Previous page

Pi(e) Mathematics

Gentle reader, I apologize for the dearth of updates recently. But with a new month comes new opportunity for mathematical investigation, so let's dive right in!

In keeping with my summertime theme of mathematics and food (see e.g. here and here), I'd like to share with you a story about a recent dinner I shared with my better half. After a day spent apartment hunting, we decided to treat ourselves to a dinner out.

Everything we learned about treating ourselves we learned from Parks and Recreation.

In keeping with the theme of treating ourselves, we ordered two desserts at the end of the night, and both looked quite delicious. We agreed to each eat half of one dessert and then trade for the second half.  One was in the general pie family of desserts.

Given a slice of pie, the most natural way to divide it in half is to bisect the angle formed at the end of the slice.


One slice of pie, cut in half by bisecting the green angle.

To cut a slice of pie in this manner, one generally...

Asking the right questions

If you read about math and enjoy the internet, chances are you saw this op-ed in the New York Times over the weekend.  The piece, titled "Is Algebra Necessary?," argues that math requirements, algebra in particular, are prohibitively difficult for many people, and may be contributing to high school and college dropout rates.  Instead of imposing an algebra restriction, author Andrew Hacker suggests restructuring the curriculum around "citizen statistics" and "quantitative reasoning."  Despite the jargon-y names, he insists courses like this could be developed without sacrificing rigor or dumbing down the curriculum.

As might be expected, the piece has furrowed quite a few brows.  A few friends have asked me for my opinion, but I'm a little late to the game, and there are a number of people who have expressed my views in their own words quite well.  I'll briefly add my own to cents, peppered with links throughout.

First, I agree with Dan Meyer that the question "Is Algebra Necessary...

Hot Dog Mathematics (a.k.a. Hot Dog! Mathematics!) Part 2

Last week we talked about hot dogs.  Though I spent most of my time discussing how the dog's surface area changes if it is cut lengthwise (also known as a butterfly cut), my original inspiration came from much more sophisticated wiener slicing.  Around the fourth of July, the following video went viral.  Take a look; it's hard not to see the merits of this suggested technique for cooking hot dogs.

As the curly fry is to the regular fry, so too is the spiral cut dog to the regular dog.  Indeed, it's hard to find a reason why one should not choose a spiral cut dog over a regular dog, if given the choice.  But from a mathematical standpoint, as with the butterfly cut discussed last time, arguably the most interesting feature of the spiral cut hot dog is the increased surface area.  Unlike the butterfly cut dog, however, computing how the surface area changes when dealing with a spiral cut dog is not so straightforward. In particular, it is difficult to compute the additional surface...

Hot Dog Mathematics (a.k.a. Hot Dog! Mathematics!) Part 1

For many people, summer wouldn't be summer without a good old fashioned cookout.  And though the Fourth of July has passed, there are many warm days and late evening sunsets still ahead.

With the season of grilling comes the season of grilling advice.  Not all of it is consistent - some places tell you to only flip your burgers only once, while others tell you to flip them as often as you like.  Trying to sort through so many conflicting words of wisdom can certainly be confusing, especially for an inexperienced grill operator.  But no matter what philosophy you subscribe to, one piece of advice seems fairly consistent: the greater the surface area of the object you're cooking, the better off you'll be.  Increased surface area gives the meat more room to react to the heat, and increases the area that undergoes the Maillard reaction; in other words, more surface area = more deliciousness.

Surface area is something to consider in sweet treats as well as savory ones.  See, for example...

Should You Try to Escape the Friend Zone?

Last week I tried to provide a bit of dating advice through an exploration of the half your age plus seven rule. This week, I'd like to continue on this theme by analyzing what you should do if you find yourself trapped in the friend zone.

For those of you not hip to the lingo, the friend zone is a sort of platonic purgatory people find themselves in when they have unrequited feelings for a close friend. It is a commonly held belief that one winds up in the friend zone by waiting too long to make a move, and though the friend zone is typically thought of as a place where men wind up, women can easily find themselves there too. Here's a link to Joey explaining the concept to Ross on an episode of Friends (sorry, embedding for the video has been disabled). For a satirical look at the zone, you may want to read this article from The Onion.

Suppose you find yourself trapped in the friend zone, and want to make a break for it by confessing your true feelings to your heart's desire....

A Rule for Summer Lovin'

With summer now in full swing (in the northern hemisphere, at least), romance is undoubtedly in the air.  The longer days are perfect for evening walks on the beach, dinner by sunset, or the always romantic late-afternoon pie eating contest.  And while it is easy to let your better judgment swim away through the humid air, it is sometimes important to consider how your relationship may be viewed by your peers.

One of the most well-known rules of thumb is the half-your-age plus seven rule.  This rule tries to quantify the intuitive idea that if you are dating someone younger than you, they should not be TOO much younger than you.  Specifically, the rule says:

  1. You should not date anyone before the age of 14.
  2. Once you are 14, you should not date anyone whose age is less than half of your age, plus seven years.

Originally, this rule was conceived of as a means to compute a wife's ideal age compared to her husband (namely, half his age plus seven).  It has since evolved, however, to...

CNN Light Years Guest Post: How Professors' Dads Made Math Fun

Hi all,

This weekend's Father's Day celebrations have inspired my monthly article over at the CNN Light Years blog.  Here's a sample:

There are many misconceptions about mathematicians in popular culture. For example, windows and mirrors do not make for the best writing surfaces, despite what you might assume from "A Beautiful Mind" or "Good Will Hunting." Mathematicians are also frequently portrayed as painfully socially awkward. And while this is sometimes the case, the true range of personality types is much more varied. Even among the more socially awkward, it is not uncommon for mathematicians to fall in love, marry and start a family. What must it be like to grow up in a household with a mathematician? In the spirit of Father's Day, I spoke with two mathematicians whose fathers were also mathematicians about what it's like being raised in a mathematical household

Click here for the rest!

Were the San Francisco Giants #1?

Last month, I posted a review of a new book titled "Who's #1?" on the mathematics of ranking and rating - if you're interested, you can purchase a copy via the Amazon sidebar on the right.  Today I'd like to study the San Francisco Giants with one of the techniques used in this book: the offense-defense rating method.

Why the Giants?  It's really just a personal preference.  For the non-Giants fan, though, it's worth pointing out that the Giants won the World Series in 2010, but failed to even make the playoffs in 2011.  Let's try to investigate why this is the case.  Baseball fans may have their own explanations for this observation, but for a moment let's focus on the math.

As the name suggests, the offense-defense rating method rates a team's offensive and defensive capabilities.  Of course, these two things are highly interdependent - if a baseball team scores 10 runs in a game, for example, is it because they have a couple of excellent hitters, or is it because the team they...

Math in Books: Math Puzzles

Presh Talwalkar, fellow blogger and founder of the game theory/personal finance website Mind Your Decisions, has recently released an e-book composed of 70 math puzzles previously featured on his blog.  He was kind enough to send a review copy my way, so if you enjoy a good math puzzle, read on!

The book is organized into three sections, divided by general subject.  There are twenty five counting/geometry puzzles, twenty five probability puzzles, and twenty strategy/game theory puzzles.  Some of the puzzles are inspired by discussions Presh has had with his readers over the years, though many are not unique to this book and some are moderately well known.  In fact, the intersection of the puzzles in the book with things I have talked about here is nonempty - some examples of overlap can be found here and here.

William Poundstone's book on the history of Microsoft and the puzzle-based job interview, How Would You Move Mt. Fuji?, is probably the most commonly cited text in Presh's collection...

CNN Light Years Guest Post: Did 'Avengers' really own box office records?

Over at CNN this month, I talk about the phenomenal success of Marvel's The Avengers in its stampede over old box office records.  But how much stock should we put in these records?  Is this blockbuster really the top dog in the record books?  Here's a sneak preview of the article:

When the Avengers assemble, the world opens its collective wallet.  In just under three weeks since its international opening, "Marvel's The Avengers" has earned more than $1 billion worldwide.  In America, it blew through the $200 million mark over opening weekend alone, and now holds the title of best three-day opening in film history.  Or does it? While dollar signs fuel the engine of Hollywood movie production, they are not necessarily the most objective measure of a film's success.  Most importantly, the dollar is not a static unit of measurement like the meter; as a result of inflation, a dollar in 2008 has more purchasing power than a dollar in 2012.  If we search for a better way to measure film's...

Page 2 of 19

Next page