GMY-02

Heron area

Any triangle.

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GeometryHeron

Governing equation

s=(a+b+c)/2,\\;\\Delta=\\sqrt{s(s-a)(s-b)(s-c)}

where

a: a (—)
b: b (—)
c: c (—)
\Delta: Δ (—)

Lecture brief

Historical brief

Pythagoras, Heron, spherical trigonometry and the sphere’s volume are the measuring arts that predate calculus. The sheets compute length, area and angle on plane and sphere. This sheet (GMY-02 — Heron area) is the form associated with Heron. Working symbols: $a$ , $b$ , $c$ $\rightarrow$ $\Delta$ . Any triangle.

Purpose

Purpose: compute

\Delta

from

a

b

c

in Geometry via

s=(a+b+c)/2,\\;\\Delta=\\sqrt{s(s-a)(s-b)(s-c)}

Any triangle. Use it when a real geometry question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

a = 5.000\,\mathrm{—}

b = 6.000\,\mathrm{—}

c = 7.000\,\mathrm{—}

, the governing relation

s=(a+b+c)/2,\\;\\Delta=\\sqrt{s(s-a)(s-b)(s-c)}

yields

\Delta = 14.6969\,\mathrm{—}

. Any triangle. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

a a5 —b b6 —c c7 —

Outputs

Δ \Delta14.6969 —

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Narration of this film

Any triangle.

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