Puzzler: a squarable region from Leonardo da Vinci

It is famously impossible to square the circle. That is, given a circle, it is impossible, using only a compass and straightedge, to construct a square having the same area as the circle. I will let you read elsewhere about the exact rules behind compass and straightedge constructions. The punchline is that if you begin…

A pyramidologist’s value for pi

Recently I came across two theories about the design of Great Pyramid of Giza. If we construct a circle with the altitude of the pyramid as its radius, then the circumference of the circle is equal to the perimeter of the base of the pyramid. Said another way, if we build a hemisphere with the same…

A game for budding knot theorists

Thanks to Sam Shah for introducing me to this fascinating online game: Entanglement. The rules are simple. You are given hexagonal tiles, one at a time, each adorned with six short segments of rope. Use them to construct the longest possible knot (measured in segments) before running into a wall.  Entanglement is fun and addicting!…

The left-handed boy problem

A few months ago Gary Foshee was scheduled to speak at the Gathering for Gardner. He got up and gave a presentation that was all of three sentences. He said: I have two children. One is a boy born on a Tuesday. What is the probability I have two boys? This deceptively simple problem quickly made…

Mathematical magic tricks for kids

My six-year-old son loves the website ActivityTV.com, especially their science, origami, cooking, and magic videos. I watched a few of the magic how-to videos with him and was pleasantly surprised to see that some of them had a distinctly mathematical feel to them. For example: Jumping rubber bands: topological properties of circles and linked circles…

A card trick that will probably amaze your friends (solution)

Warning! Spoiler alert! This post contains the secret behind the card trick that I described in my last post. Read that post before reading this one. First the bad news: this card trick is not fool-proof; it is a probabilistic card trick. The good news is that in my experience, it has a high probability…

A card trick that will probably amaze your friends

Here’s a neat card trick that I learned a few years ago. I can’t remember where I read about it. If anyone knows the source of trick, please post it in the comments. [Update: I now know more about the origin of this trick. I’ll write more in my follow-up post.] Thoroughly shuffle an ordinary…

Kindergarten mathematics

This is a call for help. My son’s kindergarten teacher has invited parents to come in and talk about their careers. I’d like to go in and talk about math. I’d like to have some interactive hands-on mathematics activities for the kids to do. I also want them to be activities outside the typical kindergarten…

More on twin primes and Pythagorean triples

Pat B. wrote a response to my last post on the number 867-5309. In that post I pointed out that: 8675309 is a prime. 8675309 is a twin prime (8675311 is also prime). 8675309 is the hypotenuse of a (primitive) Pythagorean triple: 86753092 = 24602602+83191412. Pat asked: What is the smallest number that would meet…

What is a howicide?

I’m a huge fan of HBO’s series The Wire. Today, while I was watching the 4th episode of season 4, I saw a curious word on the strap hanging around Sgt. Landsman’s neck: HOWICIDE. At first I thought this was a mistake or an easter egg. Why would they misspell homicide? But then I quickly…

Infinite hat problems (solutions)

Yesterday I stated four hat problems. Today’s post contains the solutions to those problems. 1. Alice and Bob are wearing hats. The hats are either red or blue. They can see each other’s hats, but not their own hat. They are tasked with guessing their own hat color. If either person gets the color right, then they…

Infinite hat problems

I got back from MathFest yesterday after a long 3-leg red-eye trip across the country. It was a great meeting. It is always fun to hear some good talks, visit a new city, and see old friends (and meet another math blogger). The first talk that I attended was given by Alan Taylor: “Predicting Values of…