Last Math Monday: Conway’s Game of Life
Last Monday we learned Conway’s Game of Life, create mathematician John Conway, who created an enormous body of highly original mathematics based largely on his insightful study of puzzles and games.
Here are some interesting Life patterns:
Last Monday we learned to count the number of ways to rearrange the letters in the word STOP. Six of the ways make words — STOP, TOPS, POTS, POST, SPOT and OPTS, but if you count all the ways there are to put the four letters in a row, you will find that there are 24 different orders, which mathematicians call permutations. Permutations are not usually taught in math class until college, but anyone who can add and multiply can learn the basics. Besides, rearranging words is fun!
Here’s the slide show from the event, and the video replay.
Go deeper. Here is a catchy song that helps you learn the formula for counting permutations and combinations. The examples are good, the rhymes are clever, but unfortunately it doesn’t explain why the formulas work.
Here’s a good explanation of why the formulas for permutations and combinations work.
https://medium.com/i-math/combinations-permutations-fa7ac680f0ac
Discover the anagrams in your name. Did you know that the letters of CORONAVIRUS rearrange to spell CARNIVOROUS? Or that CLINT EASTWOOD rearranges into OLD WEST ACTION? Discover the anagrams hidden in your name by Googling the Internet Anagram Server.
In this session we made up Bongard Problems — logic puzzles named for Russian computer scientist Bongard, who included many of these puzzles in his 1967 book Pattern Recognition.
Here are a couple Bongard problems that participants invented during our session. The question for each picture below is what do the objects on the left have in common that makes them different from the objects on the right. Scroll to the end of this email for answers.
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Further puzzling
Math writer Alex Bellos presents several Bongard Problems
Gödel, Escher, Bach, by Douglas Hofstadter
The nature of consciousness, as explored through art, music, math, DNA and other lenses. By Indiana University cognitive scientist Douglas Hofstadter. Hofstadter uses Bongard problems to illustrate the immense subtlety of pattern recognition — human or otherwise. His graduate student Henry Fondalis took up the challenge of writing a computer program that attempts to solve Bongard problems — a challenge that was out of reach when Bongard first posed his problems, and remains difficult for computers.
Research on the Bongard Problems
Article by Henry Fondalis.
https://www.foundalis.com/res/diss_research.html
Index of 333 Bongard Problems, including all of Bongard’s original problems, and problems by Henry Fondalis, Doug Hofstadter, and many other people.
https://www.foundalis.com/res/bps/bpidx.htm
About Math Monday
Invite your friends! I started Math Monday as a weekly online event to give families a way to learn together at home by playing fun math games. Activities are aimed at kids aged 6-12, and are fun for adults as well as kids. Sign up to get weekly invites here: http://mathmonday.net
— Scott Kim, Chief Puzzle Officer
Answers
Quick reminder: Our next Math Monday will be tomorrow Tuesday, May 26 at noon PST, not today, because of the Memorial Day holiday. I hope you many of you get to enjoy a day outdoors with your families.
Get ready for magic! Our guest host Spencer Bowen will show us a mathematical magic trick. Then he’ll give us a puzzle involving colors and counting.
CLICK HERE on TUESDAY at NOON to join Math Monday.
Be sure to bring: about 20 each of 4 colors of stackable objects, like Lego blocks, poker chips. Or if you don’t have those, bring four colored pencils and some blank paper.
And if you like magic & math, check out these mathematical magic tricks. The best part is that knowing how the tricks work only makes them more interesting.
Parents: plan on sticking around for the event so you can play these games with your kids. If you can’t make the event, no worries — I send a replay to everyone after the event.
Math Monday is a weekly online event that gives families a way to play fun math games at home, using things you have around the house. Activities are aimed at kids aged 8-14, and are fun for adults as well as kids. If you want friends to invite others to join Math Monday, send them this link: http://mathmonday.net
— Scott Kim, Chief Puzzle Officer
Color Counting
Last Monday we learned to count to 100, and even 1000 on our fingers, and I showed what counting in binary sounds like on the piano. The trick is to let some fingers stand for numbers bigger than 1, so that when you raise several fingers, they can add up to a much bigger number.
Here’s the slideshow from the event. And here’s a video replay of the event.
Further Finger Math
Flash Anzan demonstration. Blindingly fast mental calculation using an imaginary abacus.
Short documentary video on Flash Anzan.
Article by math journalist Alex Bellos:
Abacus basics. How the soroban (Japanese abacus) works.
Abacus demo. A young girl adds big numbers superfast. Good demonstration of what fluent abacus looks like. The abacus is still taught in much of Asia, and there are schools all over the world that teach it.
Chisenbop lesson. The Korean system of using your hands as two columns of an abacus. Nice demonstration of the basics.
Chisenbop on Johnny Carson. A young chisenbop expert impresses Johnny Carson with adding numbers on her hands.
Finger multiplication — on Mathologer. How to multiply numbers between 6 and 10 on your fingers. And this being Mathologer, how to extend the technique further, into negative fingers and beyond. By the droll mathematician/juggler/ambigrammist Burkard Polster
How high can you count on your fingers? Lesson by James Tanton, wonderfully animated by TED ED. Covers the same topics as my Math Monday.
Vi Hart counts in binary. The mathemusician Vi Hart adds stylish hand dancing to counting in binary on your hands. Makes counting look cool.
Replays. Last Monday we learned to play the game of Nim, and the strategy that lets you win every time. Here’s the slide show from the event, and the video replay.
Teach it yourself. For tips on teaching Nim, see this fabulous video and lesson plan by math educator Dan Finkel.
Go deeper. There’s a clever winning strategy for general Nim, which relies on the base 2 representation of numbers. Watch this video from the ever-charming James Tanton. It’s substantial mathematics, but if you understand base 2, you can follow it.
Here’s the slide show from the event, and the video replay.
Last time on Math Monday: Finger Twisters
Last Monday we played finger-twisting math games that explore symmetry, permutations, and problem solving. We learned the International math salute, explored symmetry by crossing our arms the wrong way, twisted our hands 720° while balancing a glass of water on our palm, drew different shapes in the air with our two hands at the same time, and ended with a trick involving two pen caps.
Here’s the slide show from the event, and the video replay.
Go deeper. Here’s James Tanton, creator of the Global Math Project, demonstrating the International Math Salute.
The cup-balancing arm-twisting movement is featured in Binasuan, a folk dance from the Philippines that is traditionally performed with full goblets of wine.
https://www.youtube.com/watch?v=o5RN2P-0D3w
Here’s a video that explains the tricky move in the 2 pen-cap trick (you can also use two wine corks, two rooks, or two chapstick tubes):
https://www.youtube.com/watch?v=1vnLa-5vml0
Here’s the slide show from the event, and the video replay.
I showed my favorite family math games, and we played some of the games together as a group.
Start your own family game night
Looking for ways to keep math fun in your family? One of the best things you can do is play math board games as a family. It’s fun, it connects your family, and it helps develop a love of mathematical thinking. Yes, playing games with your kids is as important for math literacy as reading books with your kids is for language literacy.
So how do you make math games part of your family culture? Here’s how:
Math Game recommendations
Here are my favorite math games — games that both kids and parents enjoy, that are both fun and educational.
Math Dice. Buy. For teachers. What numbers can you make with 3 dice?
Set: Buy. For teachers. Addictive game of visual logic. Our family favorite.
Rush Hour: Buy. For teachers. Slide the cars to escape grid lock.
Prime Climb. Buy. For teachers. Move from 1 to 101 by multiplying & adding.
Santorini. Buy. For teachers. Simple rules, deep strategy, beautiful building.
Pattern Blocks. Buy. For teachers. Endless fun making 2d patterns.
Geometiles. Buy. For teachers. Build 3d shapes. Better than Magnatiles.
Other lists of recommended math games
Big list of Mathematical Board Game from Mind Research
Fun Math Board Games from Bounce Back Parenting
