GMY-05

3-D distance

Euclidean.

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Geometry3D distance

Governing equation

d=\\sqrt{\\Delta x^2+\\Delta y^2+\\Delta z^2}

where

\Delta x: Δx (m)
\Delta y: Δy (m)
\Delta z: Δz (m)
d: d (m)

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-05 — 3-D distance) is the form associated with 3D distance. Working symbols: $\Delta x$ , $\Delta y$ , $\Delta z$ $\rightarrow$ $d$ . Euclidean.

Purpose

Purpose: compute

d

from

\Delta x

\Delta y

\Delta z

in Geometry via

d=\\sqrt{\\Delta x^2+\\Delta y^2+\\Delta z^2}

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

Live realistic example

In symbols

Live case. Given

\Delta x = 3.000\,\mathrm{m}

\Delta y = 4.000\,\mathrm{m}

\Delta z = 12.000\,\mathrm{m}

, the governing relation

d=\\sqrt{\\Delta x^2+\\Delta y^2+\\Delta z^2}

yields

d = 13.0000\,\mathrm{m}

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

Calculator

Inputs

Δx \Delta x3 mΔy \Delta y4 mΔz \Delta z12 m

Outputs

d d13.0000 m

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Narration of this film

Euclidean.

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