Math Is Fun Forum

I've written a paper on beauty in mathematics for my English 101 class that uses the Fibonacci sequence to show why I feel math is an art and not a science. I'm wondering if anyone would be willing to look it over... If so, what's the best way to make a copy available to read? Is there a way to upload an attachment or do I have to give out my email? It's currently saved as a word (2003) file.

Thanks in advance.

Everyone on at my favorite forum (this one) has some special skill that they contribute. I've thought long and hard about what mine could be, I'm not especially good at math (although I very much enjoy it), I have very little patience, and I'm not particularly level headed. But I do read a lot, and mostly math books at that. So I thought I could start reviewing the books I read, and my reviews might serve some purpose to someone.

This is a trial run. I'm starting with a classic book that (hopefully) many of you read, that way you can send all sorts of feedback my way. I'll keep posting reviews until someone asks me to stop. If there's a book you want me to review, let me know. If you feel that my writing style is no good, let me know. If you have something to add, or grammar correction, of a review of your own, please post it.

Also, a question for the mods, as time goes by and I have another review to add, should I edit this post, or post a new one?

With out further ado (I really am long winded, aren't I)....

-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

Flatland
By Edwin A. Abbott

Math Quality: 8/10
Readability: 9/10
Overall: Must Read!

     I know it might be a bit cliché to say it, but Flatland really is a really great book. It was written in 1884 but is still relevant in many ways. Equal parts cultural commentary and math book, Flatland is a fictional story about a square (naturally named “A. Square”) and his interactions with a sphere from “spaceland.”

     Being a flatlander, A. Square lives only on a two-dimensional plane, there is no such thing as “up” or “down.” His interactions with the sphere open his mind and the reader’s mind as well. As he starts to understand the third dimension, we may begin to understand the fourth. Dimensional analogies quickly give way to religious metaphors, but the mathematical content is contained. It is completely devoid of any formulas or equations, which makes it a pretty good gateway math book (use it to get your friends hooked on math! What could be better?)

     Being an older book, it does have some clunky qualities, and depending on your reading style, you might consider it to drag in spots, but any shortcomings it has due to age are very much balanced by the classic quality it possesses. It’s also very interesting in a historical context (consider its horrific treatment of women as a satire of Victorian age society). It's quite amazing that as a reader you eventually find yourself caring and rooting for geometric shapes, Who would have thought? Geometry lovers will smile continuously while reading this book, geometry haters might find out geometry is not actually all that bad. A powerful mixture of quaint and profound, Flatland has something to offer for all ages.

     NOTE: I’ve noticed that there’s an “Annotated Flatland” as well as an “Illustrated Flatland” I have not read either.

The mutilated chessboard problem is a very popular classic math puzzle. If you're not familiar with it, google "mutilated chessboard" and read the proof as to why it's impossible, it's pretty cool. Essentially it boils down to the question, "If two opposing corners of a chessboard are removed, can the mutilated board be completely covered with 31 dominoes in such a way that each domino covers 2 squares?"

Let's discuss variations on this problem here!

Variation 1: Consider an 8x8 chessboard with one corner missing (so a total of 64-1=63 squares). Can it be covered with 21 triominoes (dominoes that are 3*1 squares instead of the traditional 2*1)? What if the triominoes are in an L shape instead of a line?

Board with one corner missing:
______________
|_|_|_|_|_|_|_|_|
|_|_|_|_|_|_|_|_|
|_|_|_|_|_|_|_|_|
|_|_|_|_|_|_|_|_|
|_|_|_|_|_|_|_|_|
|_|_|_|_|_|_|_|_|
|_|_|_|_|_|_|_|_|
|_|_|_|_|_|_|_|                                                __
               _____                                              |_|_
triomino: |_|_|_|          trinomino (L variation):  |_|_|

Based on playing around with pictures my suspicions are no, a board with a missing corner piece cannot be covered, but I lack a proof.

So go ahead, post your variations here!

(PS: anyone who wants to produce some legitimate pictures as apposed to my sloppily typed one is more than encouraged to).

I'm teaching an accelerated math class of 9 sixth graders. Today we talked a little bit about googol and googolplex, but I wanted to follow up with something else next week. So i've googled googol and looked at the info, but I can't find anything about practical or mathematical applications.

Does googol have a purpose or is it just interesting because it's so big? It seems odd that in popular culture it's better known than e but has less of an impact on mathematics and the world in general.

So I guess my question is, "why do I care about googol?"