Gauss's Area Formula for Irregular Shapes

Authors

  • Jacob Gechlik Saratoga High School
  • Hayk Sedrakyan UPMC---Sorbonne University, Paris, France

Keywords:

Shoelace theorem, area formulas, irregular polygons, alternative algorithms

Abstract

To find the area of an irregular shape, we break the shape into common shapes. Then we find the area of each shape and add them, but this approach does not always work. In this paper we investigate Gauss’s area formula (for irregular shapes), also known as the shoelace formula or the shoelace algorithm. This theorem is outside the scope of school program. Nevertheless, we provide several applications that emphasize the importance and usefulness of this theorem. Most of the applications provided in this paper are created by the authors.

Author Biographies

Jacob Gechlik, Saratoga High School

Jacob Gechlik is a Junior at Saratoga High School in Saratoga, California. His academic interests include the study of mathematical problem solving, mathematics history, and mathematics contest problems. Jacob is also an avid runner, competing in middle- and long-distance events with the Saratoga track and field team.

Hayk Sedrakyan, UPMC---Sorbonne University, Paris, France

Hayk Sedrakyan is a scientific researcher, his co-authored works recently received Erdos Award (one of the highest international awards in mathematics, given for major contributions to mathematics globally). He is an IMO medal winner professional mathematical Olympiad coach involved in the American Mathematical Competitions (AMC and USAMO) and International Mathematical Olympiad (IMO). Hayk is a Doctor of mathematical sciences in the USA, France, Armenia and holds three master’s degrees in mathematics from institutions in Germany, Austria, and Italy. He has worked as a scientific researcher for the European Commission, has been one of the Team Leaders at Harvard-MIT Mathematics Tournament (HMMT) and was an invited speaker at Imperial College London. Hayk is an author of multiple math competition preparation books used throughout the USA and internationally (published by top publishers such as Springer), and an author of multiple scientific articles published in the top scientific journals such as Springer and Elsevier.

References

Sedrakyan, H., & Sedrakyan, N. (2021). AMC 8 preparation book. Independently published.

Sedrakyan, H., & Sedrakyan, N. (2021). AMC 10 preparation book. Independently published.

Sedrakyan, H., & Sedrakyan, N. (2021). AMC 12 preparation book. Independently published.

Sedrakyan, H., & Sedrakyan, N. (2023). AIME preparation book. Independently published.

Sedrakyan, H., & Sedrakyan, N. (2023). AMC and AIME geometry must-know techniques. Independently published.

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Published

2024-07-02

How to Cite

Gechlik, J., & Sedrakyan, H. (2024). Gauss’s Area Formula for Irregular Shapes. hio ournal of chool athematics, 97(1), 12–29. etrieved from http://voyager.janeway.systems:9999/index.php/OJSM/article/view/9651

Issue

Vol. 97: Summer 2024

Section

Articles

License

By submitting this agreement, the author hereby grants to The Ohio State University, on behalf of its University Libraries