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Bicycle Riding on Square Wheels
Roland Piquepaille writes "Before starting our long working week, let's relax with this story of a bicycle with square wheels. No, it's not a joke. And it even rides smoothly. But there is a trick: the road must have a specific shape. The Math Trek section of Science News Online tells us more about this strange bicycle -- actually a tricycle with two front wheels and one back wheel. Read this overview for some excerpts and a picture of the tricycle, or the original article for an additional animation."
This is basically the same principle as the odd-shaped pieces in your old Spirograph set....
Seems to me this is a good analog to proprietary file formats. Instead of having people pay tolls, maybe the government should build roads with inverted caternary bumps and sell the square wheels!
The best ones conform the invention's design to fit the environment, not the other way round.
They say the first thing to go is your penis. Well, it's either that or your brain. I forget which...
wouldn't a common circular wheel, while going over a steep hill
No, because the hill is really at best a half circle.
I'm not sure if tank tracks count as a wheel since they don't orbit a central axis. Even if they were, the tank treads aren't flat when they are in use. They're a sort of oblong shape. You might as well say a wheel is also a line because if you cut the inner tube in half it lies down and becomes a line.
If the wheel is circular, then the road would have to be circular as well. Like going around a small, perfectly spherical asteroid. But is it still a road if it doesn't actually lead anywhere?
way
too
much
time
on
his
hands.
Well, circular, with a diameter approaching infinity, of course. :-)
What you're talking about is, in essence, a suspension system. Which is used to overcome a rough ride. What you're all trying to say is "The smoothness of a ride is determined by how much axle movement is passed along to the rider". Or something like that.
'Standards' in computing only impress those who are impressed by things like 'standards'.
It seems like a flat road on a spherical earth would be the same shape.
Except for the fact that the post is messed up, and the bike is actually an normal tricycle, with 1 front, and 2 rear wheels
Anthropic principle: We see the universe the way it is because if it were different we would not be here to see it.
Eeghh, cmon Mods. +4 Interesting? At least it wasn't informative. Look at the coin, where is the center of mass? In the center! What happens when the coin rolls? The center moves up and down. What happens to the center of mass? It MOVES! What the equal diameter allows you to do is roll something flat over a coin and not have -that- move vertically, but the CM of the coin will move.
I vote for the smartwheels with zillions of radar-guided extending foot-spokes, a'la Hiro's motorcycle or Y.T's skateboard in Snow Crash.
I'd say being able to skateboard smoothly down stairs would probably give you the upper hand in the simpler conditions of municipal roadway battles.
"We have to go forth and crush every world view that doesn't believe in tolerance and free speech." - David Brin
OK, so the parent post was kind of silly, but it gives me a chance to mention Imre Lakatos, my favorite mathematical philosopher. (Yes, I have a favorite favorite mathematical philosopher. Don't you?)
He wrote a marvelous little book called Proofs and Refutations -- here's a very brief bit of summary and context -- which present a very interesting very of the process of mathematical discovery: instead of accumulating an ever-increasing series of perfect truths, he argues, mathematicians are constantly shifting their perceptions of what is true, because they're constantly shifting the very definitions of the things they're writing the proofs about. (This happened in a major way with calculus during the 19th century, for example, when limits, derivatives and integrals were redefined more formally, giving birth to the field of analysis.)
The book is a lot of fun, and actually not such a hard read. It takes place in an imaginary classroom, where the students and the professor, having just proved a simple little theorem about polyhedra, start coming up with counterexamples by "stretching" their notion of what a polyhedron is. (Should a cylinder be a polyhedron? Why not? What about a box with a box-shaped hole on the inside? etc.)
Through their arguments, they end up sharpening the definition of "polyhedron", eventually replacing their naive notion with something clearer and more formalized through a process of proofs and refutations.
So, Stan Wagon challenges our definition of "wheel" with an apparent counterexample: Does the bike have no wheels? Or are wheels not round? We might propose sharpening the definition of "wheel" to account for the new counterexample:
A wheel is a solid object designed to rotate about an axle, with its perimeter in constant contact with some other surface.
(Make a ridiculous post, get a ridiculous reply!)