One way of mathematically representing a very simple sphere in 3D space is,

r^{2} = x^{2} + y^{2} + z^{2}

where r equals a radius of the sphere. Solving in terms of x, y, and z, we get,

x = √(r^{2} — y^{2} — z^{2})

y = √(r^{2} — x^{2} — z^{2})

z = √(r^{2} — x^{2} — y^{2})

## A Sphere Reciprocal

Now a sphere may be the most aesthetically pleasing of the simple geometric curves. So it is natural to wonder, concerning a sphere, *what if…*? So what if we convert the equation into an equation for a sphere reciprocal? No, not turn the sphere inside out. Rather an inverse of the equation of a sphere? What is the graph of,

r^{2} = 1/( x^{2} + y^{2} + z^{2}) ?

Is it ordinary, or could it be something “romantic,” perhaps something like the popular image of a black hole? Do you have the mathematical skills and (hopefully) the graphing software so you can produce a visual of the curve? If so, and you are willing to share the image, please do. Click *Contact Us* and attach it along with any *narration*. I would be pleased to credit you for the image and include it with this article.

**Note:** You might also enjoy Collapsing Then Expanding the Equation for a Sphere

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