Tessellate

A tesselation is a tiling of the plane so that there are no gaps or overlaps - like a tiled countertop. M.C. Escher used tessellations in much of his work. Some were pure tessellations, like the first picture below, others used a tiling that changed into something else, like the second and third pictures below. The following images are his works (for more see the official M.C. Escher site).

Shodor has a great interactive website where you can make your own tessellations with the help of a Java Applet. I used it to make the tessellation at the top of this post. You can change colors and can choose to begin with a triangle, rectangle or hexagon and can alter these shapes using their sides or corners. I started with a hexagon. The computer helps you alter them in ways that will fit together. Have fun!

Who is Your Role Model?

WHO IS YOUR ROLE MODEL?

Try this without looking at the answers......

Please don't look at the comments section until you do it, you'll love it I promise........no peeking?

GET A CALCULATOR (YOUR COMPUTER HAS ONE ON IT)

1) Pick your favorite number between 1-9

2) Multiply by 3 then

3) Add 3, then again multiply by 3 (I'll wait while you get the calculator....)

4) You'll get a 2 or 3 digit number..

5) Add the digits together

Now click on "comments" ..............

Note: I just got this email tonight - from a friend who claims not to like math! For all the people who say they don't like math it's amazing how many emails like this are circulating around out there!

MatheMAGIC

Click HERE to see a show by MatheMAGICIAN Arthur Benjamin.

Gifted?

Looks can be deceiving! Robin's REAL gift is with mathematics rather than with presents.

Click here to see her in action.

Can you figure out how she does this?

If you are in my Math 20 class and doing this for extra credit, see below for directions:

This is the final extra credit project for spring 2009. Try the trick. It should work every time. If you try it, and it isn't working, then you are not following directions correctly, so try again until you are able to follow the directions correctly. Then try it a few times to get a feel for how it works. Try to figure out what is going on. One approach is to look for a pattern. Can you figure out what gift she will say even without doing the math? What is she doing to make it work each time? A deeper question, that you need to answer in order to get all 10 points, is "Why does this work?" This is due on Thursday, April 23 at the beginning of class. Turn it in to my desk as you come in. GOOD LUCK!

Where Do I Stand?!

Many optical illusions have mathematics at their foundation. Speaking of a foundation, where is the one in this image? Some optical illusions have their roots in the "impossible shapes" created by mathematicians Roger and L. S. Penrose, as can be seen in the work of M. C. Escher who frequently used these shapes as a basis for his art. Click here to find an optical illusions slide show.

Results of Division by Zero

I have unsuccessfully searched for the creators of these. (The first and third are slightly altered forms of the originals.) Please let me know if you have any copyright information so that I can give credit to the artists.