and volume" relations, which has consistently helped users of theorem!

Regards!

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