Romancing the Sphere

Some may find this unique table helpful in understanding spheres.

Beyond the purely mathematic, this fully symmetrical regime may also find application in physics, sociology, ontology and economics.

Note: Using the diametric mode for calculations (mentally or on paper) can be quicker than employing the formal (radial) convention, especially when working with hyper-dimensional domains, exponential growth scenarios, or when one is in need of an easier way to factor between domains of differing dimensionality.

Diametric dimensionality

If you would like a personal, complimentary copy of this chart in PDF format (8.5″x11″ – but infinitely scalable) use the form below. Comments optional.
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Notes:

All versions since 2004 have reflected the much needed repair of the broken symmetry found in the 0-sphere definition under the prevailing n-sphere generalisation.

If you prefer the formal mode for transforms between exterior and interior space, simply use •r/d instead of •D/2d.

If you’re a student, check with your professor before applying these principles in your work. If you are the professor, just use your best judgement …and maybe get a second faculty opinion. 😉

Jan. 19, 2011 – Image updated from 2004 version to new 2011 version.

Jan. 22, 2011 – Minor aesthetic changes; image updated.

Jan. 23, 2011 – Diametric ext values adjusted by -1; image updated.

Oct. 26, 2011 – Minor text/aesthetic changes; explicatory notes added.

Dec. 28, 2011 – Declared dimensions as a single-character variable (d);
image not updated — use request form below for most current version.

Jan. 10, 2012 – Image updated.

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