Crazy?

Tear a piece of paper in half. Stack up the two halves. Now tear that stack in half and stack up the resulting four pieces. Now tear the stack of four in half and stack again. Imagine continuing to do this until you had torn and stacked 50 times. (Don't actually try to do this - the stack of paper gets too narrow and too thick, and you just can't.)


IF you could do this tearing and stacking 50 times, how tall would the stack be?

Assume that the paper is regular binder paper - about 0.003 in. thick (three-thousandths of an inch thick).

Just for the sake of argument, let me put it this way. The moon is about 250,000 miles away from earth. If someone said to you they thought this stack of paper would reach farther away than the moon would you think they were crazy? Would they be wrong? If they are wrong is it because their estimate is too high or too low? If they are wrong, how far off are they?

Comic Book Math

Tonight while I was at Border's with my friend Tammy, her son Noah was reading DC Comic Books. He found a riddle in one of them and tried it on me.

Here's the set-up. The supervillian Felix Faust tries to lead the readers to believe he can read their minds. He says the following:

"Choose a number between 1 and 50, but don't tell me what it is.
Add 8 to it,
then subtract 5,
then add 7,
then subtract 6,
and then subtract your original number from that result."

He is then able to tell you what number you get as your answer, even though he didn't know what number you started with!! Yikes! Should you fear the mind-reading powers of this supervillian?





But then one of the superheros from the Justice League of America pops up and reassures the reader that supervillian Felix Faust is not really mind reading but that it is just a trick and encourages the reader to try it on friends to see that it works every time.

What number did Felix Faust say you came up with?

Does it work every time?

Would it work for numbers bigger than 50?

Chocolate Math

I often get forwards like the following in my email, and I thought I'd share this one here.

Fwd: Chocolate Mathematics


Just got this and its too cute not to share. :-)

Subject: CHOCOLATE MATHEMATICS?

This is really cool..................and it really works!!!
ENJOY!
Pretty Cool, just give it a try!
You can check your math skills with
the below quiz.

CHOCOLATE MATHEMATICS

This is pretty neat how it works out.

DON'T CHEAT BY SCROLLING DOWN FIRST
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. (try for more than once but less than 10)

2. Multiply this number by 2 (Just to be bold)

3. Add 5. (for Sunday)

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!!!!!)





THIS IS THE ONLY YEAR (2009) IT WILL

EVER WORK, SO SPREAD IT AROUND

WHILE IT LASTS. IMPRESSIVE, ISN'T IT?

Mandelbrot Zoom

This looks like a piece of art but is a mathematical graph. Just have fun with it, though - watching the colors. Math can be beautiful!

Towers of Hanoi

To play the game you see below click here. It's called The Towers of Hanoi. A history of the game is given below the picture. When you go to the site where you can play it, you can choose how many disks to use, and you can also have the computer solve it for you if you get frustrated!



According to Math Around the World by Lawrence Hall of Science :

"The Tower of Hanoi (sometimes referred to as the Tower of Brahma or the End of the World Puzzle) was invented by the French mathematician, Edouard Lucas, in 1883. He was inspired by a legend that tells of a Hindu temple where the pyramid puzzle might have been used for the mental discipline of young priests. Legend says that at the beginning of time the priests in the temple were given a stack of 64 gold disks, each one a little smaller than the one beneath it. Their assignment was to transfer the 64 disks from one of the three poles to another, with one important provisonal large disk could never be placed on top of a smaller one. The priests worked very efficiently, day and night. When they finished their work, the myth said, the temple would crumble into dust and the world would vanish."

Truth or Dare!

Math isn't just numbers and shapes. It's logic too. The riddle in the video clip below from the movie Labyrinth is modeled after puzzles by logician Raymond Smullyan (whose books I highly recommend!!). Would you have figured out the right door to go through? Below the clip is a riddle for you to figure out. Good luck!




You are on a new reality TV show, you are the last survivor. You have dropped by parachute on a very bizarre island in the middle of the Pacific. There are two types of people living on this island, Northerners, who ALWAYS tell the truth, and Southerners who ALWAYS lie. You will win one million dollars if you can figure out the identity (Northerner or Southerner) of each of three people that you are presented with. If you cannot figure it out, you don't get the money, the program doesn't air, and you're left on the island for life.

The first of the three natives says something, but you don't hear it. The second of the natives says, "The first guy said he was a Southerner." The third native says, "Don't believe the second guy; he's lying. What the first guy said was the truth."

Who's who?

Math by Abbot & Costello

7 x 13 = 28
Right?!

Lou Costello of the comedy team Abbot and Costello can prove this three different ways.
Would you be able to explain to him why he's wrong?!
If not I guess you'll just have to accept that he is right!

Nim Game

To play the version of the game of Nim pictured below, click here. (Here is another interactive applet for Nim.) Nim is an ancient game. There are many ways to play. In some versions the person who takes the last object (or number) is the winner and in other versions that person is the loser. It is thought to have originated in China; the earliest references to Nim in Europe date to the 1400's. It is often played with whatever objects are at hand (pebbles, toothpicks, matches, coins), but it can also be played verbally, without objects, as desribed below.




In order to play Nim verbally, find a partner and choose a number that you will count up to. You also need to choose the maximum amount of numbers you can count off at a time. For example, let's say you and I are playing, and we decide to count to 21. We also decide we can say up to three numbers at a time. I might start by saying: "1, 2, 3," and you might then say "4, 5." I might follow up with "6," and you might say: "7, 8, 9." We could continue in this way until we got to 21, and the person to say "21" loses the game.

This is a great game for a road trip, and there is a very straightforward strategy for winning every time (no matter what the ending number or the maximum amount of numbers chosen). Can you figure out the strategy??

Impossible Triangle & MCE

This object is known the Penrose Triangle or Penrose Tribar, after Sir Roger Penrose, the mathematical physicist (and recreational mathematician who created it. Dutch artist M. C. Escher was interested in mathematics and used this impossible mathematical shape twice over to create his lithograph "Waterfall" in 1961. Can you see where and how it is used? After figuring that out, you might want to check out the wild video on YouTube posted below Escher's work.

Mind Reader 2

Check out the Flash Mindreader Page and see if they really can read your mind!

(At the site, if you scroll down, you'll see they've provided a place for you to do your work so that you don't even have to do it in your head!! How's that for a deal?)

The image at left is a lithograph done in 1935 by artist M.C. Escher, much of whose work uses mathematical ideas.

Mind Reader 1

If you want this guy to read your mind click on http://www.digicc.com/fido/

See if you can stump him. You might want to use your calculator to that you can work quickly and accurately.