Friday, May 29, 2009

7up Math

Lisa and Marguerite inspired this one. Their chocolate math triggered the memory banks. I ran into this trick a while ago. I'm not sure why Hershey's and 7up are putting out math puzzles. (Geek bait?) The question is, how does it work? This page has been up for a while so googling it is cheating. Don't even think about it. Let the problem burn a little.

Thursday, May 28, 2009

Chocolate and Math 2

I'm glad I can safely combine my two addictions: chocolate and math. British Psychologists at North Umbria University have conducted a study that suggests flavanols present in chocolate (especially dark, my favorite) boost your ability to do certain mathematical tasks. Here's the article in the Telegraph.

pic by mararie

Wednesday, May 27, 2009

Geek of the Week: Ken Colangelo

I have received my first ever geek-resumé. It came via email about a week ago. It almost knocked the slide-rule right out of my shirt pocket. Here are the contents of that message.
I’d like to nominate myself.

In my spare time at home (spare time mind you) I’ve been creating code to generate optimized 3D models of Menger sponges.

I used to use huge amounts of CPU time on the VAX at CCSU as a student exploring strange attractors, Julia sets, cellular automata and n-body gravitational simulation.

They even gave me a degree for it.

This rendering I found hangs in my bathroom. 4th level Menger sponges…for the bathroom…ha!
This, combined with my frequent and popular (?!) emails about when to see the ISS passing over and my geektastic panoramic photography I think puts me in the running.

Also, I got my first paying computer job when I was 9. Seriously. I used those monster 8-inch floppy disks and installed CPM on old 8088 computers.

I’ve got a goofy picture of me covered in electrodes and another wearing safety goggles and a breather if you need them for my geek-of-the-week portrait.

I’ve got my fingers crossed.

He had me at Menger sponges, but he throws in a follow up email just to make it hurt.
I’m a rabid Scrabble player.
N.S.A.* member number 602852
*National Scrabble Association

Tuesday, May 26, 2009

The Brain and Math

Christia sent me this interesting article on new psychological research done on math. Blow it up and read it. You're a mathematician whether you want to be or not. Embrace the inner geek.

Monday, May 25, 2009

The Institute of Figuring

This is one of the more bizzare websites I've stumbled upon. The kelp-like exhibit you see above is actually a collection of crocheted hyperbolic planes residing at the Institute for Figuring in California. Here's their statement of purpose.
The Institute For Figuring is an organization dedicated to the poetic and aesthetic dimensions of science, mathematics and the technical arts.
The institute is kind of hard to describe. They have a lot of online exhibits. One I thought Jesse might like is called Philosophical Toys. They also will teach you how to crochet one of those cool hyperbolic planes. Time to get out the knit sticks!

Friday, May 22, 2009

Chocolate Math

Marguerite and Lisa sent this to me yesterday. Hersheys has got a way to figure out your age without you even having to tell how old you are. How do they do it? By chocolate math! Below is the email:
Don't tell me your age; you probably would tell a falsehood anyway-but the Hershey Man will know! YOUR AGE BY CHOCOLATE MATH

This is pretty neat.

It takes less than a minute .
Work this out as you read .
Be sure you don't read the bottom until you've worked it out!
This is not one of those waste of time things, it's fun.

1. First of all, pick the number of times a week that you would like to have chocolate (more than once but less than 10)
2. Multiply this number by 2 (just to be bold)
3. Add 5
4. Multiply it by 50 -- I'll wait while you get the calculator
5. If you have already had your birthday this year add 1759 ..
If you haven't, add 1758.
6. Now subtract the four digit year that you were born.

You should have a three digit number
The first digit of this was your original number
(i.e., how many times you want to have chocolate each week).
The next two numbers are
YOUR AGE! (Oh YES, it is!!!!!)
My answers as I worked through were
1) 3
2) 6 (multiplied by 2)
3)11 (added 5)
4) 550 (multiplied by 50)
5) 2309 (added 1759)
6) 342 (subtracted 1967)
Hersey Man, how do you do it!
Let's let the number of times I eat chocolate a week be c. Here's what Hershey Man does with my number.
1) c
2) 2c
3) 2c+5
4) 50(2c+5)
5) 50(2c+5)+1759
6) 50(2c+5)+1759-birth year

Now let's rewrite this expression using the distributive property and then combine some like terms:
50(2c+5)+1759-birth year = 100c+250+1759-birth year = 100c+2009-birth year
Look at the first part of 100c+2009-birth year. Multiplying any single digit number by 100 moves the digit from the ones to hundreds place. That is why the number of times you eat chocolate a week ends up in the 100's place.
The second part of the expression, 2009-birth year, simply calculates your age.

A couple of things. Chocolate math only claims to work in the year 2009, but can be easily updated next year by having people add 1760 or 1759, instead of 1759 or 1758. Also, if you are over one hundred years old, you'll break chocolate math. A woman that is 105 and eats chocolate 4 times a week will be told by chocolate math that she eats chocolate 5 times a week and is 5 years old.

Thanks Marguerite and Lisa!

pic by cursedthing

Thursday, May 21, 2009

Math and Dishware

This page of the CB2 catalog was calling my name. I'll let you guess why. "Excuse me, miss, do you have those in a hexagon?"

Wednesday, May 20, 2009

Geek of the Week: Vadim Korf

Vadim wins Geek of the Week for solving one of the blog problems I wasn't able to solve. Not only solving it, but providing one of those elegant solutions that leaves you saying, "Of course, how come I couldn't think of that?" I hope you enjoy it as much as I do. Here's the problem:
A town creates a committee of six people to solve a new math problem. In the town, everyone is either a friend or an enemy. Prove that there are at least three friends or three enemies on the committee.
And here's Vadim's proof.
Six people: A, B, C, D, E, F

Two kinds of relationships: X, Y
---- r(A,B)=X means A and B have relationship of type X.
---- r(A,B,C)=X means that r(A,B)=r(A,C)=r(B,C)=X

We have to prove that we have at least one r(P1,P2,P3)=X (or Y), where P1,P2,P3 could be anyone from {A, B, C, D, E, F}

Consider A (anyone). It has a relationship of type X (could be either friend or enemy, whichever has a bigger count for A) with at least three other guys, for example B, C, D (and possibly E and/or F as well), so r(A,B)=r(A,C)=r(A,D)=X

If r(B,C)=X then r(A,B,C)=X
If r(B,D)=X then r(A,B,D)=X
If r(C,D)=X then r(A,C,D)=X
If neither 1, 2, or 3 is true, then
r(B,C)=r(B,D)=r(C,D)=Y, then r(B,C,D)=Y
If you are not picking up on his notation, basically he's saying: consider any person in the group of six. That person has a relationship with 5 other people. He/She is either friends with 3 or more people or enemies with 3 or more people. That gives you two cases. The following proof will work in either case, so we just have to look at one. Assume that A is friends with B, C, and D. Vadim has given us a diagram to help visualize the argument. The red line between any two people means they're friends.
Consider the relationship between B and C, if they are friends, we have the picture. (Note: the green lines represent that the relation between them is unknown.) So A,B, and C are all friends. Therefore, there are three friends on the committee. In fact, the same is true if either BD or CD are friends. So what about if BC, CD, and BD are all enemies? Here's Vadim's picture. Remember the red lines represent friendship and the blue lines represent enmity. (Note: ignore the 4. Too lazy to edit it out.) But then B, C, and D are all enemies, so we have at least three enemies on the committee. All done.

Tuesday, May 19, 2009

Mathematical Poetry

I found a mathematical poetry blog currated by Kaz Maslanka. The equation above is one of many interesting examples in which the language of mathematics is used to articulate a relationship between poetic constants: life, love, affection, sacrifice, and relationship.

Monday, May 18, 2009

Missing Algebra?

Coming down after your intermediate algebra final? Don't know how you are going to fill up the summer hours without all the homework problems? YofX is here to help. Here's a problem to both reinforce and extend your algebraic superpowers.
Given distinct positive real numbers, x,y,z such that is true. Write x,y,z in increasing order from left to right, and justify your answer algebraically.
Problem stolen from Awesome Math camp's application. Their camps look really fun. I wish I was 15 again!

Friday, May 15, 2009

The Japanese Census

This is an incredible visualization of Japanese census data rendered by Soma. The first thing to understand is the Japanese census is a little different than our own. Here is Soma's description.
Let's jump right into this: Japan has the absolute best census in the history of my known world. Not only does it include normal things like age, sex, and the height of each of your pets, but it also legitimizes the gossipy question of What Are You Doing Right Now? Japan slapped a bunch of people with notebooks and a sacred Numbers Mission: keep a log of what you do during the day, in fifteen minute intervals. And those people did!
I've lost a lot of hours playing with these graphs!

Thursday, May 14, 2009

great pic

Photo taken by Swisscan that I picked up on the Flickr photo group, Everything's Geometry. (My sentiments exactly.) I take the feed. Join up, geek out.

Wednesday, May 13, 2009

Geek(s) of the Week: Academic Support Center

Every semester the tutors in the Academic Support Center miraculously save a good number of my students. I'm not sure how they do it but I know it involves a lot of work. Check out a couple of videos I made for an old course shell project. Who wouldn't want to talk math with either one of these guys? There are plenty of others in the ASC, too. I don't have videos of them, but that is just a matter of time. Keep up the great work!



Tuesday, May 12, 2009

Game of Life

One of Lee's comments on the mandelbrot set led me to something called The Game of Life. I found lots of interesting sites on the game and tons of videos on Youtube. For the uninitiated, these two videos featuring John Conway, the game's creator, are a good intro to the rules of the game. They also help to explain why the game is so interesting.

Part 1

Part 2

This video is my favorite Life simulation. I was thinking someone has to have mapped the patterns of Life into the audio field. And sure enough, you get both the audio and visual representation of the patterns in this video to I think a much more engaging effect.

Monday, May 11, 2009

A mathematical who-done-it?

Sue tells me her oldest has discovered the joy of logic problems. Here's a fun one from the exercises in Enderton's A Mathematical Introduction to Logic:
There are three suspects for a murder: Adams, Brown, and Clark. Adams says "I didn't do it. The victim was an old acquaintance of Brown's. But Clark hated him." Brown states "I didn't do it. I didn't even know the guy. Besides I was out of town all that week." Clark says "I didn't do it. I saw both Adams and Brown downtown with the victim that day; one of them must have done it." Assume that the two innocent men are telling the truth, but that the guilty man might not be. Who did it?
pic by martinmaters

Friday, May 8, 2009

The Improbable Power of Exponentiation

If you are a math teacher, you're probably familiar with this activity.
Get a big sheet of paper and a good paper cutter. Cut the sheet in half, and stack the pieces together. Turn the pile 90 degrees, cut it in half again, and stack the cut pieces again. Keep doing this until you've cut and stacked the sheet 100 times.

If your cutter is really good, so that it cuts a thick stack of paper as quickly and easily as a single sheet, and it takes ten seconds to make a cut, stack the pieces, and position them for the next cut, then you'll be finished in 16 minutes, 40 seconds.

If the paper is 0.1 millimeter thick (about 0.004 inch), like ordinary medium-weight letter paper, then a stack of 500 pieces would be 50 millimeters (about 2 inches) thick.

The question is: How thick will the pile be after you cut and stack the paper 100 times?
Jay sent in a nice website to guide students through the activity. Make sure to look at the answer. Jeff Root does an excellent job at getting one to understand in a physical way 2^100.

Thursday, May 7, 2009

Feather Knot

I ran into this Kate MccGwire sculpture via Drawn!. Kind of reminds me of a knot problem. I'm also thinking, how long did it take to place all of those feathers? I thought Algebra was for the patient.

Wednesday, May 6, 2009

I play Spaghetti and Math Balls

Sue brought this in for her Number Systems class. Her youngest, Nick, is a budding math geek and this is his game. Here's how you play. One moves along the board by answering basic addition and subtraction questions. Each time you pass start you get a meatball. The goal is to be the first one to fill your bowl with six meatballs. Warning: this game can make you hungry. Bon Appetit!

pics from BoardGameGeek

Tuesday, May 5, 2009

The Worst Reason to Study Math

All over China, parents tell their children to stop complaining and to finish their quadratic equations and trigonometric functions because there are sixty-five million American kids going to bed with no math at all.
- Michael Cunningham
A friend forwarded this to me recently. I get sent a lot of quotes and stats of this flavor. I appreciate the aid in trying motivate my students to do math. I'm always looking for another tool in the, "When will I ever use this" battle. However, something about these quotes always seems to turn my stomach. It is either the tatic of fear-mongering or the unanalyzed assumption that the world is ultimately a better place if America continues it's preeminence among nations. I'm wondering what your reactions are? I'm looking forward to some good comments.

Monday, May 4, 2009

May Issue of Wired

I really enjoyed the new issue of Wired. It's put together by guest editor, J.J. Abrams, who I'm ashamed to say I've never heard of, but whose issue as an homage to puzzling. He comes at it from various angles from a feature story of an artist who has been able to stump the best cryptographic minds in the world to an "enigmatrix" of the network connections between math, board games, plot, mysteries, magic code, and game theory. Best of all, it is full of puzzles. Enjoy the one above!

Friday, May 1, 2009

Geek Goodness

Mike Z sent me a really a great link that will allow you to use your geek powers to feed the world. The site is called FreeRice. When you enter FreeRice, you get a math question like 13 * 5. If you answer the question correct, you have just donated 5 grains of rice to the UN World Food Program. You can play as long as you want, so fill up your bowl. If you get tired of math questions, you can always switch to something else like vocabulary words or chemical symbols. Who pays for all that rice? I just filled up a bowl and my sponsors were World Hunger Relief 2008, Unilever, and a private donor. Pretty cool, huh. Thanks, Mike!