what is sqrt(2)?

Answer 1

Perhaps, related to "What is arccos(sqrt(Pi)/2)?"

... which is the trigonometric function that defines the vertex angle of a Pythagorean triangle that squares the circle:

arccos(.88622692545275801364908374167057..)

= 27.597112635690604451732204752339.. degrees.

For a circle having a diameter equal to 2, the triangle's long side (circle's chord; side of its square)

= sqrt(Pi) and its hypotenuse = 2 (circle's diameter), with the vertex point on the circumference.