Get Math Help

GET TUTORING NEAR ME!

By submitting the following form, you agree to Club Z!'s Terms of Use and Privacy Policy

    Abi-Khuzam Inequality

    Alternate name
    Definition

    The inequality sin A sin B sin C<=((3sqrt(3))/(2π))^3 A B C, where A, B, and C are the vertex angles of a triangle. The maximum is reached for an equilateral triangle (and therefore at A = B = C = π/3) and has numerical value 0.56559562463... (OEIS A127205). The inequality was proven by Abi-Khuzam, also considered by Klamkin, and mentioned by Flanders as "an interesting related result" for the product sin A sin B sin C of the three angles A, B, and C of a triangle.

    Related term

    Brocard angle

    Find the right fit or it’s free.

    We guarantee you’ll find the right tutor, or we’ll cover the first hour of your lesson.