Hostname: page-component-586b7cd67f-dlnhk Total loading time: 0 Render date: 2024-11-24T14:30:07.366Z Has data issue: false hasContentIssue false
  • English
  • Français

Theorems on Quadriplanar Coordinates

Published online by Cambridge University Press:  03 November 2016

R. T Robinson
Get access Rights & Permissions [Opens in a new window]

Extract

Given a tetrahedron of reference ABCD, let λ, μ, ν, π be the cosines of the angles made by a line with the perpendiculars to the faces BCD, ACD, ABD, ABC respectively, these perpendiculars being drawn all inwards or all outwards; where

Aλ1 + Bμ1 + C½1 + Dπ1 = 0

Aλ2 + Bμ2 + C½2 + Dπ2 = 0

A, B, C, D being the areas of the faces BCD, .. If P1 (α1, ²1, γ1, δ1) and P2 (α2, β2, γ2, δ2) are any two points, the lines PP1 and PP2 can be written

(α - α1)/λ1 = (β - β1)/μ1 = (γ - γ1)/ν1 = (δ - δ1)/π1 = θ1,

(α - α2)/λ2 = (β - β2)/μ2 = (γ - γ2)/ν2 = (δ - δ2)/π2 = θ2,

to find the cosine of the angle between PP1 and PP2.

Type
Research Article
Information
The Mathematical Gazette , Volume 27 , Issue 273 , February 1943 , pp. 13 - 19
Copyright
Copyright © Mathematical Association 1943

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)