[paradoxparalax]

I have learn more geometry from trying to solve the unsolvable "squaring the circle" problem than all the Geom. classes I had in my life. For example: No one ever has told me in school that for all squares, the length of the diagonal equals The Square Root Of Two times the side of the square's, so for a square where the side is 1 meter, the diagonal will be Sq.Rt.o'2 meters (around 1,4 m), And I came to find that by myself doing the exercise of the unsolvable. Also, more recently early this year, I found that the diagonal/diameter of a Pentagon was the Cubic Root of 3, or this was the hexagon, and the heptagon was the S.q.rt.o'2 multiplied by C.rt.o'3 or something like this, the thing is that they follow a sequence, Its always something with the square and cubic roots of 2 and 3 and I guess 5 or 7 will appear later in the sequence for polygons with more sides, noting that for a "infinite sides 'polygon' " , which would be a circle, the number that relates the diagonal with the "'sides'", or in this analogy, the Perimeter , is Pi...Anyway, good exercises. p.s: I have remembered that back then I thought maybe Pi was Square Root of Infinity, and now just came to my mind that maybe would be the Infinite Root of something...But off course just joking thinking, but nice exercise.

[mrleiter]

> For example: No one ever has told me in school that for all squares, the length of the diagonal equals The Square Root Of Two times the side of the square's, so for a square where the side is 1 meter, the diagonal will be Sq.Rt.o'2 meters (around 1,4 m), And I came to find that by myself doing the exercise of the unsolvable.

That's actually the Pythagorean theorem. How did you arrive at that by doing the "unsolvable"?

[avian]

The “unsolvable problem” the parent refers to is the problem of geometrically constructing a square with the same area as a circle. It has been proven to be impossible.

https://en.m.wikipedia.org/wiki/Squaring_the_circle

[raverbashing]

> No one ever has told me in school that for all squares, the length of the diagonal equals The Square Root Of Two times the side of the square's

This is basic knowledge (and as someone said, comes from the Pythagorean theorem) and taught on school in a lot of places.

[paradoxparalax]

Yes, thats exactly what im saying, everyone knows the pythagorean theorem by memory, but something even more basic, a simple constant, not a formula, in a simple square, if you ask around, at least in my experience, no one knows.