Abi-Khuzam Inequality

From ProofWiki
Jump to navigation Jump to search

Theorem

Let $\triangle ABC$ be a triangle.

Then:

$\sin A \cdot \sin B \cdot \sin C \le k A \cdot B \cdot C$

where:

$A, B, C$ are measured in radians
$k = \paren {\dfrac {3 \sqrt 3} {2 \pi} }^3 \approx 0 \cdotp 56559 \, 56245 \ldots$


Proof


Source of Name

This entry was named for Faruk Fuad Abi-Khuzam.


Sources