This Might Be The Strangest Constant in Math

Comments · 134

• DE

  @DeriviaYT · 5 months ago (edited) · pinned

  Note:<br>Changed up the colour scheme following some of your feedback in previous videos. If you don&apos;t like it, let me know (please)!<br>I can switch most easily between popular terminal colour schemes, as these are easiest to plug into manim (their color palettes are readily available as an svg). If you&apos;d prefer I use a different one, feel free to leave a suggestion.<br><br>Edit:<br>I&apos;ll fix up the colours that are too faded with the background (probably just make them closer to the white text, so they still are less important elements, but much more visible). Thanks for all your feedback :)

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• DI

  @DissoluteGambler · 5 months ago

  I ran across it in physics and my first thought was WTH is that doing in there. &nbsp;After a lot of thought my reaction years later is WTH is that doing in there.

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• BS

  @BsktImp · 5 months ago

  <a href="https://www.youtube.com/watch?v=jNRIRXIsKxs&amp;t=141">02:21</a> This is what I&apos;ve always loved about any STEM teaching. You can go from explaining the unit square to, in the very next sentence, pulling out a double integral from nowhere.🤣

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• RO

  @robo3007 · 5 months ago

  And if you add the reciprocals of the hexagonal numbers together you get... 2 ln(2)

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• TO

  @topquark22 · 5 months ago

  In high school I computed the n-volume of an n-sphere, using volumes of revolution. It is amazing that a power of pi appears every 2 dimensions, starting with dimension 4. That is because, every 2 dimensions, the volume of revolution integral is a trigonometric integral, that requires an inverse trig function to evaluate it. This really means that even dimensions are fundamentally different from odd dimensions, and this fact appears in many places in geometry.

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• PO

  @pointlessformalisms · 5 months ago

  &quot;the logarithm is doing real work here, not just smoothing things out&quot;<br>GPT video, it&apos;s over.

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• OW

  @owenheckmann6962 · 5 months ago

  Has anyone ever figured out how Apéry derived the series representation on which his proof relies? Unless Apéry&apos;s garden is more interesting than I imagine

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• LA

  @ladylaylowjk · 5 months ago

  I have been stuck on this number for quite some time.. !

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• PE

  @PetersPuzzles · 5 months ago

  I have nothing to add but ζ(3) is how you all should write it in your comments. I may be a bit ocd, lol.

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• TI

  @Tineard · 5 months ago

  So.. maybe electrons have this sort of interactive coefficient, because they are not 3d but 4d, not just a sphere, but a sum of 3d spheres, that add up to 4d object, kinda like you can make a 3d sphere from 2d circles.<br>I always feel like a lot of effects point towards this sort of thing - like Kasimir effect or quantum jumps or maybe even entanglement. Shame my brain is not big enough to test this myself, but still, very interesting how those clues keep lining up :)

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• JO

  @johnsolo123456 · 5 months ago (edited)

  QED and Apery&apos;s Constant intimately linked is entirely debatable. It may be more a quirk of the mathematical machinery used where you get zeta (n) values showing up in complicated ways in the infinite series. Remember it&apos;s an actual infinite series and I believe all the zeta(n) numbers start accumulating in the coefficients the farther you calculate.This can happen often in analysis. Basically it could be a more mathematical thing than an ontological thing. Also, in certain cases it&apos;s been shown than the feynman path integral math can be completely obviated.

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• GR

  @gregsarnecki7581 · 5 months ago

  <a href="https://www.youtube.com/watch?v=jNRIRXIsKxs&amp;t=324">5:24</a> But, sigma n=0 to infinity of [(-1)^n /(2n+1)]^x <i>does</i> give rational multiple of powers of pi, for all integer x, including 3. Thus, sigma n=0 to infinity of [(-1)^n /(2n+1)]^3 = pi^3 /32. You just have to avoid the even terms (1/2^3, 1/4^3, 1/6^3, etc) and alternate the remaining odd terms. In this way Catalan&apos;s constant is kind of like the power-of-two version of Apery&apos;s constant.

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