Mirror Puzzle

 

 

This puzzle is a practical one; you can solve it with pen and paper, but it's a lot more fun to try this real-world phenomenon for yourself.

 

Imagine you are standing before a small wall-mirror. This is no funhouse mirror; it is perfectly flat, and mounted flush with the vertical wall on which it hangs.

 

How much of yourself do you see in the mirror?

What if you take a few steps backward, away from the mirror? Can you see more of yourself? Less of yourself?

How big of a mirror would you need to see your entire head reflected back at you, at a given distance? How big of a mirror would you need to see your entire body reflected back at you? (Bear in mind: The mirror depicted in the art at the top of this post has not been drawn to scale.)

 

Credits: The original puzzle is Here at i09.

 

Solution: You need a mirror at least half your height to see the entire length of your body. Said another way: It is possible to see twice as much of yourself as the length of any normal wall-mounted mirror. It does not matter how far you stand from the mirror.

 

Hexaflexagons

Hexaflexagons were invented by a Princeton University student in 1939, but Flexagons were introduced to the general public by the recreational mathematician Martin Gardner in 1956 in the first Mathematical Games column which he wrote for Scientific American magazine. In 1974, the magician Doug Henning included a construct-your-own hexaflexagon with the original cast recording of his Broadway show The Magic Show.

Hexaflexagons are folded figures that have more "sides" than the two you can see. This one has six different sides as you flex through them, but three of those are very hard to find. Print out this figure (right click on strip, choose "print") and then carefully cut it out. Follow the instructions on how to fold it (you can use tape instead of glue). Get help from the link below, if needed. Have Fun!


If you can use some help or hints, try Wikipedia.

Mobius Strips

The Möbius Strip

Want to experience something mind-boggling in the next few minutes? Then try this twisty trick!

What to Do

Cut out a strip of paper. Give the strip a half twist and tape its ends together, as shown at right. You have just made a Möbius (MUH-bee-us) strip, a fascinating object created by German mathematician Augustus Möbius.

You can explore the many thing you can do with a Mobius strip Here at the Highlights page, where this image is from.

If you live in the Spokane, Washington area, you can visit the Mobius Science Center. They have moved into the 2nd floor of the downtown library building for the Summer. They will finally be in the power house building overlooking the Spokane River. They have a hands-on display to experiment with Mobius Strips.