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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.
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