Timeline for Can different bicycles leave the same tracks?
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
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| May 6, 2013 at 18:57 | comment | added | user112109 | In every point you can calculate the radius of curvature, using the well-known formula. And in every point you have a certain front angle. Both force the rearwheel to follow according to the Pythagorean formula. | |
| May 6, 2013 at 17:46 | comment | added | Douglas Zare | As the front angle oscillates between $-\pi/2$ to $\pi/2$ as you trace out something which looks like a figure-$8$, which circle is this approximating? | |
| May 6, 2013 at 10:52 | comment | added | user112109 | @Douglas: Every piece of the tracks can be considered to be a piece of a circle (depending only on the momentary angle of the frontwheel). | |
| May 6, 2013 at 0:13 | comment | added | Douglas Zare | The relationship between inner and outer circles was mentioned earlier. However, the main question is what happens if the curves are not circles. I don't understand the sense in which "every curve can be considered as an approximation of a circle." | |
| May 5, 2013 at 17:40 | comment | added | user112109 | @Yoav: I don't think so. You are right, it is possible, for instance, to have a circle with radius $r_2 = 0$ But as soon as $r_1$ is changed also $r_2$ will follow by the given Pythagorean equation such that never limit- or start-effects can take pace. | |
| May 5, 2013 at 17:31 | comment | added | Yoav Kallus | Does the fact that for two different bicycles different points on the front track match the same point on the rear track lead to a problem with this argument? | |
| May 5, 2013 at 16:58 | history | answered | user112109 | CC BY-SA 3.0 |