The Time of Your Life!

I came across this interesting list of factoids about time. They are all pretty intriguing, but what made me think this particularly blog-worthy is #10:

"10. A lifespan is a billion heartbeats. Complex organisms die. Sad though it is in individual cases, it’s a necessary part of the bigger picture; life pushes out the old to make way for the new. Remarkably, there exist simple scaling laws relating animal metabolism to body mass. Larger animals live longer; but they also metabolize slower, as manifested in slower heart rates. These effects cancel out, so that animals from shrews to blue whales have lifespans with just about equal number of heartbeats — about one and a half billion, if you simply must be precise. In that very real sense, all animal species experience “the same amount of time.” At least, until we master #9 and become immortal."

It makes me wonder - I thought that exercising and keeping active were supposed to lengthen one's lifespan, but doesnt your heart-rate increase during activity? Perhaps this is just averaging species' lifespans by scale in general, I cant imagine that a couch potato would have a longer life expectancy than a marathon runner - so it almost seems that on an individual basis the opposite is true, that relative to other individuals within the same species, the more lifetime heartbeats the longer they live on  average? Im not sure, but its pretty fascinating and is another demonstration of how numbers affect every part of our world.

Between the Folds

Happy New Year everyone! Almost time to get back to class, but it should be pretty fun. In the first week back I plan on showing my students the film Between the Folds, a very interesting look at origami, some of its eccentric artists, and the way it relates to math and mathematical thinking. I recommend this film to anyone interested in the arts, creativity, and/or math, from a couple very simple rules (one page, no cutting or pasting) you can produce an infinite array of figures, and in fact it is these limitations that feed the creative force behind the artform.

Classic case of Girls v. Boys

Verdict: case thrown out. Ive never really given too much trust to these types of studies of one gender performing better or worse than the other. Unless the figures consistently come out overwhelmingly lopsided either way, we dont have anything to worry about with this issue.

Sometimes it seems that people assume that these types of results have to be exactly 50/50, but that not true. In reality, one side is almost always going to come out a little bit better than the other, just like coin flips - sure each side is equally as likely on average to come up, but flip a coin 100 times and I'll be surprised if you get a perfect 50/50.

I count myself lucky to get to witness an age in which all sorts of glass ceilings are being shattered, and understand how these types of studies could have interesting facets and social implications, but it seems like they are conducted just to have a headline either way and its always implied that "something must be done because the losing gender is falling behind." I think it would be more constructive to focus on better teaching to both genders in general rather than worrying too much about one or the other.

Today I learned...

That the reason pizza becomes strengthened and doesnt drop all the cheese and toppings onto your lap when you fold a slice down the middle is due to the mathematician Gauss's Theorema Egregium. Something you always know intuitively but dont know why.

From Wikipedia:
"An application of the Theorema Egregium is seen in a common pizza-eating strategy: A slice of pizza can be seen as a surface with constant Gaussian curvature 0. Gently bending a slice must then roughly maintain this curvature (assuming the bend is roughly a local isometry). If one bends a slice horizontally along a radius, non-zero principal curvatures are created along the bend, dictating that the other principal curvature at these points must be zero. This creates rigidity in the direction perpendicular to the fold, an attribute desirable when eating pizza, as it holds its shape long enough to be consumed without a mess. This same principle is used for strengthening in corrugated materials, most familiarly corrugated fiberboard and corrugated galvanised iron."

Car Talk Algebra Puzzler

I came across a math puzzle from Click & Clack on NPR's always entertaining Car Talk, see if you can figure it out, it goes like this:

"RAY: Last month, Tommy and I decided that we were going to take a trip north to see the foliage. Tommy drove the first 40 miles. I drove the rest of the way. We looked at the foliage for three or four minutes, then decided to head home.

We took the same route home.

On the way back, Tommy drove the first leg of the trip and I drove the last 50 miles.

I got home and my wife said, "Who did the driving?"

I explained that Tommy drove the first 40 miles, then I drove the rest of the way. On the way back, Tommy drove the first leg of the trip, and I drove the last 50 miles.

She said, "But who did most of the driving?"

I told her, "You can figure it out. In fact, you can even figure out how much more of the driving was done by that person."

And that's the question. Who drove the most -- and how many more miles did that person drive?"

Creating Art Using Only Lines and a Circle

Have you ever used a Spirograph? If you have ever been drawn toward the geometric patterns and colors created by this nostalgic toy, then you should try using some of the techniques described here at MathCraft and here at Jill Britton's website. Both of these wonderful sites teach you how to create intriguing works of art using very simple supplies: just a compass and straight edge, or a needle and thread.


Straight lines can be deceptive, as you can see see in the pictures to the side, believe it or not these pictures are made using nothing but straight lines! Notice the circle in the middle of the top picture is made by the outlines of the inside of 6 different colored pentagrams. The heart-shaped cardioid below has the same kind of outline, getting its curves from the perfectly straight lines composing its border. The same principle can be used by weaving a needle and thread through a piece of paper or fabric, as demonstrated on the Jill Britton site.

Take a look and try it out on your own, at the very least youll have something to doodle in class that actually uses math.

Visualizing Global Population Trends

In the video to the left, NPR explains visually how much the world's population has exploded in recent history. Its interesting to think about, it almost seems like we are in an age of flux, between an old time and a new future. How will our global culture as a species change just within the next hundred years or so? Will individuals naturally decide to have less children as a conscious or subconscious reaction to longer lifespans, better medical services, less food, water, & other resources to divide between an ever growing population? Is there a self-regulating limit that nature silently exerts on all of us, like an inflating balloon aware of the pop?