An introduction to Minkowski geometries

Abstract

The fundamental ideas of Minkowski geometries are presented. Learning about Minkowski geometries can sharpen our students’ understanding of concepts such as distance measurement. Many of its ideas are important and accessible to undergraduate students. Following a brief overview, distance and orthogonality in Minkowski geometries are thoroughly discussed and many illustrative examples and applications are supplied. Suggestions for further study of these geometries are given. Indeed, Minkowski geometries are an excellent source of topics for undergraduate research and independent study.

Keywords:

• Minkowski geometries
• teaching
• distance
• orthogonality
• Pi

2010 Mathematics Subject Classifications:

• 51F99
• 51K05
• 97G99

Acknowledgements

The author wishes to acknowledge helpful and insightful conversations on this topic with David S. Barth-Hart, Elmer L. Young, and Joshua M. Fitzhugh of Rochester Institute of Technology, and Patricia M. Burgess of Monroe Community College.

Disclosure statement

No potential conflict of interest was reported by the author.