Suppose you have a differential equation that you want to solve numerically. An approach you might take is collocation, which is based on the idea that an unknown function $u(z)$ can be approximated by a sum of $N+1$ basis functions $\phi_n(z)$: $$ u(z) \approx u_N(z) = \sum_ …
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Mathematical Curio
If you take any integer and rearrange the digits however you like, the difference between the original number and the rearranged number will always be divisible by 9.
For example:
number = 12345 rearranged = 43215 difference = 43215 - 12345 = 30870 difference / 9 = 3430More generally, you can do the same with numbers …
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My initial approach to the tiling problem was to find all the possible configurations, calculate a measure of the distance between same-colour tiles for each, and then select the configuration with the maximum distance. While this does reliably find the optimal solution, it also very quickly becomes infeasible as the …
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We have a play-mat: eight rubber tiles, two of each colour, that fit together. We had put it together in a 4x2 arrangement, without considering the colours. The result was ... displeasing. Two pink tiles were right next to each other, but all the other pairs were separated. It just looked …
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