Yes, Sheldon he has separate American and British English versions of pages!!!
For example, Kross bicycle (2017) had a Schwalbe tyre with markings:When inflated, the tires were about 3.5cm wide as measured with a ruler.
And the Mavic A319 rim had markings:
622x19C
In this:
- ISO (Etrto): 42-622. So:
- 42 is the inner rim width. The actual inflated tire is going to be even wider.
- 622 is the bead seat diameter. The actual inflated tire is going to be even wider.
- imperial: 28 x 1.60
- French: 700x40C:
- meaning of the "C" asked at: bicycles.stackexchange.com/questions/16190/what-does-the-c-in-bicycle-tire-size-mean
Besides being useful in engineering, it was very important historically from a "development of mathematics point of view", e.g. it was the initial motivation for the Fourier series.
Some interesting properties:
- TODO confirm: for a fixed boundary condition that does not depend on time, the solutions always approaches one specific equilibrium function.This is in contrast notably with the wave equation, which can oscillate forever.
- TODO: for a given point, can the temperature go down and then up, or is it always monotonic with time?
- information propagates instantly to infinitely far. Again in contrast to the wave equation, where information propagates at wave speed.
Sample numerical solutions:
www.youtube.com/watch?v=tq7sb3toTww&list=PLxBAVPVHJPcrNrcEBKbqC_ykiVqfxZgNl&index=19 mentions that it is a bit like a dot product but for a tangent vector to a manifold: it measures how much that vector derives along a given direction.
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