Elizabeth Zeigler
Winner of the Judges’ Choice Award for Best Math Presentation
When looking at the set of natural numbers, we see that not every natural number is a perfect square or the sum of two squares with 3 being the first number this occurs. However, we can write 3 as the sum of three squares as shown: 3 = 1 + 2 = 1 + 1 + 1
Next, we look at 7, which cannot be written as the sum of three squares, but we can write 7 as the sum of four squares as shown: 7 = 1 + 6 = 4 + 3 = 1 + 1 + 5 = 1 + 4 + 2 = 1 + 1 + 1 + 4
To show all natural numbers can be written as the sum of four squares, we will use number theory techniques along with quaternions.
Elizabeth Zeigler is a senior mathematic dual engineering major from Bonneau, SC. She has been a manager for the Lander University Softball Team and worked for Lander Athletics as a photographer/videographer. Elizabeth plans to attend Clemson in the fall of 2022 to pursue a civil engineering degree and work in the bridge construction industry.