Bicycle Riding on Square Wheels 406
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."
Spirograph (Score:5, Insightful)
Proprietary Roads! (Score:3, Insightful)
A Lesson about Inventions (Score:3, Insightful)
Re:The answer is - A circle! (Score:3, Insightful)
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?
Let me be the one to point out the obvious, (Score:3, Insightful)
too
much
time
on
his
hands.
Re:Read the whole article? (Score:4, Insightful)
Bigger nitpick, you're confused. (Score:3, Insightful)
Re:*BOOM* (Score:2, Insightful)
Re:Tricycle sounds like the Dymaxion Car (Score:3, Insightful)
Re:Reminds me of the british 20p coin (Score:2, Insightful)
Re:Bigger nitpick, you're confused. (Score:4, Insightful)
A rotating cam designed to smooth out bumps inherent to the wheel isn't fundamentally much different than a spring designed to smooth out bumps inherent to the road, except that because the bumps inherent to the wheel are calculated and predictable, a spring would be a poor solution. The road bumps, on the other hand, can't really be predicted, so it needs a more flexible (no pun intended) method of shock absorption.
Pointless little sidenote: As far as I can see, if you had a square-wheel bike with a correcting cam, and ran it over the bumpy road described in the article, the wheel would ride smoothly, and the cam would overcorrect, so you would still need a shock absorber to go over that road. It'd just be bumping in the opposite phase compared to a normal tire.
Smartwheels! (Score:3, Insightful)
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.
Errant pedant prompts Lakatos reference (Score:3, Insightful)
He wrote a marvelous little book called Proofs and Refutations -- here's a very brief bit of summary and context [wikipedia.org] -- 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!)