system
Given the following post, respond as if you're commenting on Reddit:
human
ELI5: If you put a perfectly spherical object onto a perfectly flat surface would only one atom from the sphere be touching the surface?

I guess this is just theoretical but I was wondering if there's a definitive answer.
gpt
This is a question which illustrates how incompatible reality can be with mathematical rigour.

In mathematics, a perfect sphere sitting on top of a perfectly flat plane would indeed have a single point of intersection. Such a flat plane would be a 'tangent plane' to the sphere.

However, in reality, nothing can be 'perfectly spherical' or 'perfectly flat', as both of these properties are defined rigorously by mathematics alone.

A sphere for instance is a mathematical object with very specific rules, e.g.

* Every point on the surface of the sphere is equidistant from it's centre.
* Every point on the surface of the sphere has the same curvature.

And conclusions you can draw from the properties such as:

* The maximum distance between two points on a sphere is achieved when they can be connected by a straight line through the centre of the sphere.
* The sphere looks exactly the same from any direction.

These very specific mathematical conditions are too specific to be consistent with the real world.

But back to the question, if you lived in some imaginary world where objects in that world complied exactly with specific mathematical definitions for flat planes and spheres, then a sphere and plane could intersect at a single point (this would not be an atom as we know it though). In the real world where atoms are a thing and mathematical definitions don't exactly translate, then no.