Tag Archives: balloons

Alphametics, Hyperbolic Crochet, and a Puzzle Contest

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!

Purple hyperbolic plane

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!

Bon Appetit!

Balloons, Numbers, and Mathemusic

Welcome to this week’s Math Munch!  We’ve got a full plate for you.

Vi Hart and Balloon Art

Vi Hart is a “recreational mathemusician,” which means she spends a lot of her free time making math, music, and art of all kinds.  She is best known for her “doodling in math class” videos, but her website is full of cool and creative projects.  This week we’re featuring Vi’s balloon art. There are lots of cool pictures and instructions to make your own balloon creations!

Landon Curt Noll

Next up, Landon Curt Noll is a number theorist, computer scientist, and astronomer who does and makes all kinds of cool things.  Three different times, he discovered the largest prime numbers anyone had ever found!  Here’s a link to his list of curious patterns in the prime numbers.  In another venture, Landon wrote a neat little program that tells you the English name of a number.  How do you pronounce 1,213,141,516,171,819?  Give it a try.  I know million, billion, trillion, quadrillion, and quintillion, but what’s after that?  Check it out: Landon lists the first 10,000 powers of ten!

Finally, the connections between math and music often inspire awesome creations.  Here’s a beautiful video by Michael John Blake in which he converts the digits of pi to notes, and we get to hear what pi sounds like.

Here’s a similar video by Lars Erickson who wrote an entire symphony based on the idea.  “The Pi Symphony” also includes the sound of e, another important math number which is about 2.71828…

Bon appetit!