Hostname: page-component-7dd5485656-zlgnt Total loading time: 0 Render date: 2025-10-24T00:49:12.507Z Has data issue: false hasContentIssue false
  • English
  • Français

Some polygon area theorems

Published online by Cambridge University Press:  15 October 2025

John R. Silvester
John R. Silvester*
Affiliation:
Department of Mathematics, King’s College, Strand, London WC2R 2LS e-mail: john.silvester@cantab.net
Get access Rights & Permissions [Opens in a new window]

Extract

Figure 1 shows an arbitrary triangle Z1Z2Z3, the base triangle, with similar isosceles triangles Z1Z2V1, Z2Z3V2 and Z3Z1V3 drawn outwards on the respective sides Z1Z2, Z2Z3 and Z3Z1, all with base angles (the angles at Z1, Z2 and Z3) equal to α. We call ΔV1V2V3 the outer α-triangle of ΔZ1Z2Z3. Note that, if ΔZ1Z2Z3 is positively oriented (that is, if the labels go around the triangle in anticlockwise order), then so is ΔV1V2V3, but the triangles Z1Z2V1, Z2Z3V2 and Z3Z1V3 are negatively oriented (that is, the labels go around the triangle in clockwise order).

Information

Type
Articles
Information
The Mathematical Gazette , Volume 109 , Issue 576 , November 2025 , pp. 433 - 448
Check for updates
Copyright
© The Authors, 2025 Published by Cambridge University Press on behalf of The Mathematical Association

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.)

Article purchase

Temporarily unavailable

References

Coxeter, H. S. M. and Greitzer, S. L., Geometry revisited, Mathematical Association of America (1967).CrossRefGoogle Scholar
Silvester, John R., Some triangle theorems by complex numbers, Math. Gaz. 107 (November 2023) pp. 454–473.10.1017/mag.2023.98CrossRefGoogle Scholar