Absolutely a discriminatory thread.

The simple circle is described by:

r² = x² + y²

And the simple sphere by:

r² = x² + y² + z²

People here are ignoring, or discussing without understanding of the most trivial sort, the entire class commonly (and insultingly) called "supercircles" or "superspheres" described as:

rⁿ = xⁿ + yⁿ

and:

rⁿ = xⁿ + yⁿ + zⁿ

(or in the latter case)

rⁿ = xⁿ + yⁿ + zⁿ + tⁿ

In as discriminatory and derogatory comments as have been made here invariably arise from insufficient familiarity with the many fine members of a class other than the limited ones with which the speaker is intimately familiar, it is to be suggested that each and every participant here should immediately construct - as a minimum - at least one "circle" of the kind

r⁴ = x⁴ + y⁴

and become familiar with it's true characteristics so that future discussions can be more informed.

(For extra credit, or for those who just wish to show off a little, n=9, or some other value, might be used as well.)

EQUAL RIGHTS - AND DUE RESPECT - FOR ALL THE KINDS OF CIRCLES!

(and for superspheres, blobs, and objects of indeterminate construction.)

John