# Automatic Envelope

This isn’t something you’d normally find in a math class, but I find it incredibly useful to know how to turn a simple sheet of paper into the envelope you can mail it in. The letter you write goes on one side, and the address and stamp go on the other. Try it and see how you like it!

Because of of all the folding, the envelope is actually quite small when you’re done with it. If you want a regular-size envelope, tape two sheets of paper together to get a big 11×17″ sheet.

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# Kaleidocycles and Hexaflexagons

Kaleidocycles are a three-dimensional paper sculpture you can turn around and round! Flexagons were first created by Arthur Stone at Princeton University in 1939, which were later published in 1959 to the general public in *Scientific American*.

These are simple to make and fun to play with. When I first showed them to my own kids, they immediately made one for each kid in their class, and also stumped the teacher that day when they asked how it worked. Please login or register to read the rest of this content.

The video below is made by Vi Hart, a smart and spunky mathemusician who has made amazing videos about the history of hexaflexagons that are fast-paced and fun.

# Fold a Cube

There’s more than one way to fold a cube. So print out the attachment, grab some tape and sticky notes and we’ll have some fun with geometry! How many different shapes can you use to make a cube?

**NOTE: You’ll want to pause the video when the screen says, “Circle your answers!”** (This is at about the 2:02 mark on the video timer). Wait until you’ve recorded your predictions to view the end of the video so that the fun isn’t spoiled for you.

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# Möbius Strip

Although the Möbius strip is named for German mathematician August Möbius, it was co-discovered independently by Johann Benedict Listing, a completely different German mathematician, but at around the same time in 1858. Weird, right? But that’s not the only strange thing about the Möbius strip. It’s a non-orientable surface. This means it has a path that will take a traveler back to their point of origin. Are you completely confused now? That’s okay! Just watch the video and I’ll explain.

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# Stepping Through a Sheet of Paper

Did you know that you can step through a sheet of paper using just a pair of scissors to help? Does this sound impossible? Well, this is where math and magic come together! Watch the video and I’ll explain.

**NOTE: pause the video after the introduction – at about 0:30 mark on the video timer – so that you don’t learn the answer before you’ve had a chance to think about the solution.**

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# Sizes of Geometry

Remembering and visualizing most shapes is pretty easy, right? An octagon can be a challenge for some (it has eight sides, while the commonly-confused hexagon has six sides). In this experiment, we try to recall and draw some everyday objects such as a quarter, a playing card, and more, at their actual size. What objects around your house can you think of to use and test yourself? Watch to see how I do estimating the size of objects.

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# Freaky Fractals

* Fractals *are new on the mathematics scene, however they are in your life everyday. Cell phones use fractal antennas, doctors study fractal-based blood flow diagrams to search for cancerous cells, biologists use fractal theory to determine how much carbon dioxide an entire rain forest can absorb.

Fractals are in the mountains, clouds, coast lines, central nervous system, flower petals, sea shells, spider webs… they’re everywhere! And the really nifty thing about fractals is that they are not only cool, they’re super-useful in our world today.

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# Pantograph: Early Copy Machines

A pantograph, first invented in the early 1600s, was used to make exact copies before there were any Xerox machines around. It’s a simple mechanical device made up of four bars linked together in a parallelogram shape.

Here’s how it works: by simply tracing an object with the pointer, the pantograph makes a copy larger or smaller depending on which point you attach your pen and pointer.

Some pantographs were adjustable – meaning that they could change their pivot points to adjust the size of the copies.

We’re going to make one of these to see how geometry can really be used in the real world. Are you ready?

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# Graphical Multiplication

The trick looks impressive, so be prepared for jaw-drops when you show this to kids and adults. But can you figure out how it works? I’ll give you a hint: think about how to represent placeholders of powers of 10…

Ok, so now watch the video:

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# Water Drop

You’ll be amazed at the physics of a simple water drop! This water drop was filmed in ultra-slow-motion at 2000 frames per second, and includes an explanation by a local mathematician (in plain, every English, too!).

Here’s a super-fun experiment you can do with a water drop.