Some fractions are a part of everyday life; dimes, quarters, nickels, hours, minutes, seconds, etc. These are relatively easy to manage mainly because we deal with them so often. Everyone just “knows” that 1/2 is 0.5, and 1/4 is .25, and 1/10 is 0.1; we’ve had it ingrained in us through massive amounts of repetition. I go one step further; I can usually estimate the decimal equivalent of just about any fraction that comes up in my life. Super useful? Maybe not, but it has good show-off value, and I think it’s fun!

Learning the first 12 fractions can make it super-easy to do division in your head and produce answers down to the 10ths or even 1000ths quickly and easily. Let’s take a look:

There you have them, the first 12 fractions for easy memorization. Amaze your friends! Astound your kids! Become even more of a know-it-all than you already are! I joke, but I guess you’d be surprised how often I use these, I know I am.

The Count

Every once in awhile, I come across a video (usually on Youtube, isn’t that where everthing ends up) that quite elegantly illustrates something math-related. I haven’t been collecting them long, but I thought I’d share a couple of them with you all. Please enjoy them as much as I have.

Ah, Mother’s Day. Admittedly, Math isn’t the first thing you think about when scrambling for that 1-800-Flowers phone number (I always forget that one) or that last box of chocolate from the drugstore. However, one of the memories that sticks in my mind most about my Mom is arguing with her about Math during dinner about .9 repeating and 1. Before you think we’re crazy, please keep in mind she’s a Math teacher, and I have some small interest in the subject myself. So here’s to you, Mom. I finally realized you were right some time ago, but don’t think I ever said so.


I didn’t really have any good arguments for my side of the case. What can I say? I was 8 or 9 and saying things like “1 minus 0.9 repeating is 0.0 repeating with a 1 at the end” made perfect sense to me. I also have to say I didn’t listen that much to Mom’s arguments, so I’m not sure she used these following proofs, but I’m pretty sure they should convince just about anyone.

First, there’s simple addition. If you agree that 1/3 = 0.3333(repeating), then:

Now, how could the Count pass up a chance to talk about that most numerically significant time of year, Tax Time!? With lots of talk about rising tax rates and socialism this year, I thought it might be fun and informative to take a look at tax tables from previous years and compare them to recent times.

Using a spreadsheet I found on the internet1, I created a table of tax burdens by year for different income levels. While the tax brackets have seen highs in the 90s percent in the post-war 40s and 50s, and started with lows of 1-7% in the early 1910s, I figured 1970 was a good starting point for modern relevancy. I further pared this information down to just the years after fairly significant changes to the tax codes, as many of the annual lines were very similar. I also chose to use the Married Filing Singly tax table, as it was most often the same as Single, and almost always half the income amounts of Married Filing Jointly for the same tax. Here’s is the resulting data:

• The percentage tax burden isn’t the tax “bracket”, it’s the total amount paid in taxes if your income was at the displayed level. Of course, tax shelters exist, but this is based on “taxable income”, the number you use when you look up how much tax you owe.
• Quite obviously, the 1970s were not a good time to be making money. Yes, home interest rates were in the teens, so anyone who owned a home had quite a nice write-off in the interest they were paying, but good Lord, that’s some high taxes!
• 1988 was a good year to make a lot of money, where people making $100k actually paid a (slightly) higher percentage of their income in taxes than those making 3 or even 5 times as much!

Finally, I notice that only at 1993 do we see a marked rise in taxes, and only for those making $100k or more; it seems that taxes have done nothing but drop since 1970 except for that one year. Of course, things like the Alternative Minimum Tax and changes to Capital Gains taxes change the landscape, making it very difficult to get a clear picture of true tax liabilities.

This is quite interesting! People are never happy paying taxes, but I think it’s refreshing to see we’ve got it quite lucky nowadays compared to our parents, tax-wise. Now, if only we could get that money spent just the way we want it, no? But that’s another topic. I sense a post about unusual budget items! Look for it in the future; right now, I’ve got to go file my taxes.

The Count

1. Historical US Tax Tables

Interested in the data I compiled for the above chart? Here it is:

Happy Pi Day! Yes, it’s that time of year again when the month and day (in the American form of date representation) for those legendary 3 digits 3/14, also known as the beginning of the mathematical term Pi1. Being The Count, however, I’m certainly not satisfied with just one Pi Day each year, or just matching 3 digits of Pi for my festivities. No, I must venture forth to find other Math-related dates to share the joy that is the geeky holiday.


Now, Pi Day comes every year but only in America, as the European version of date display comes Day then Month. Unfortunately, this leaves Europe with no way to put forth 3.14 (note, they use a period (.) instead of a slash (/)), as alas, there are only 12 months. For the most part, Europe seems to be out of luck. After searching several dozen math constants2, and I can’t find any that start with a number from 1-30, and have 2 digits after the decimal that form a number less than 13. Viswanath’s Constant3 comes closest, but it looks like we’ll just have to exclude Europeans from our celbratory antics… No pie for you!

Not so fast! Let’s try not to leave them out of all the fun. I present below some alternatives to Pi day, some of which can even be translated to Day before Month!

We’ll have to wait a bit for these extra-geeky days to arrive, but at least we have today! So, those of you who can celebrate Pi day, run out to your Marie Callander’s or Coco’s, or even the local Denny’s, grab a slice, and enjoy! Save some room for Super Pi Day in a few years though, ok?

The Count

1. Pi – the math constant, not the pastry
2. Math Constants
3. Viswanath’s Constant
4. What kind of pie are you?
5. XKCD on e and Pi

What?! Another birthday so soon!? No, you haven’t lost 6 months of your life, and The Count isn’t 41… yet! Due to the overwhelming popularity of my Birthday article, it became clear to me that even those people that weren’t born during the awesome year of 1969 would like to be able to see their own age in huge-numbered detail.


After many hours of toil, The Count has made available to you, his loyal reader, a page designed to give you all the joy he felt in seeing his age in Earth years converted to galactically-large numbers of other units. Simply click the link below, and enjoy!

The Count

Have you ever had a problem stuck in your head, and you couldn’t find the answer? I was recently reminded of a problem I first came up with while doing a statistics workbook the summer of my 3rd grade year (yes, my math-teacher mother gave us workbooks to do during summer break… hey, it got results). The book dealt with dice and the probabilities of a 1 showing on a 6-sider, or the sum of 2 rolled dice being 7, etc. but my question had a twist I couldn’t quite solve. Now it’s easy to see that the probability of rolling a 1 on a 6-sided die is 1 in 6, but what probability exists, in rolling 2 dice, of seeing at least one 1 (on either die, or both)?


So there I was, 7 years old and stuck with a math problem I couldn’t solve. Well, what would you do? That’s right, I asked people. Over the next 9 years, I asked math teachers and other adults I thought might be able to help, but no one seemed able to explain it to me. Of course, I could brute force the answer for 2 or even 3 dice quite easily as well (and did), but by that time I wasn’t interested in just the single answer to my problem, but a more general solution for N dice. The difficulty of the problem comes from the “at least one” phrasing. Using discrete math, you could end up having to compute the probability for each of the numbers of dice smaller than your requested count and use alternating subtraction and addition to account for subset solutions and overlap.

Of course, I did come up with (or was given) attempts at a quicker solution. They usually fell into 2 types. The first type was the simplest; since we were rolling two dice, and the probability with 1 die was 1 in 6, the new probability must be 2 in 6. Unfortunately, this easily extrapolates to say that when rolling 6 dice, you absolutely must get a 1, 2, 3, 4, 5, and 6. Anyone who plays Yahtzee can certainly see the flaw there. The second type of false solution came from, at some point, someone recalling some remnant of a college statistics course (the part where previous rolls shouldn’t affect subsequent rolls) and concluding that the answer must be still 1 in 6. This answer also fails to satisfy quickly when you consider more than just 2 dice being rolled. How could the probability of getting at least one 1 when rolling 10 or even 100 dice still be just 1 in 6?

It wasn’t until I reached college and took an actual course in statistics that I found the answer. Fortunately, there’s an easy method. If you ever find a statistics problem that uses the “at least one” phrase, the best bet is to turn it around. What are the odds of not getting any 1s on those dice? As it happens, that’s merely 5 in 6 for each die rolled, multiplied together. In my problem, with only 2 dice, the probability of not getting a 1 is 5/6 * 5/6 = or 25 in 36. Now, since all the other possible results must contain a 1, we’re left with a solution of (36-25) = 11 in 36! This method works for N dice as well, with the probability of getting at least one 1 out of N dice rolled being:

I’m a football fan… well, more specifically the NFL. I hear that colleges other than the one I went to actually have their own teams and that quite a lot of people think that the outcomes of these “college football games” are important, but I never saw the appeal. Anyway, as I said, I follow the NFL. This year, as the season has proceeded, I’ve found myself noticing quite a few long winning and losing streaks occuring this year. With 2 teams reaching 10-0, and a few teams having streaks of 6 and 7 wins (or losses), I decided to track the actual numbers and determine just how abnormal this season is.

Using one of the many available NFL statistic sites, I was able to compile the number of streaks that occured at each of the 10 lengths available at week 11 (which was just completed). Note that only 10 games have been played by each team at this point, and that I ignored the bye week, allowing streaks to continue through the bye uninterrupted. The following are my results:

About two years ago, I got interested in Geocaching1. I call it “organized littering”. Essentially, people have taken the time to hide caches (usually tupperware containers full of bric-a-brac) all over the world. They then log the lat/long coordinates of their stash, and enter them along with a description on the GeoCaching site2. The rest of us use that site to find caches near where we’ll be, and off we go using our portable GPS units to find these little pockets of fun all over the world.

Our family was vacationing in the Pocono Mountains when we starting ‘caching. I had researched several caches in the area, so one day my father, my wife, my son, and I all headed out into the wilderness. We spent all day traipsing around and seriously enjoyed ourselves getting dirty. The locations we found were a little remote and, since it was summer, the foliage was dense enough to block the view of much. When I decided to write about it, I got to thinking how cool it would be to look for caches in exotic locations. So here they are, some of the coolest locations in the Northern Hemisphere to go looking for litter.

Now, I know you’re just going to run out and fly to all these great places just to go find the closest cache, right? Ok, maybe not, but I hope I peaked your interest in Geocaching, it’s a great way to learn about global coordinate systems and geography. The next time you have a free Saturday afternoon or want a reason to take a hike, give it a try.

The Count

1. Geocaching on Wikipedia
2. GeoCaching site