# Archive for category Off the Beaten Math

### Today’s Thought on Kinda Big Numbers

Posted by jim in Fun With Numbers, Lost in Space, Off the Beaten Math on June 9, 2012

If you look up at the sky on a clear night away from obstructions and light sources, you will see a beautiful wash of stars. An awful lot of them, right? It has been estimated that a typical human can see a few thousand stars under such conditions with the unaided eye. This is out of the 100 billion or more stars in the Milky Way Galaxy. So, what’s the comparison?

Imagine that for every star you see, there is an entire night sky worth of stars. Now imagine that for every star in your new super-crowded night sky, there’s an entire night sky worth of stars again.

Chances are, you’d still be a little short.

And don’t forget that the Milky Way is just one of over 100 billion galaxies.

### Sorry, It’s Still M*A*S*H

Posted by jim in My Bent Brain, Off the Beaten Math on February 8, 2011

I’m getting a little sick of the repeated announcement (thank you, corporate sports whores at the NFL) that this past Sunday’s game was the most popular TV event in US history. And of course, this is quickly followed by the “fact” that last year’s game is in the number two spot with the finale of M*A*S*H having dropped to third. Here are the numbers that have been swirling around lately:

1. Super Bowl XLV — 111 million viewers (2011)

2. Super Bowl XLIV — 106.5 million viewers (2010)

3. *M*A*S*H** series finale — 106 million viewers (1983)

I guess it helps if you conveniently ignore the fact that while there are an estimated 307 million people in the USA right now, that value stood at a mere 233 million in 1983. So if you look at it in terms of the percentage of people who chose to watch, M*A*S*H beats the pants off of both of them. And no, I am not some manner of disgruntled M*A*S*H fanatic. I thought the original movie was better than the TV show.

### Email Hoaxes and a Little Math

Posted by jim in Off the Beaten Math on October 11, 2007

Recently I received emails from two associates regarding a “get rich quick” scheme. It’s made the rounds before and quite frankly I was surprised to see it poke its ugly head up again. While these hoaxes are mildly irritating, it only takes a moment of thought to determine that they absolutely must be false. Why don’t people think?

The premise of this particular scheme is that Bill Gates has teamed up with AOL to create a new email tracking system. It must be true, the message says, because the author heard it on Good Morning America. In essence, you forward the message to a bunch of people. For every person you forward the message, you receive $24,000. For every person that this group forwards to, you net $23,000, and so on. The author of the message states in closing that there are only two weeks left in the trial period and that he has just received a check in excess of $800,000. In other words, get in on the action now while you still have time.

OK, let’s assume you don’t know anything about urban legends, never heard of Google, Snopes and the like, and are in general, a credulous person. Hopefully, you know a little math. A very simple calculation shows that the scheme is impossible. I don’t know how many people watch Good Morning America, but I’d guess maybe a million or more. Let’s assume only 10,000 actually respond to this. Further, let’s assume that each responder forwards to only 10 other people (in the emails I received, I was one of at least 20 recipients). The second tier will contain 100,000 recipients, and if they do likewise, the third tier will have a million. Even if the fourth tier only forwards the message to one or two persons each, the payout will be an order of magnitude greater than the entirety of Mr. Gates’ fortune.

Duh.

### Euler’s identity

Posted by kemibe in Off the Beaten Math on August 1, 2007

Here’s some stuff about math I never knew until today.

First, a few things I did know, tidbits most of you probably knew as well.

*e*, the base of the natural logarithm, = 2.7182818…*i*is the “imaginary unit,” such that*i*^{2}= -1- The value of π, the artio of a circle’s circumference to its diameter, is 3.141592…

Are these numbers related? On the surface, there’s no reason why thy should be. Yet the following relationship has been proven:

### Euler’s identity

Posted by kemibe in Off the Beaten Math on August 1, 2007

Here’s some stuff about math I never knew until today.

First, a few things I did know, tidbits most of you probably knew as well.

*e*, the base of the natural logarithm, = 2.7182818…*i*is the “imaginary unit,” such that*i*^{2}= -1- The value of π, the artio of a circle’s circumference to its diameter, is 3.141592…

Are these numbers related? On the surface, there’s no reason why thy should be. Yet the following relationship has been proven:

### Cryptography 101

Posted by jim in Fun Is Where You Find It, Off the Beaten Math, Techies & Technology, What The Heck Is That Thing? on July 25, 2007

This week’s NOVA Science NOW on PBS has an interesting piece on the Kryptos sculpture in front of CIA headquarters. The segment does a decent job of showing some of the basic techniques used such as substitution and transposition, in just a few minutes.

I am not a cryptographer but it is an area I have studied a little. It’s a great topic to introduce to my first and second year programming students. Some of them really perk up when we start talking about it. Invariably, someone will ask if I can show them how to “crack” protected software. I always tell them that, although I have the knowledge, it would not be ethical. Some of them give me strange looks at this point.

### 07/07/07: Sometimes a number is just a number

Posted by docbushwell in Doc Bushwell, Off the Beaten Math on July 7, 2007

So last year we had the dreaded 06/06/06, and lo! No apocalyptic beasts appeared in the heavens. This year, it’s our lucky day: 07/07/07!

Seven is considered a “lucky number,” a prime of a magical, mysterious signficance. So where does the source of this luck derive? Why, from the Bible, of course! At least in part. From LiveScience, 07/07/07: Is This Your Lucky Day?

### Good Math, Bad Math, Literal Math

Posted by jim in Off the Beaten Math on May 11, 2007

MarkCC over at Good Math, Bad Math offers up some enjoyable elements from time to time. Between the good and the bad, is there space for humorous literal math?

Yes, it’s final exam time here at the college and I received the following from a colleague (the exam paper is **not** from one of his courses):

I *almost* want to give the guy a bonus point for making me laugh (particularly due to the little “etc.” scrawl at the bottom).

### A-Rod’s projected 2007 stats

Posted by kemibe in Off the Beaten Math on April 24, 2007

After 18 games, or one-ninth of the regular-season schedule, the New York Yankees’ Alex Rodriguez is on pace for these totals (Major League records in parentheses):

Home runs — 126 (73, B. Bonds)

Runs batted in — 306 (191, H. Wilson)

Batting average — .400 (.426, G. Sisler)

Slugging average — 1.053 (.863, B. Ruth)

Hits — 270 (262, I. Suzuki)

Runs — 234 (177, B. Ruth)

Total bases — 711 (457, B. Ruth)

I’d wager that Rodriguez, who has already tied the major-league record for home runs in April (14), winds up much closer to his usual studly totals (.300 or so, 45-50 homers, 120-130 RBI) than to any records. I’m not a cynic, just a big believer in the tendency toward the mean. 162 games make for a long season in pro sports (football is one-tenth that number, hockey and basketball about half).

A-Rod also owns the richest deal in the history of professional sports, having inked a deal before the 2001 season that guaranteed him $25.2 million a year over ten years, plus incentives and aircraft and stuff, and not including endorsements. As someone who grew up a Red Sox fan, I also find it worth noting that Rodriguez certainly did his part to shit up the 2004 American League Championship Series, when the Yankees improbably blew a 3-0 series lead and dropped four in a row the eventual World Series Champion Sox.

### Out-of-tune reasoning: the anthropic fallacy

Posted by kemibe in Off the Beaten Math on March 29, 2007

Jason Rosenhouse spent some time last week sitting in a Knoxville, Tenn. auditorium and listening to Intelligent Design creationists Lee Strobel (really more of a standard Biblical creationist), Jay Richards, and Stephen Meyer sling hokum and buncombe around.

Jason is detailing his madcap adventures in a series of posts, and apparently, the irrationally gleaming stars of the show were unusually focused on the “universe is too well suited for life to have been an accident” line of crap. I’ll spend some time explaining why this romantically alluring tactic is, in fact, crap — trivially inane, when you get right down to it.

### That mathematical oddity that is the NHL

Posted by kemibe in Off the Beaten Math on February 24, 2007

I was perusing the National Hockey League standings on Friday evening and discovered something strange. Out of 30 teams, only 7 have losing records about three-quarters of the way through the regular season.

This would seem to suggest that there is relative parity among the best teams, with the losing teams being especially bad (i.e., having won-loss records that are significantly worse than the “mirror images” of the best teams’ records).

However, this is not the case. Five teams have won more than twice as many games as they have lost, with these teams averaging a robust 38.6 wins and 16.4 losses; of the seven losing teams, only one (the 16-36-9 Philadelphia Flyers) has lost at least twice as many games as it has won.

This pattern, precarious by statistical definition, is not likely to hold until season’s end. Still, I wonder when the last time a major sports league featured at least a three-to-one won-loss imbalance of this sort.

I remember when the league had only 21 teams, 16 of which qualified for the playoffs. Even having a regular season under those conditions was practically a joke — no more than a reason to watch Gretzky take another shot at 200 points. If the season ended today, the Calgary Flames, at 31-21-9, wouldn’t even make the postseason.

Anyway.

### A whopper of a calculation?

Posted by kemibe in Off the Beaten Math on June 12, 2006

Just as I turned off the TV before heading out the door for a run last night, an unseen but jaunty-sounding fellow confided from within the idiot box that there were 1,537 ways to order a Burger King Whopper® (about 1.2 to 3 per calorie provided, I later ascertained). Being a numbers sort by inclinaton, I had no choice but to try to figure out, armed only with basic knowledge about the sandwich in question and lingering skills from my academic salad days, how the BK geek squad had come up with this figure.

## What Hominids are Saying