# I'm largest when I'm five, what am I?

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?

• From the title I guessed "an open hand with five digits extended", but the text went somewhere completely different. Oct 4, 2019 at 2:44

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.

• I'd be surprised if this isnt it. Oct 2, 2019 at 15:55
• Correct, well done :) Will accept in a bit!
– Zoir
Oct 2, 2019 at 15:56
• (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 2, 2019 at 16:03
• 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. Oct 2, 2019 at 22:04
• @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 ;-)) Oct 2, 2019 at 22:18