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Joseph Wolstenholme and the Trigonometry of Tetrahedra

Daniil Rudenko

Abstract

We describe the results in the trigonometry of tetrahedra obtained by Joseph Wolstenholme in the last few years of his life. 'The late Professor Wolstenholme, M.A., Sc.D., shortly before his death, handed to me a scrap of paper, on which he had hastily scratched the following equation in tetrahedra, saying he had proved it ...' (Richardson, 1897).

Joseph Wolstenholme and the Trigonometry of Tetrahedra

Abstract

We describe the results in the trigonometry of tetrahedra obtained by Joseph Wolstenholme in the last few years of his life. 'The late Professor Wolstenholme, M.A., Sc.D., shortly before his death, handed to me a scrap of paper, on which he had hastily scratched the following equation in tetrahedra, saying he had proved it ...' (Richardson, 1897).
Paper Structure (3 sections, 1 theorem, 8 equations, 7 figures)

This paper contains 3 sections, 1 theorem, 8 equations, 7 figures.

Table of Contents

  1. Joseph Wolstenholme and the trigonometry of tetrahedra
  2. Wolstenholme's Theorem
  3. The 'Woolly One'

Key Result

Theorem 1

Let $T$ be a Euclidean tetrahedron with lengths of edges $l_{ij}$ and dihedral angles $\alpha_{ij}.$ Then there exist number $\lambda\in \mathbb{R}$ such that

Figures (7)

  • Figure 1: Problem 7425. Educational Times, Vol. 36, August 1883.
  • Figure 2: Problem 7509. Educational Times, Vol. 36, November 1883.
  • Figure 3: Examples for Practice in the Use of Seven-figure Logarithms, p. 41.
  • Figure 4: Problem 13521. Educational Times, Vol. 50, June 1897.
  • Figure 5: Problem 13605. Educational Times, Vol. 50, October 1897.
  • ...and 2 more figures

Theorems & Definitions (1)

  • Theorem 1: J. Wolstenholme, 1889