Welcome to the first Math Munch of December!
Did you know that SEND + MORE = MONEY? Or that DOUBLE + DOUBLE + TOIL = TROUBLE? It does if you replace the letters with the appropriate digits! These very clever puzzles, where the digits in numbers of addition, subtraction, or multiplication problems are replaced by letters in words, are called alphametics (or sometimes cryptarithms). Mathematician, software engineer, and writer Mike Keith calls them the “most elegant of puzzles” on his page devoted to some alphametics he’s found and created. Check out the “doubly-true” alphametics – puzzles where the words are numbers – and Mike’s alphametic poetry. In this poem, written in what Mike calls “Strict Alphametish,” the last word in each line is the sum of the previous words in that line! Wow!
Next, take a look at these cool objects!
If you draw a line on a hyperbolic plane and a point not on that line, you can make an infinite number of lines parallel to the first line through the point.
These are models of hyperbolic planes crocheted by Cornell University mathematician and artist Daina Taimina. A hyperbolic plane is a surface that is kind of like the opposite of a sphere: on a sphere, the surface always curves in towards itself, but on a hyperbolic plane, the surface always curves away from itself.
Before Daina figured out how to crochet a hyperbolic plane, mathematicians had no durable, easy-to-use models of this very important geometric object! But now, anyone with a little crocheting skill (or a willingness to learn!) can make a hyperbolic plane! Here are instructions on how to crochet your very own hyperbolic plane, and here’s a link to Daina’s blog.
By the way, our favorite mathematical doodler Vi Hart also makes models of hyperbolic planes out of balloons.
Finally, do you like to play with Rubik’s Cubes, stacking puzzles, or other physical math puzzles? Think you could make one of your own? These are some of the entries in the 2011 Nob Yoshigahara Puzzle Design Competition. Here are the winners! The designer of the first-place puzzle won this cool trophy!