These problems are my attempt to give high school students, like you, a glimpse into "real mathematics" by creating a math puzzle which will challenge you to think in ways that you have never thought before. Typically, in your high school math classes, you are given a problem to solve and a fixed step-by-step procedure for solving that type of problem — follow the steps, and you are certain to get an answer. However, "real mathematics" is not like that. When mathematicians work on problems, they often start off with no idea about how to solve the problem. There are lots of math questions that no one yet knows how to solve. I invite you to stretch your mind and take my mathematics challenge. I look forward to see what you come up with — Joseph DiMuro, Associate Professor for the Department of Math and Computer Science.
Circles in Triangle
This month’s problem comes from the 1995-1996 California Math League Contest, a math contest for high school students. This problem stumped me when I was in high school; perhaps you can do better.
Here we have an equilateral triangle with three circles inside. Each circle is touching two sides of the triangle, and the circles are all touching each other. If each circle has a radius of 1, then how long is each side of the triangle?
Joseph DiMuro (email@example.com) by February 28, 2017.
I will review your submission and whether you are correct or incorrect, I will be in touch with you to provide personal feedback, guidance, and background information regarding the problem.