Fun Math Reviews!

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.

There’s some eery numerology associated with 9/11.

www.theforbiddenknowledge.com lists a number of interesting facts, mostly around the events surrounding September 11, 2001 and the number 11. Here are just a few of them.

• The date of the attack: 9/11 - 9 + 1 + 1 = 11.
• Each building had 110 stories.
• After September 11th there are 111 days left to the end of the year.
• September 11th is the 254th day of the year:  2 + 5 + 4 = 11.
• State of New York - The 11th State added to the Union.
• New York City” has 11 letters.

Other web-sites exist with numerology studies of 9/11. Google for the words numerology September 11 and you’ll ind quite a number of such sites.

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.

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.

Well, this post is not so “mathy.” It’s about anagrams, which are permutations of the letters of one or more words, and about a fun site to play with generating anagrams.

If you take the letters of my name, Sol Lederman, and rearrange them one of the many possible phrases is this post’s title, Male Nerd Sol. A less complimentary anagram of my name is Lame Nerd Sol.

Many fun anagrams have been found, many undoubtedly with help from a computer. Some fun ones are:

Desperation = A Rope Ends It
The Morse Code = Here Come Dots
Slot Machines = Cash Lost in’em
Clothespins = So Let’s Pinch
A Domesticated Animal = Docile, as a Man Tamed it
Snooze Alarms = Alas! No More Z’s

The anagrams above, and others, are listed at the Anagram Hall of Fame. Wordsmith.org is also the site where I found anagrams of my name.

Enter your name into the Internet Anagram Server and see what you come up with:

Have Fun,

Male Nerd Sol

How many of you remember doing geometry proofs in High School? How many of you enjoyed writing them? I don’t know about you but I’ve always preferred pictures to words when it comes to understanding how something works.

“Proofs Without Words: Exercises in Visual Thinking” by Roger B. Nelsen is a wonderful book that provides visual insights into how one might go about proving mathematical theorems. The Pythagorean Theorem has always been a mystery to me. How are the squares of the sides of a right triangle related to its hypotenuse? “Proof Without Words” has five clever illustrations that guide readers in writing their own proofs.

If you ever doubted that algebra and geometry were related, the diagrams demonstrating how to compute sums of series will produce aha! experiences.

Writing proofs when one is guided by visual cues is a much more fulfilling endeavor than stringing together dry facts from memory. This book delivers much fulfillment in exploring theorems in geometry, algebra, trigonometry, sequences, and other aspects of Math.