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I'm very common and often you see me,
Everything's believed to be made of me.

Make no mistake, I look largest when I'm seven,
But I'm largest when I'm five, it is proven.

But alas at those ages you've never seen me,
For you've seen me only when I'm three.

Unlike you mortals who grow old and die,
I keep shrinking and shriveling by and by,

I don't die when I'm seventy, eighty or ninety,
I only kneel and perish after the infinity.

What am I?

Zoir
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    From the title I guessed "an open hand with five digits extended", but the text went somewhere completely different. – Criggie Oct 04 '19 at 02:44

1 Answers1

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My guess:

An n-dimensional sphere.

I'm very common and often you see me,

There are lots of spheres

Everything's believed to be made of me.

This could refer to the https://en.wikipedia.org/wiki/Bohr_model of atoms...

Make no mistake, I look largest when I'm seven,

But I'm largest when I'm five, it is proven.

That was one of the keys:

As the diagram at https://en.wikipedia.org/wiki/Hypersphere shows: The surface of the sphere is largest in dimension 7. But the volume reaches its peak at dimension 5.

But alas at those ages you've never seen me,

For you've seen me only when I'm three.

We can see a sphere only (or at most) in 3 dimensions

Unlike you mortals who grow old and die,

I keep shrinking and shriveling by and by,

I don't die when I'm seventy, eighty or ninety,

I only kneel and perish after the infinity.

The surface and the volume of an n-dimensional sphere approach zero when n goes towards infinity. Even at 70 or 80 dimensions, there's hardly anything left.

Marco13
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    I'd be surprised if this isnt it. – Certainly not a dog Oct 02 '19 at 15:55
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    Correct, well done :) Will accept in a bit! – Zoir Oct 02 '19 at 15:56
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    (I meant the second line to be rot13(ryrpgebaf, cebgbaf, naq arhgebaf) as they are widely believed to be spherical but certainly your interpretation would work too) – Zoir Oct 02 '19 at 16:03
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    It's worth noting that statements like "the n dimensional sphere has largest volume in dimension 5" are only true for spheres of radius 1. Spheres of radius 2 are largest in dimension 24. Spheres of radius 3 are largest in dimension 56. The truth, as boring as it may be, is that it is meaningless to compare volumes of different dimensions. You wouldn't say that the volume of a sphere is larger than the area of a circle because volume and area have different units. For the same reason, it is nonsensical to say that a 5-dimensional sphere has larger volume than a sphere in any other dimension. – Brady Gilg Oct 02 '19 at 22:04
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    @BradyGilg True, but although I have some affinity towards mathematics and preciseness, I didn't go the extra mile of talking about the "n-dimensional unit-sphere" or something like a ~"dimensionless measure of volume". It was a good riddle, IMHO (and I spent more time than I'd like to admit reading about things like regular polytopes, symmetries, and honeycombs, while hunting for the answer ;-)) – Marco13 Oct 02 '19 at 22:18
  • @BradyGilg You are definitely right! The problem is any of those two characteristics would look very out of place in the clues, and IMO it is okay to sacrifice a bit of mathematical precision for a better worded riddle. :) – Zoir Oct 03 '19 at 01:00
  • @Zoir Note that the spheres we can see, that live in 3-dimensional space, are commonly called 2-spheres by mathematicians. A circle is a 1-sphere. Quirky mathematical fact there that messes a bit with your poem. No one has ever really seen a 3-sphere, unless our universe (disregarding time) turns out to be one. – Arthur Oct 03 '19 at 07:26
  • @Arthur That's a really interesting fact! I based the riddle on the Wikipedia graph Marco13 referred, so is that graph wrong? Or is that term just ambiguous? The footer on that graph says that those are volumes of n-spheres. – Zoir Oct 03 '19 at 08:07
  • @Zoir From that article: "It is a manifold of codimension one—that is, with one dimension less than that of the ambient space." If you look at the $y$-axes in the image, you can see that for each n, the blue curve shows the n-1-dimensional surface area of the n-1-sphere, while the purple curve shows the n-dimensional volume of the region bounded by that same object. So for n = 3 in the graph, you get the standard volume and surface area of a ball as we know it (denoted as V(3) and S(2) if you click the image and hover over the points). – Arthur Oct 03 '19 at 08:27
  • @Arthur Thank you for the clarification - I researched a bit on the subject so I learned something too! I don't think the riddle should be changed because a lot of people does conceive the 2-sphere when they see "3-dimensional sphere". Even though, thank you very much for telling me about this! – Zoir Oct 03 '19 at 10:37
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    @BradyGilg the reason you wouldn't say the volume of a sphere is larger than the area of a circle is that you think of physical quantities. There's no such thing as a radius 1 in the real world, only a radius e.g. 1 metre or 1 inch. But for mathematical circles and spheres, that's not an issue. – leftaroundabout Oct 04 '19 at 02:50
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    @leftaroundabout It is the exact same issue. Volume is defined as the number of unit N-cubes that would fit inside the object. – Brady Gilg Oct 04 '19 at 16:13