An Educational Approach to the Famous Theorems of Heron, Ptolemy, Brahmagupta, and Simson

The target audience of this brief article are senior high school and freshmen college mathematics students. It is the aim of this article to provide mathematics students and teachers with a new insight into the work of Heron, Ptolemy, Brahmagupta, and Simson regarding the triangles and cyclic quadrilaterals. We provide a brief overview of the history of ancient to modern mathematics to show how the work of these four mathematicians is intertwined and how their discoveries could have been inspired by the work of their preceding astronomers and mathematicians. We conclude the article with a GeoGebra applet as a technology tool.