Measure of Trihedral Angle formed by 3 Mutually Perpendicular Half-Lines

Theorem

Let $Q$ be the trihedral angle formed by $3$ half-lines each of which is perpendicular to the other two half-lines.

Then $Q$ measures $\dfrac \pi 2$ steradians.

Proof

This theorem requires a proof. In particular: Prove that $Q$ subtends $1/8$ of a sphere then use Measure of Total Solid Angle around Point You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by crafting such a proof. To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{ProofWanted}} from the code. If you would welcome a second opinion as to whether your work is correct, add a call to {{Proofread}} the page.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): solid angle
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): solid angle