Sphere and Plane are the most common surfaces. Sphere is a surface of genus 0. It has a constant Gaussian curvature of 1. It is a surface such that every point on the surface is equal-distant to particular point C. Sphere is the 3-dimensional analogous of a circle.

Algebraic formula: x^2+y^2+z^2==r^2, where r is radius.

The following formula is a sphere of radius 1. u goes from 0 to π. v goes from 0 to 2 π. u is the horizontal sweep. v is the vertical sweep.

ParametricPlot3D[{Cos[u] Cos[v], Sin[u] Cos[v], Sin[v]}, {u, 0, 3}, {v, 0, 6}, PlotPoints -> {10, 20}]

Mathematica file of various ways to draw a sphere

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