Spheric piramid

If we input three random superficial points on a sphere where r is the radius, we get a sphere triangle. If we connect the three vertex with the center of the sphere we get a spheric pyramid.

What would be the average volume of the spheric pyramid given infinite three random superficial points?

#Geometry

Easy Math Editor

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Comments

Please express the question more concisely. If I understand you correctly, then what you are looking for is related to what is called the solid angle. In any case, I would recommend reading up on spherical trigonometry.

A Former Brilliant Member - 2 years, 8 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$