The most useless piece of geometric trivia?

Question

Wikipedia gave me this absolute gem, which is utterly inapplicable to life as we know it:

"Square wheels can roll perfectly smoothly if the road has evenly spaced bumps in the shape of a series of inverted catenary curves. The wheels can be any regular polygon, but one must use the correct catenary, corresponding correctly to the shape and dimensions of the wheels."
http://en.wikipedia.org/wiki/Catenary

So: Either come up with an even more useless piece of geometric trivia
OR:
tell me something profound about the concept of a world with catenarymobiles (like if your steering direction is even slightly off, you get out of phase, and nasty things happen. Maybe an automatic navigation system for a catenarymobile would use the increasing noise to correct steering...? Although it would be easy to design a handbrake into the road. Tire design might be problematic though.)

Answer 1

snow plowing would be hilarious.

they used a very bad example to illustrate the principle, but you seem to have got the idea they presented very well.

There are only five regular solids that fit inside a sphere with the corners touching the surface of the sphere. (the platonic solids)

edit. I am picturing your example in my mind and enjoying it immensely

Answer 2

Well, this comment about the bicycle with square wheels isn't meant to be taken seriously, of course. Even mathematicians like to make jokes, and, when you think about it, this one is pretty funny. From a practical standpoint, the square-wheeled bicycle has some issues, not the least of which is that it can't turn left or right. It does make for an interesting visual, however - see the graphic on the following page:

http://www.sciencenewsforkids.org/pages/puzzlezone/muse/muse0299.asp

So, you want some interesting but essentially useless geometric trivia? OK, how about this: In a regular pentagon, the ratio of the length of a diagonal to the length of a side is the Golden Ratio.

Answer 3

WOW ! that is the most non-useless bit of trivia !

Can you imagine a private road from a security site. The only vehicles that can travel smoothly and quickest, would be the ones with the uniquely sized square wheels for that compound. Any other intruders, whether on foot or driving, would be faced with a hazard.

What's the bet that Area 51 with its UFOs and aliens will start changing the access roads now

... LOL

Answer 4

We all know (or should know ☺) that a circle is defined as x² + y² = r². But, in the limit as n -> ∞
x^n + y^n = r^n is a square. And in the limiting case of a regular polygon, as the number of sides n -> ∞ it becomes a circle.

Nice, isn't it? ☺


Doug

Answer 5

That greater people die each year by using DONKEY'S than by using airplanes! i did no longer comprehend donkey's hated us plenty! I recommend, try explaining that one anyplace you wind up! lol and you may sneeze with your eyes open, they proved it on Mythbusters. this is basically a organic reaction to close your eyes once you sneeze.

Answer 6

not seem to be

Answer 7

a trivial qn.....