Triangles and variance of the distance to the boundary

Authors

  • Alastair Fletcher Northern Illinois University
  • Katherine Fletcher Northern Illinois University
  • Joseph Wasiqi Northern Illinois University

DOI:

https://doi.org/10.33043/ydyzb82y

Abstract

We consider the variance of the distance to the boundary for planar triangles. Our main result is that if g is a line segment joining a vertex of a triangle to a point on the opposite side, then the variance restricted to g is a convex function.

Author Biographies

Alastair Fletcher, Northern Illinois University

Alastair Fletcher is a Professor at Northern Illinois University and currently Director of Undergraduate Studies. He finds assisting students at all levels and of all backgrounds fulfilling, and puts up with the department making him wear Halloween costumes.

Katherine Fletcher, Northern Illinois University

Katherine Fletcher holds a Master’s in Mathematics, teaches at Elgin Community College and is Director of the MathLab. She enjoys helping students reach their potential.

Joseph Wasiqi, Northern Illinois University

Joseph Wasiqi is currently a Master’s degree student at Northern Illinois University. He hopes to carry his mathematical knowledge into medicine and/or bioinformatic.

References

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S. E. Strawbridge, A. Kurowski, E. Corujo-Simon, A. N. Fletcher, J. Nichols and A. G. Fletcher, insideOutside: an accessible algorithm for classifying interior and exterior points, with applications in embryology, Biol. Open, 12, no. 9 (2023): bio060055.

E. Study, Vorlesungen über ausgew"ahlte Gegenst"ande der Geometrie (German edition), Cornell University Library, 1911.

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Published

2025-03-28

How to Cite

Fletcher, A., Fletcher, K., & Wasiqi, J. (2025). Triangles and variance of the distance to the boundary. Mathematics Exchange, 18(1), 65–76. https://doi.org/10.33043/ydyzb82y

Issue

Vol. 18 No. 1 (2024): Mathematics Exchange

Section

Articles

License

Copyright (c) 2024 Alastair Fletcher, Katherine Fletcher, Joseph Wasiqi

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.