“All 20 diagonals are drawn in a regular octagon. At how many distinct points in the interior of the octagon (not on the boundary) do two or more diagonals intersect?” Submit your solutions to LBB by Wednesday, February 19.
Every Wednesday at lunch, I introduce the solution to last week’s Problem of the Week and post the new problem around campus. This week’s problem is from the 2013 American Mathematics Contest for 10th grade students. The AMC 10 is a 25 question multiple-choice test that uses algebra and geometry knowledge and includes problems that range in difficulty level. The AMC is a qualifying exam for the American Invitational Mathematics Examination, which is a qualifying exam for the USA Math Olympiad. This Wednesday, across the country, students will be participating in the AMC 10 and AMC 12.
At the first Wednesday lunch when I introduced the Problem of the Week, a student asked, “What’s the point??!?!” What is the point? Why solve the Problem of the Week? Why do math outside of math class? Why do math in math class? At that Wednesday lunch I responded emphatically, “For the glory of mathematics!” I believe in the glory of mathematics. I don’t see math as a means to solve science problems. I also don’t see math as art. I see math as an opportunity for creativity and challenge, as I’m sure science teachers and art teachers see science and art.
I always post the Problem of the Week next to the doors of the math classrooms. My morning chore is cleaning the math classrooms and entryway with two students. We vacuum, mop, clean tables, and wipe the dry erase boards. I also clean fingerprints and various smears off the large glass doors. On Friday morning, I noticed more intention to the grime on the door. If I looked at the glass from the right angle, I saw a large octagon with 20 diagonals traced by a greasy finger.
-Lilly Betke-Brunswick, Math Teacher & Chewonki Semester School Alum (MCS 35)
Lilly and her co-leader during their fall Semester 51 wilderness trip to the Mahoosuc Range.