Mathematica(@mathemetica):Numbers x and y sit end to end under a semicircle and instantly rank their four classic averages by length. The tallest vertical is the arithmetic mean (x + y)/2. The vertical at their meeting point is the geometric mean √(xy). The long slant from the center top is the quadratic mean √((x² + y²)/2). The shortest vertical is the harmonic mean 2xy/(x + y). These lengths always obey QM ≥ AM ≥ GM ≥ HM, and the triangle drawn around the small circle has area xy. Electricians size household AC wiring with the quadratic mean because it gives the effective voltage that produces the same heating as a steady DC current.

2026.07.26 04:41

Numbers x and y sit end to end under a semicircle and instantly rank their four classic averages by length. The tallest vertical is the arithmetic mean (x + y)/2. The vertical at their meeting point is the geometric mean √(xy). The long slant from the center top is the quadratic mean √((x² + y²)/2). The shortest vertical is the harmonic mean 2xy/(x + y). These lengths always obey QM ≥ AM ≥ GM ≥ HM, and the triangle drawn around the small circle has area xy. Electricians size household AC wiring with the quadratic mean because it gives the effective voltage that produces the same heating as a steady DC current.