The guest lecture is free and open to the public.
Goins’ presentation shows that the three points (0,0), (3,0), and (3,4) form a 3-4-5 triangle. In particular, the distance between each pair of points is an integer. In 1945, Paul Erdos and Norman Anning showed that for any integer of at least 3, there is a collection of n points in the plane, not all on a line, such that their pairwise distances are integers.
In 2000, Nate Dean asked: “Are there four points on a parabola such that each pairwise distance is a rational number?” Garikai Campbell answered this question in 2003 using elliptic curves.
But what about shapes other than lines or parabolas? Richard Guy, in his book Unsolved Problems in Number Theory, asked: "What is the largest number of points in the plane such that (1) all pairwise distances are rational numbers, (2) no three of the points are on a line, and (3) no four of the points are on a circle?"
Goins will discuss the results discovered by his students who worked on this problem in 2010. His talk will also feature the personal relationships he gained working with African American mathematicians to find points on conic sections at rational distances.
Goins' lecture is dedicated to the life, works, and friendship of the late African American mathematician Nate Dean, who passed away in 2021.
Goins will also give a separate lecture earlier the same day as a part of the Cal Poly Humboldt Mathematics Colloquium. That lecture titled, “Clocks, Parking Garages, and the Solvability of the Quintic: A Friendly Introduction to Monodromy,” will begin at 4 p.m. in Room 166 of the Behavioral and Social Sciences (BSS) building. The colloquium talk is also free to the public. Learn more about the Mathematics Colloquium.
Goins grew up and attended school in south Los Angeles. He attended the California Institute of Technology, where he majored in Mathematics and Physics, and earned his doctorate in Mathematics from Stanford University. He has worked as a researcher at both Harvard and the National Security Agency; and has taught at both Caltech and Purdue University.
He has published more than 25 journal articles in areas such as applied mathematics, graph theory, number theory, and representation theory; and on topics such as Diophantine equations, elliptic curves, and African Americans in mathematics. He runs a federally-funded Research Experience for Undergraduates program titled Pomona Research in Mathematics Experience.
The Kieval lecture series is named for Mathematics Professor Emeritus, Harry S. Kieval, who taught at Cal Poly Humboldt from 1966 to 1979. The series includes topics on popular and/or broad aspects of mathematics attractive to undergraduates and the public. Learn more about the Kieval Lecture.