by Burkard Polster and Marty Ross
The Age, 17 August 2009
It started without a peep, nobody noticed, and now it’s too late. They are everywhere. The pentapeds have taken over the world!
Not long ago, our offices were occupied by simple, square four-legged chairs. But they have all been replaced by five-legged oddities. How did this happen? Ask your OHS representative. They’ll likely tell you that five legs are more stable than four. Nonsense!
How do we determine the stability of a chair? The natural measure, used by quality control folk, is the distance from its center to one of its sides. So the pictured four-legger and five-legger have the same stability.
Okay, so which is better? Well, to ensure the same stability the legs of the four-legged green chair have been made slightly longer, 14.4% longer to be precise. So it is easier to stumble over a green leg. But there are more red legs to stumble across… Anyway, let’s agree that the five-legger is winning, 0–1.
Also, the five-legger will distribute your weight more evenly, which may make it easier to roll around on a carpeted floor: 0–2.
On the other hand, the combined length of the red legs is about 9% greater. So it is less expensive to build the four-legger: 1–2.
What about storage? If you want to store that extra chair out of the way, note that a five-legger needs a 12% wider space. We’re at 2–2.
One final test: wobbliness. Rolling around on an uneven surface, chances are that both chairs will wobble. However, as we have written on previously (see our archive at www.qedcat.com), the four-legged chair can usually be rotated on the spot to eliminate the wobble. This is not possible for the five-legger. (Of course a three-legger would never wobble, but that’s another story).
The four-legger wins, 3–2! Of course, there is plenty of room for debate. But overall, we simply don’t see an advantage in having five legs over four.
So how did the pentapeds manage to take over the world? Well, more is better, right? And 5 is more than 4. Perhaps it was easy to convince people that five-leggers were superior simply because “it’s obvious”.
We predict that it will soon be “obvious” that six-leggers are better still. And then we’ll have seven-leggers, and then eight-leggers, and then … Oh, the horror!
On Sunday, August 23, 11:30-12:30, as part of the ``A Day in Pompeii" exhibition at the Melbourne Museum, Burkard Polster (aka Burkardus the Conquerer) will give a free presentation: "Rome vs. Mathematics".
For details and bookings, visit:
http://www.mav.vic.edu.au/public-lectures/2009/index.html
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