
Ask HN: Whats your favourite piece of math? - zython
Anything goes.
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gvb
Laplace transform[1]. Starting with a signal in the time domain, you can take
the Fourier transform to map it into the frequency domain and then the Laplace
transform (Z-transform[2]) to map it into discrete time domain. Discrete time
is what digital computers do. At this point implementing the control loop on a
digital computer is remarkably straight forward.

Taking your system's closed loop transfer function[3], you can use the above
Laplace and Z-transforms to produce the desired closed loop control algorithm
to "optimally" control your system. (I put "optimally" in quotes because it is
optimum for the system as defined; if your understanding / definition of your
system is wrong, it will be optimally controlling for a _different_ system and
be suboptiomal for your actual system.)

[1]
[https://en.wikipedia.org/wiki/Laplace_transform](https://en.wikipedia.org/wiki/Laplace_transform)

[2]
[https://en.wikipedia.org/wiki/Z-transform](https://en.wikipedia.org/wiki/Z-transform)

[3] [https://en.wikipedia.org/wiki/Control_theory#Closed-
loop_tra...](https://en.wikipedia.org/wiki/Control_theory#Closed-
loop_transfer_function)

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Chamuco1198
The Fourier transform and its computational offshoot, the Fast Fourier
Transform. We wouldn't have any of modern electronics and telecommunications
without the mathematical insight that the FT brought. The fact that you can go
from the time domain to the frequency domain and back again is nothing less
than astounding. Optics was also benefitted by the FT because you can use is
to filter unwanted optical frequencies and diffraction effects from your
images using Fourier transformation.

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itamarst
Cantor's diagonal proof that א ≠ ₀א.

[https://en.wikipedia.org/wiki/Cantor%27s_diagonal_argument](https://en.wikipedia.org/wiki/Cantor%27s_diagonal_argument)

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pmdulaney
Shouldn't "favourite" -> "maths"?

