## Sneak peek: People’s Math Directory

As the regulars here know my passion is all about making Math fun and accessible to as many people as possible. If you're new you can read more about me in my about page. I'm also learning about Internet entrepreneurship as my plan is to have my Internet ventures produce enough income by the end of 2008 to pay my day-to-day living expenses.

Toward the intention of sharing my love of Math via the Internet I've started a new web-site: The People's Math Directory. The site doesn't yet have many listings so I'm not going to create a lot of buzz about it just yet but I wanted to leak information about it here and there to get feedback about the site. The pages linked to from the footer aren't there yet and there are other tweaks I need to make for the site.

The idea behind the People's Math Directory is to provide a forum for people to submit their favorite Math sites, to find neat Math sites, and to review and make comments on the listings. It's a mini community of sorts. While there are other Math directories out there this one is unique for a few reasons:

- The other directories are not easy to get listed in.
- The People's Math Directory will focus on providing listings for Math-related things that are fun and accessible. While I won't turn down research-oriented web-sites for example (and I even have a category for those) my focus when I personally add pages will be to add those that appeal to a wider audience.
- I'll be updating the People's Math Directory several times a week, approving listings as they're submitted. You won't see that turnaround in the other directories.
- The other directories are not designed for interactivity.
- The other directories, except for Yahoo!, don't have a vehicle for paid ads. Listings for educational, non-profit, and non-commercial sites will always be free and Math web-site owners will be able to buy listings.
- I have the passion to make the directory succeed - it's much more than a business venture.

Note that I will be approving all listings and all comments so there won't be any spam nor will there be any non-Math listings.

The People's Math Directory is the second (this blog being the first) of four Math-related web-sites I'm planning to have up and running early in 2008 so keep reading this blog!

So, go check out the directory, share your opinion, and please submit your Math-related blogs and favorite non-commercial Math websites to the directory. And tell a few of your friends.

## Carnival of Mathematics #23 posted

Brent has posted Carnival of Mathematics #23: Haiku Edition at The Math Less Traveled. This edition has 17 posts and Brent wrote a 17-syllable Haiku poem apropos to each post. Wow!

Check the Carnival of Mathematics page from time to time to see who's hosting next or see the end of Brent's Carnival post to learn how to submit your post or for information on contacting Alon about hosting the next Carnival or a later one.

## Some of us have been “blogged”

Blogged.com just added a Math Blog Directory. I never heard of blogged.com before.

Anyway, there are 26 Math blogs listed as of this writing although not every single one is a Math blog. There are even some Math blogs I hadn't heard of that I'm going to check out.

Will it make those of us who got listed rich and famous? I doubt it. But, hey, a link is a good thing and maybe it will bring visitors.

And, if you didn't get listed go and submit your blog.

## Fractions and their decimal expansions: An exploration

I've been thinking about expanding fractions into decimals recently because I want to do some videos that demonstrate mental Math techniques other than multiplication. I've been reading about the Vedic approaches to division and will cover some of those in future posts or videos.

Related to Vedic division and to decimal expansion of fractions is an exploration I want to suggest that should be accessible to many readers of this blog.

Given two integers, a and b, consider the ratio of the two integers, a/b. Determine for any a and b which of the following conditions is true:

- a/b expands to a non-repeating decimal. 5/8 = 0.625 is a non-repeating decimal.
- a/b expands to a repeating decimal with n non-repeating digits followed by r repeating digits.

1/70 = 0.0142857142857142857... It has 1 non-repeating digit, 0, and 6 repeating digits, 142857.

So, n=1 and r=6.

Assuming that 0 < a < b for integers a and b can you come up with an algorithm that determines n and r given a and b?

For example, d(5,8) = {3,0} because 5/8 = .625 has 3 repeating digits followed by 0 non-repeating digits.

Another example: d(15,99) = {0,2} because 15/99= .15151515..., which has 0 non-repeating digits followed by 2 repeating digits.

For this exploration we won't consider an infinite string of 0's or 9's to be repeating digits.

Here are some ideas to guide your exploration:

- Start with a numerator of 1 in all of your fractions when looking for patterns.
- Is there a relationship between the number of repeating and non-repeating digits in fractions when the numerator is 1 and when it isn't?
- Does the prime factorization of the denominator of a fraction give you any insights?
- What do the denominators of all fractions with non-repeating decimal expansions have in common?

I've done some of the exploration of this problem but not all of it. Hopefully this problem isn't harder than I think. Or, if it is then that could be a good thing.

Enjoy.

## Math bloggers: What was your most popular post in 2007?

I hope everyone had a great Christmas.

I'm stealing this great idea from Problogger.

Come join a virtual New Year's Eve party right here and reminisce a little about 2007. Leave a comment with this message stating what your most popular post was, using any criteria you desire. It could be the post with the most views, the one with the most comments, or maybe the one that was linked to the most. You decide. Brag a little about the successes of your blog this year as well, sharing some highlights of the year.

I've already bragged about my most popular post in my State of the Blog address but I'd love to know yours and I bet other Math bloggers would as well.

If I get enough comments - all comments are due by the night of December 30 - I''ll write a new post on New Year's Eve that incorporates all of your comments. If I do write this post everybody who participates will get a little bit of extra visibility for their blog from visitors to my blog. That's a good thing for everybody.

If you write a "year in review" post in your own blog the let me know about it and I'll link to it if I get enough comments to write a post about all of our successes.

Also, while you're thinking about the successes of your blog this year don't forget to heed Brent's call for submissions by tomorrow for Friday's Carnival of Mathematics. I'm not sure what time he wants them tomorrow but send them early in the day to avoid the rush

## 12 days of Christmas: an exploration in counting presents

A popular winter Math problem is the counting of presents given during the 12 days of Christmas.

On the 1st day of Christmas my true love gave to me a partridge in a pear tree.

On the 2nd day of Christmas my true love gave to me 2 turtle doves, and a partridge in a pear tree.

On the 3rd day of Christmas my true love gave to me 3 french hens, 2 turtle doves, and a partridge in a pear tree.

... and so on through day 12.

The problem is to count the number of presents received during the 12 days, and for the truly masochistic, the cost of the twelve day's worth of presents in today's dollars.

I love this type of problem because it's an algebra problem and it involves sums of series, two favorite subjects of mine.

## Optical illusion: the spinning girl

Here's an optical illusion that's making its way around the net and has now become my very favorite illusion. Look at the animated gif below. What direction is the girl spinning in, clockwise or counterclockwise? Can you make her change directions with your mind? Can you see her spinning either clockwise or counterclockwise at will? What is going on?

I don't know who to credit since there are lots of copies of this image around. The first one I found was here. That web-site and a number of others you can find via this Google search claim that this is a right brain vs. left brain test but not everyone agrees about what is going on here. You can read more about lateralization of the brain (the functions of the two sides of the brain) in this Wikipedia article.

If you like optical illusions, check out Might Optical Illusions, a pretty comprehensive collection of such things in a blog format. This site even has an Optical Illusion of The Day Widget so say can effortlessly get your daily fix.

## Review: Martin Gardner’s Mathematical Games CD

I remember riding the subway to high school in the late 1970's. I rode from Manhattan to the Bronx five days a week for four years. When I wasn't chatting with one of the other kids I'd often be reading some "Mathy" thing or working out a Math problem. Yes, I was geeky even back then. A number of my very favorite mathematical excursions came from Martin Gardner's "Mathematical Games" column in Scientific American. Gardner's column ran from 1956 to 1986. Gardner is one of my Math heroes, and I know his writing is enjoyed by many many people who enjoy recreational mathematics. In my opinion, Gardner has done more than anyone to popularize recreational Math in the US.

Over the years I've read a number of Gardner's books and enjoyed many of his diversions. A year ago for my birthday I received a copy of Martin Gardner's Mathematical Games CD, published by the Mathematical Association of America. The CD contains every single one of Gardner's articles in Scientific American. Wow! I was pleased.

## My other blog

Those of you who have read my about page know that I spent 25 years in high tech. A couple of months ago I left the company my brother founded, Deep Web Technologies, to dedicate myself to sharing my passion about Math and to learning about Internet entrepreneurship. This journey is turning out to be a really nice expression of a number of my talents: computers, writing, teaching, and Math.

Just when I thought I was done with high tech, a few weeks ago my brother asks me, the blogger in the family, to start a blog for his industry, federated search. Federated search is the process of finding content in databases that one usually has to fill out search forms to access. Google and the other "crawlers" follow links from web pages to gather content that they then index for later searching. Federated search engines search content live, they search multiple sources at once, and often they search scientific and technical databases that house content that Google doesn't know about. The search technologies behind Science.gov and Scitopia.org are two good examples of what Deep Web builds.

If you want to know more about federated search, or if you want to just see a different persona of mine, check out my new blog: Federated Search Blog. If you know of any librarians or people who follow the search engine industry please tell them about the blog as well. Given how few blogs there are dedicated to federated search and given Deep Web's expertise in this area I'm quite confident that this blog will grow and serve as a valuable resource to the industry.

## Free Sudoku resources for kids

There are zillions of Sudoku web-sites geared toward adults. I've gotten interested in finding Sudoku sites for the little ones, in particular my 6 and 8 year old nieces. While Sudoku is not strictly "about Math" it is a great exercise in logic, it engages kids with numbers and patterns, and if kids aren't careful they might enjoy Math more if they solve Sudoku problems.

I decided I wanted to find free resources, not that I have anything against commercial sources of puzzles. I was also interested in finding sites with more than just one or two puzzles.

Here are a few resources I found:

- Daily SuDoKu for kids has a daily puzzle of varying difficulty plus an archive of puzzles going back a year, including kids puzzles rated easy, medium, and hard. The puzzles can be printed in medium or large sizes along with the solutions.
- MyPuzzle.org has online Sudoku puzzles. The puzzles are randomly generated, they come in selectable difficulties, and they have a timer kids can use to see how fast they can solve them.
- Puzzle choice has some 2x2 and 2x3 puzzles for kids.
- Sudoku Score has large (9x9 divided into 3x3 squares) computer-generated puzzles with four levels of difficulty and an optional clock.
- Ababasoft has 9x9 computer-generated puzzles with one level of difficulty. You can play the games online or download the game to play offline. Please be cautious about downloading this or any program from an unfamiliar sites as unknown software may contain viruses or spyware.