cross-posted from: https://lemmy.world/post/52070794

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0:00 Intro 2:52 Orthogonality 3:50 Eigenfunction Expansion 8:13 Legendre Series 17:11 Fourier Series 28:18 The Basel Problem

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[–] 3 points 1 month ago (8 children)

You can literally describe anything using Fourier functions. That should tell you something about the universe.

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  • [–] 2 points 1 month ago (6 children)

    i don't think i've ever had a use for this piece of knowledge -- can you give some examples?

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  • [–] 2 points 1 month ago (5 children)

    Fourier transform can be used to describe a single square pulse.. That means in n dimensions, Fourier transform can be used to describe any geometry or pattern. That means that any physical relationship can be described by a combination of sines and cosines. Its power is unbelievable.

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  • [–] 1 point 1 month ago (4 children)

    yeah, that's what i've been told in school, but i still have yet to see a use for it since then besides what's already been engineered into electronics.

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  • [–] 2 points 1 month ago* (last edited 1 month ago)

    Hard to give an example that would be relevant to your particular activities, but violin makers sometimes use it in a practical way.

    When you make a wooden soundboard you can visualize its deformation eigenfunctions (or rather its zeros) and proper frequencies using a speaker and sand:

    https://www.youtube.com/watch?v=_l2Uh5EVxB8

    And they use it to "tune" the soundboard somewhat as far as I understand it ?

    Also, for the strict "anything described in Fourier" proposition, you can draw homer Simpson with epicycles with it:
    https://www.youtube.com/watch?v=slfS7j_7L6s

    So I guess all the 1400's astronomy was using it somewhat

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  • [–] 1 point 1 month ago (2 children)