## Graphical Analysis

Dr. John Gresham

Teaching Vita

My area of interest in teaching is to find ways to better communicate mathematics in an online world. In particular, it is important to be able to use technology to visualize concepts with applets that can be placed on a web page. The International Conference on Technology in Collegiate Mathematics (ICTCM) has been valuable in letting teachers share the latest technology and how they use it to help students visualize concepts. I have served on the Program Committee of ICTCM since 1999. I was named an ICTCM Fellow in 2015. One of the technologies that was presented at ICTCM in 2007 was GeoGebra. Since learning about it, I have been using it to create applets to illustrate concepts in my courses in algebra, trignonometry, and calculus.

For more information, contact me at jgresham@tarleton.edu

## Essential Trigonometry without Geometry

In 2019 and 2020 Bryant Wyatt, Jesse Crawford, and I authored articles about developing trigonometry through strictly anaylytic means and without using geometric constructions. In the first article we define the sine function as the solution of a certain differential equation. We then develop all the theorems of elementary trignonometry from this definition. In the second article we generalize the definition of a sine function and are able to prove generalizations of the key theorems. A GeoGebra applet to illustrate the generalized sine function is included here.

## Functions with a Complex Twist

In 2016 and 2017 Michael Warren, Bryant Wyatt, and I authored and presented articles about the points in the complex plane for which functions have real values. We first considered polynomial functions with real coefficients over the complex plane. In a second article, we considered trigonometric, hyperbolic, and exponential functions defined on the complex plane. We used the 3D graphing features of GeoGebra to illustrate the set of points in the plane for which these functions have real values.