Welcome to this week’s Math Munch!

About a month ago I ran across an article about Abraham Lincoln and math. Lincoln is often celebrated as a self-made frontiersman who had little formal education. The article describes how two professors from Illinois State University recently discovered two new pages of math schoolwork done by Lincoln, which may show that he had somewhat more formal schooling than was previously believed. The sheet shows the young Abe figuring problems like, “If 4 men in 5 days eat 7 lb. of bread, how much will be sufficient for 16 men in 15 days?” Here are some further details about the manuscript’s discovery from the Illinois State University website and a high-quality scan of Lincoln’s figuring from the Harvard University Library.

Lincoln is also known for his study of Euclid’s Elements—that great work of mathematics from ancient times. Lincoln began to read the Elements when he was a young lawyer interested in what exactly it means to “prove” something. Euclid’s work even made a brief appearance in the recent movie about Lincoln. Thinking about Lincoln and math got me to wondering about how our presidents in general have interacted with the subject. Certainly they must all have had *some* kind of experience with math! In my searching and remembering, I’ve run across these tidbits about Ulysses S. Grant, James Garfield, and President Obama. Still, my searches haven’t turned up so very much. Maybe you’ll keep your eyes open for further bits of mathy presidential trivia?

Next up, check out these math problems about blinking on a wonderful online resource called Bedtime Math. Every day, the site posts a few math problems that parents and children can share and ponder at bedtime—just like families often do with storybooks. Bedtime Math was founded by Laura Bilodeau Overdeck. She is involved with several math-related nonprofits and is the mother of three kids. Bedtime Math grew out of the way that Laura shared math problems with her own children. A few of my favorite Bedtime Math posts are “You Otter Know” and “Booking Down the Hall“.

Today’s Bedtime Math is titled “Space Saver” and contains some problems about hexagon tilings and our mathematical chum, the honeybee. Here is today’s “big kid” problem: *If a bee builds 5 hexagons flush in a horizontal row, how many total sides did the bee make, given the shared sides?* I hope you find some problems to enjoy at Bedtime Math. You can sign up to receive their daily email of problems on the righthand side of the Bedtime Math frontpage.

Did you know that people blink differently when they lie? I’ve been thinking a lot these past few weeks about frauds and fakes as I’ve worked with some teacher friends on this year’s PCMI problem sets. PCMI—the Park City Math Institute—is a math event held each summer that gathers math professors, math teachers, and college math students to do mathematics together for three weeks. It all happens in beautiful Park City, Utah. The first week of PCMI coincides with the Fourth of July, and the PCMI crew always makes a mathy entry in the local Independence Day Parade!

The theme of the high school teachers’ program this year is “Probability, Randomization, and Polynomials”. The first problem set introduces the following conundrum:

Suppose you were handed two lists of 120 coin ﬂips, one real and

one fake. Devise a test you could use to decide which was which.

Be as precise as possible.

If you understand what this problem is all about, then you can understand my recent fascination with frauds! Over to the left I’ve shared two sequences I concocted. One I made by actually flipping a coin, while the other I made up out of my head. Can you tell which is which?

For more sleuthing fun, check out this applet on Khan Academy, which challenges you to distinguish lists of coin flips. Some are created by a fair coin, others are made by an unfair coin, and still others are made by human guesses. This coin-flipping challenge is a part of Khan Academy’s Journey into Cryptography series. You should also know that the PCMI problem sets from previous years are all online, filed by years under “Class Notes”. They are rich with fantastic, brain-teasing problems that are woven together in expert fashion.

And finally, to go along with your Bedtime Math, how about a little bedtime poetry? Check out the video below.

Sweet dreams, and bon appetit!