text: determine the geometrical figure? what will be the geometrical figure of 3 ^ (5) = 122 ^ (2) - 121 ^ (2) like 3 ^ (2) = 5 ^ (2) - 3 ^(2) satisfies the conditions of making a right triangle.similarly any given number with any given power can be expressed as difference of infinite sets of two perfect squares and the squares can be terminating decimals what will be the geometrical figures of such a case?                    6 you mean 3^2 = 5^2 - 4^2 ... dimensionally this works.  for examples, if the units are feet, then you can take a bunch of one foot by one foot ceramic floor tiles, and arrange them in a 5 by 5 square, then take away a 4 by 4 square chunk of that, and rearrange what remains into a 3 by 3 square of tiles.  translated into inches, you get (3*12)^2 = (5*12)^2 - (4*12)^2: if you have a whole lot of one inch by one inch tiles, and you make a big 60 by 60 square out of then and remove a 48 by 48 subsquare, then you can rearraqnge the remaining little tiles into a 36 by 36 square.  now consider 3^5 = 243 = (122 + 121)*(122 - 121) = 122^ - 121^2, again in feet.  when you translate that into inches, it doesn't scale the same way: the left hand side is multiplied by 12^5 but the right hand side is only multiplied by 12^2.  what kind of geometrical figure do you want to use given that it does not scale?  "take a bunch of little one by one by one by one by one foot hypercubes, and arrange them in five space ... then when you project along the ... the result looks like ..." ??? "... but subdivide each hypercube into 12^5 little one inch by ... hypercubes and what you just did no longer works".  is that really what you are looking for?