The UB Department of Mathematics is pleased to announce that Tyler Glover, a junior majoring in Mathematics, is the recipient of the 2021 Math Summer Scholarship. Under the guidance faculty mentor, Dr. Joseph Hundley, Tyler designed a special Undergraduate Research project that involved studying methods of geometric construction beyond the standard straight edge and compass, as well as their limitations and the number systems associated with them. For example, a classic result of abstract algebra states that if a segment of length x can be constructed, given a straight edge, a compass, and a segment of length 1, then x must be a root of an irreducible polynomial with integer coefficients and degree equal to a power of two.

From this it follows that it is impossible, given only a straight edge and compass, to construct a cube whose volume is twice that of a given cube (because the cube root of 2 is not a root of such a polynomial) or to construct a square whose area is equal to that of a given circle (because the square root of pi is not either).

Tyler is investigating various other construction methods, including using a straight edge with markings on it, a device which draws ellipses instead of just circles, and origami, to see which constructions become possible with more advanced tools, and which remain impossible.

Our annual undergraduate research award, established in 2017, is a result of a scholarship endowment by The Summer Math Foundation, Inc. of Amherst, New York. The endowment supports a six-week, full-time summer program for the selected undergraduate student to work with a UB Mathematics faculty mentor, and includes a $3,000 stipend.