## Q & A: When Two Spheres Touch…

Chris S. writes:

I was wondering what is the theoretical ‘area’ of contact between two spheres in contact with each other. I was unfortunately not able to locate much (if any) information on this. After some thought into this I’ve realised that the spheres would meet at a single ‘point’ however what would the area of this ‘point’ be? The only source related to this claimed the area of contact, the point, has no area. How can a point have no area? If the spheres touch, musn’t there be an area shared between them? Even if only one atom?

Hi, the issue here is that there is a vast difference between physical, real things and the mathematical ideas that model them.

Real, mathematical spheres don’t exist, plain and simple! Never could, even as a region of space— space itself has a granularity (apparently) at a scale of about 10^-33 meters. There simply cannot exist a perfectly spherical region in physical space, much less a perfectly spherical body.

But as an abstraction, the idea of a sphere is very useful: lots of things, quite evidently, are spherical for all practical purposes.

For that matter, “points” don’t exist either, and are also a mathematical abstraction. (So, too, is “area”. Real things are rough, bumpy and not at all like continuous surfaces, on a fine enough scale) But again, these _ideas_ are very good at getting at something important about lots and lots of physical things, and so have proved useful.

Tangent spheres do indeed meet in a single point, which has no area.

Spherical things meet in some other, messier way.

Hope this helps!

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