Kevin Ventullo
If you store GPS coordinates as 32-bit floats, your precision in Iowa is about two feet. In central London the precision drops to half a millimeter, and at the South Pole it’s about a trillion times finer than the Planck Length. Floating point types are Continue reading A Curious Property of Floating Point Geospatial Coordinates
Way back in 2007, I got my first taste of mathematical research. I was in an REU at the University of West Georgia run by Professors Bruce Landman and Abdollah Khodkar. They taught us some basics of graph theory and Ramsey theory, and then presented Continue reading A Silver Cube of Order 11 (and 13) (and 19, 31, 37 )
I recently collaborated with Boris Alexeev, Evan Conway, Matthieu Rosenfeld, Andrew Sutherland, Terence Tao, and Markus Uhr on a problem posed in this blog post by Tao, which has now culminated in a joint paper. While the paper and posts give a more detailed treatment, I wanted Continue reading The Guy-Selfridge Conjecture
Suppose you knew that 9,273,284,218,074,431 was a perfect 7th power. How would you compute the 7th root? This is a long overdue sequel to the previous post, in which the author promised to derive an efficient algorithm for computing exact k-th roots of integers. That Continue reading Fast Exact Integer Roots
In this post, we re going to investigate an underexplored bridge between computer science and algebraic number theory. To motivate it, consider the analogy between floating point arithmetic and the theoretical real numbers. While floating points can only approximate the precision of a real number, much Continue reading 2-adic Logarithms and Fast Exponentiation
(Or: Enforced Algebraic Structure of Commutative Accumulative Hash Functions) While there are several documented approaches to defining a hash function for lists and other containers where iteration order is guaranteed, there seems to be less discussion around best practices for defining a hash function for Continue reading Hashing Unordered Sets: How Far Will Cleverness Take You?