by John Ehrke | Feb 22, 2019 | Problem of the Week
Problem 13 – February 22, 2019 Some Are Not That Far Away Consider any five points P1, P2, P3, P4, and P5 in the interior of a square of side length 1. Denote by dij the distance between points Pi and Pj when i is not equal to j. Prove that at least one of the...
by John Ehrke | Feb 8, 2019 | Problem of the Week
Problem 12 – February 8th, 2019 Is It Really One-seventh? I learned of this problem in a session on mathematics and art at the 2003 joint AMS/MAA meeting. Given any triangle ABC, construct a line from each vertex to the opposite side as indicated in the figure below....
by John Ehrke | Feb 1, 2019 | Problem of the Week
Problem 11 – February 1st, 2019 When Are There Integer Solutions? Describe all positive integers a for which the equation x2 – y2 = a has integer solutions. Submit your answers to mathpotw@acu.edu. Details for submissions can be found here. Correct...
by John Ehrke | Jan 25, 2019 | Video Spotlight
At least once per month (or more often as I run into cool stuff) I will post a video on this blog that gives insight into some cool applications of mathematics or interesting proofs and insights to mathematical techniques. The first video, linked below, is courtesy...
by John Ehrke | Jan 25, 2019 | Problem of the Week
Find the Angle Refer to the figure below. A circle of radius 1 is tangent to a circle of radius 3. The segment OA passes through the centers of the circles. The segment OB is tangent to both circles. Find the degree measurement of the angle AOB. Submit your...
by John Ehrke | Nov 9, 2018 | Problem of the Week
Fat Setty This problem was submitted by Dr. Jason Holland. Let n be a positive integer. What is the largest number of elements that a set of integers from 1 through 2n can have so that no one element in the set is divisible by another element in the set? Submit your...
by John Ehrke | Nov 3, 2018 | Problem of the Week
Find The Largest Product This problem is from Zachary M. Franco, Butler University. Write 53 as a sum of positive real numbers so that their product is as large as possible. Submit your answers to mathpotw@acu.edu. Details for submissions can be found here. Solution...
by John Ehrke | Oct 26, 2018 | Problem of the Week
A Solution Maple Can’t Do This problem is from Dr. Ehrke. In this problem of the week we will try to solve a problem that WolframAlpha, Maple, etc.. can’t even do. Find all integer solutions to the implicit equation . An integer solution is a pair (x,y)...
by John Ehrke | Oct 22, 2018 | Mu Sigma Events
Your new officers for Mu Sigma 2018-2019 are listed below. Congratulations to those who won and thanks to all of you who participated in the process. President – Jared Barker Vice President – Bethany Witemeyer Treasurer/Secretary – Hannah Smith...
by John Ehrke | Oct 12, 2018 | Problem of the Week
Find the Sum of the Digits This problem is from Hai He, Hunter College of CUNY. Let A be the sum of the digits of 1999! (that is 1999*1998*1997*..*2*1). Let B be the sum of the digits of A. Let C be the sum of the digits of B. What is the value of C? Submit your...
