Testwiki:Reference desk/Archives/Science/2024 September 26

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September 26

Body Roundness Index formula

Body_roundness_index#Calculation gives the formula

364.2 − 365.5  × √(1 − [waist circumference in cm / 2π]2  /  [0.5 × height in cm]2)

which seems unnecessarily complicated. Why isn't it simply simplified to

$364.2-365.5\sqrt{1-(\frac{\text{waist circumference in cm}}{\pi \times \text{height in cm}}{)}^2}$ ?

Moreover, as both numerator and denominator have length units, the unit doesn't matter as long as they are the same e.g. cm, mm or inches.

Thanks, cmɢʟee⎆τaʟκ 04:31, 26 September 2024 (UTC)

Probaly because the editor who added that didn't know how to render mathematical formulae. You're welcome to change it. Shantavira|^{feed me} 09:16, 26 September 2024 (UTC)

Thanks. I don't mean the formatting but the division by 2π on top with multiplication by 0.5 below.

Presumably, they meant waist / (2π) instead of (waist / 2)π – BEMDAS is confusing! cmɢʟee⎆τaʟκ 10:17, 26 September 2024 (UTC)

Because it's left over from its derivation from the eccentricity formula for an ellipse, $\sqrt{1-\frac{b^2}{a^2}}$, where the semi-minor axis, b, is the "radius" of the waist and the semi-major axis, a, is half the body height. AlmostReadytoFly (talk) 11:05, 26 September 2024 (UTC)

Makes sense, thanks! cmɢʟee⎆τaʟκ 11:34, 26 September 2024 (UTC)