Kevin's Math Page

 Blog Kevin's Math Blog - discussions and answers to short math problems. Software: Euclid calculator - Advanced calculator with support for variables and functions. Compatible with Macintosh, Windows, and UNIX. Game/Puzzle Analysis: An analysis of Tic Tac Toe - Original research from 2006. A detailed analysis of this simple game. An analysis of the 16 Puzzle - Original research from 2000. The 16 puzzle is a very familiar puzzle with 15 scrambled tiles and 16 spaces. I derive a method of determining if a given scrambling is legal -- that is, if the puzzle is solvable. An analysis of the Higher Number game - Original research from 2016. An analysis of the Higher Number game, in which each player gets a random number and decides whether to keep it. Probability: Calling Pre-Flop All-In with KK or AK - Original analysis from 2007. Analyzing when to call pre-flop all-in when your opponent shows great strength. How To Become A Millionaire Discussion of various ways to turn \$200 into \$1,000,000. Analysis of poker bad beats - Original analysis from 2007. Analysis of pre-flop bad beats in Texas Hold'em. An analysis of the Monty Hall problem - Original research from 2003. An analysis of the infamous Monty Hall probability problem. Some new material here that I don't think has appeared elsewhere. An analysis of the expected probability of two consecutive primes having the same last digit - Original research from 2016. An analysis of the expected probability of two consecutive primes having the same last digit. Algorithms: An analysis of the Block Swapping problem - Original research from 2003. An analysis of problem concerning swapping blocks of bytes in an array. Involves some congruence arithmetic. Other Research/Analysis: My Polyominoes Page - Various topics related to Polyominoes. Some original research, along with links to other research. My Research on Egyptian Fractions - PDF document of my 1992 research paper. Egyptians had no way of writing 5/6. Instead, they would write 1/2 + 1/3 (the sum of unit fractions). My research examines ways of computing fractions as the sum of unit fractions, minimizing number of terms and/or largest denominator. My Research on Graceful Graphs - Research from 1988. Includes a PDF version. Chess Tours - 1986 research on knight's tours, bishop's tours, etc. Some extensions to 3-dimensional chess boards. Learning: Essay on non-Euclidian Geometry - From 1987. Simply a description of what non-Euclidian geometry is and some examples. Java Applets: A Java Applet that computes prime numbers - Calculates the number of primes between 2 and 2000. A Java Applet that computes Pi based on Leibniz formula - Calculates Pi using the Leibniz formula up to 5000 iterations. An INTERACTIVE Java Applet that checks a number for primality - Enter a number and it'll check to see if it's prime or composite.

Kevin's Math Page