Here is another collection of beautiful geometric problems from Catriona Agg (née Shearer). They never fail to brighten the day with their loveliness.
Monthly Archives: November 2020
Square Deal
Here is a simple Futility Closet problem from 2014.
“This unit square is divided into four regions by a diagonal and a line that connects a vertex to the midpoint of an opposite side. What are the areas of the four regions?”
See the Square Deal for solutions.
Down With Geometry
One of my favorite bloggers, Kevin Drum, decided to relieve the tedium of our current political anarchy by whacking the hornets’ nest of the high school mathematics curriculum, in particular the subject of plane geometry. You can tell from the tag list on my blog that I hold plane geometry in high regard and can’t let this gibe pass without some rebuttal, futile as it may be. Actually, I am not going to weigh in on the general issue of the current math curriculum that much, but rather make a few observations from my own experience over the years as it relates to Kevin’s post.
(Update 2/9/2021) Vindication! Continue reading
Curve Making Puzzle
Here is a problem from Five Hundred Mathematical Challenges that I indeed found quite challenging.
“Problem 235. Two fixed points A and B and a moving point M are taken on the circumference of a circle. On the extension of the line segment AM a point N is taken, outside the circle, so that lengths MN = MB. Find the locus of N.”
Since one of the first hurdles I faced with this problem was trying to figure out what type of shape was being generated, I thought I would omit my usual drawings illustrating the problem statement. There turned out to be a lot of cases to consider, but the result was most satisfying. I also included the case when N is inside the circle. Again Visio was my main tool to handle all the examples with the concomitant requirement to prove whatever Visio suggested.
See the Curve Making Puzzle