Benjamin Dickman

Quadrilaterals and Bretschneider's Formula

We talk about a formula deduced by Bretschneider in the mid-nineteenth century that not only allows the computation of areas of planar quadrilaterals, regular and irregular, but also provides a more thorough understanding of the geometry of such figures. We present one version of Bretschneiders formula and talk about its scope of application and what it can say about the possible shapes of quadrilaterals.

Root Problems: Nonroutine Algebra Tasks

Explore three original problems, the thinking behind their formulation, how they can be solved, and related extensions.

Shoelace formula: Connecting the area of a polygon and the vector cross product

Understanding how one representation connects to another and how the essential ideas in that relationship are generalized can result in a mathematical theorem or a formula. In this article, we demonstrate this process by connecting a vector cross product in algebraic form to a geometric representation and applying a key mathematical idea from the relationship to prove the Shoelace theorem.