ALG-22

Harmonic mean of two

H = 2xy / (x+y). Reciprocal of the mean of reciprocals.

Reading speed

MeansHarmonic mean

Governing equation

H=\dfrac{2xy}{x+y}

where

x: x (—)
y: y (—)
H: Harmonic mean (—)

Lecture brief

Historical brief

From al-Khwārizmī’s restoration to the quadratic formula, AM–GM, De Moivre and logarithms, algebra is the closed-form skeleton under every lab. These sheets solve, bound and compound. This sheet (ALG-22 — Harmonic mean of two) is the form associated with Harmonic mean. Working symbols: $x$ , $y$ $\rightarrow$ $H$ . AM ≥ GM ≥ HM. The harmonic mean is the right average for rates (parallel resistors, average speed).

Purpose

Purpose: compute

H

from

x

y

in Algebra via

H=\dfrac{2xy}{x+y}

H = 2xy / (x+y). Reciprocal of the mean of reciprocals. Use it when a real algebra question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

x = 6.000\,\mathrm{—}

y = 12.000\,\mathrm{—}

, the governing relation

H=\dfrac{2xy}{x+y}

yields

H = 8.0000\,\mathrm{—}

. Two positive numbers. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

x x6 —y y12 —

Outputs

Harmonic mean H8.0000 —

Reading speed

Watch on YouTube

Free library

Full library

Free PDF / open book

YouTube channels

00:0 / 00:08

Narration of this film

Two positive numbers.

AM ≥ GM ≥ HM. The harmonic mean is the right average for rates (parallel resistors, average speed).

Reading speed

Watch on YouTube