Finite and Projective Geometry: A Deeper Look into Geometry

Melissa Luther

In this project, we will see geometry that doesn't necessarily hold true under all Euclid's Postulates. Finite Geometry is just that, a geometric figure that has a finite number of points or lines. We will take an axiomatic perspective on our research and create objects that stay true under the axioms of the respective geometry. We will then progress into Progressive Geometry and see maps of images onto different surfaces, and we will show how this is possible and still holds true to the axioms.

• Melissa Luther graduated from Fox Creek High in North Augusta, SC. She is a senior majoring in mathematics and minoring in business. She also played volleyball for the school and works part-time as a coach. After graduation in May 2022, she plans to start her career in data analytics in Greenville, SC.