## Is it a triangle or a square?

Purdue Professor of Computer Science Greg N. Fredrickson is an absolute master of geometric dissections, the art and science of cutting up one or more geometric shapes and rearranging the pieces to form other shapes.

One example from Fredrickson’s web-site for his first book, *Dissections: Plane & Fancy*, is the dissection of a regular octagon to a square using only five pieces! This is quite a feat.

Creating these dissections is closely related to the field of tessellations which studies how planes (flat surfaces) can be tiled with geometric shapes.

Fredrickson’s second book, Hinged Dissections: Swinging & Twisting, explores dissections in which the pieces of the figure being dissected are held together with imaginary hinges. When parts of the figure are rotated about the hinges another figure is formed. An extremely elegant dissection is that of an equilateral triangle to a square with only four pieces!

If you want to build your own triangle-to-square hinged model using foamed rubber check out these directions. Be sure to watch the fun animation at the bottom of the page.

## Algebra help is just a click away

www.algebra.com is a great free site for students needing help with their algebra homework. People who enjoy helping others with their algebra homework sign up as volunteer tutors. Students post their homework problems and the tutors answer them, ideally providing an explanation of how they got to the solution.

Some months ago I was quite active in the algebra.com community, having solved and explained 188 problems under the moniker *joyofmath*. After having gotten bored solving the same kinds of problems over and over I started being much more selective, solving the more challenging problems that other tutors were ignoring. That was a very satisfying experience. And, if you think I’ve solved lots of problems, there’s someone with the handle *stanbon *who holds the record for most problems solved - 10,581 to date. Wow!

Algebra.com is easy for students and tutors to use and it even has a nice mechanism for formatting text so that it looks good, even when there are exponents and math symbols involved. So, if you’re needing help or wanting to help algebra.com has something for you.

## Are U.S. area codes random?

I had never given much thought to how area codes were selected. I always assumed they were random three digit numbers that, once upon a time, always had 0 or 1 as their middle digit. This morning I was browsing The Universal Book of Mathematics: From Abracadabra to Zeno’s Paradoxes and read an interesting article explaining how early area codes were determined. Here are some snippets from that article:

North American telephone area codes seem to have been chosen at random. But there was a method to their selection. In the mid-1950s when direct dialing of long-distance calls first became possible, it made sense to assign area codes that took the shortest time to dial to the larger cities. Almost all calls were from rotary dials. Area codes such as 212, 213, 312, and 313 took very little time for the dial to return to its starting position compared, for example, to numbers such as 809, 908, 709. The quickest-to-dial area codes were assigned to the places expected to receive the most direct-dialed calls. New York City got 212, Chicago 312, Los Angeles 213, and Washington, D.C., 202, which is a little longer to dial than 212, but much shorter than others. In order of decreasing size and estimated amount of telephone traffic, the numbers grew larger: San Francisco go 415, Miami 305, and so on. At the other end of the spectrum came places like Hawaii (the last state annexed in 1959) with 808, Puerto Rico with 809, and Newfoundland with 709…

At another time I will review the book - it is a wonderful encyclopedia of mathematical terms and concepts, and it is sprinkled with nice illustrations and puzzles.

## An invitation

Welcome!

Do you love Math? Do you see beauty in mathematical ideas? Do you enjoy solving Math puzzles the way some people enjoy taking cars apart? Do you get lost in excursions, finding patterns and relationships among numbers, symbols, and concepts?

Or, is Math a lot of work for you - not something you would ever associate with the words *joy*, *fun*, or *play*.

Perhaps you're a parent or teacher, wondering how you can motivate your child or your students to view Math as a whole-brain blending of the creative with the logical.

This blog is the expression of a life-long passion that I've had for all things mathematical. My sincere desire is to share articles, reviews, and links to products, services, and web-sites that inspire people of all ages to enjoy Math.

My invitation is this: Help to inspire all of us to see Mathematics as the beauty it is. Share your original content, reviews of products and services that inspire inspiration and enjoyment of all things mathematical. Share your comments and ideas about this blog.

Please leave your comments on this post or contact me via email to discuss publishing your content here.

Thanks,

Sol Lederman

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