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Singular matrices and pairwise-tangent circles

Published online by Cambridge University Press:  15 February 2024

A. F. Beardon
A. F. Beardon*
Affiliation:
Centre for Mathematical Sciences University of Cambridge, Wilberforce Road, Cambridge CB3 0WB e-mail: afb@dpmms.cam.ac.uk
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The idea of using the generalised inverse of a singular matrix A to solve the matrix equation Ax = b has been discussed in the earlier papers [1, 2, 3, 4] in the Gazette. Here we discuss three simple geometric questions which are of interest in their own right, and which illustrate the use of the generalised inverse of a matrix. The three questions are about polygons and circles in the Euclidean plane. We need not assume that a polygon is a simple closed curve, nor that it is convex: indeed, abstractly, a polygon is just a finite sequence (v1, …, vn) of its distinct, consecutive, vertices. It is convenient to let vn + 1 = v1 and (later) Cn + 1 = C1.

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Articles
Information
The Mathematical Gazette , Volume 108 , Issue 571 , March 2024 , pp. 12 - 19
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Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© The Authors, 2024 Published by Cambridge University Press on behalf of The Mathematical Association

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