What Math Equations Look Like in 3-D

http://www.wired.com/2014/06/math-equations-models/

by fahrbach • 12 years ago

36 5 12 years ago

MrMeker2• 12 years ago

"It’s one thing to check that the derivatives of a function are zero and another to feel the plaster taper to a sharp point."

Those are two very different things. A sharp point is not differentiable. A derivative of zero indicates a possible minimum or maximum of the function.

arithma• 12 years ago

In a parametric curve, a derivative of zero may indicate a cusp, which I feel is where the comparison is coming from.

I only read your comment and article but didn't see the video, so this comment may be off.

ansjmels• 12 years ago

No, they are the same thing. What this sentence is referring to is the vanishing of the Jacobian determinant [1] (which is defined using the derivatives of the defining equations).

A simple example is the equations y^3 - x^2 = 0. This is a "cusp" (use wolfram alpha to see what it looks like) and has a singularity at the origin.

The jacobian is the matrix:

[ -2x, 3y^2 ]

This has rank 1 unless x and y are zero in which case it has rank zero. The fact that the rank is less than 1 indicates a singularity.

[1] http://en.wikipedia.org/wiki/Singularity_(mathematics)#Algeb...

MrMeker2• 12 years ago

This seems to explain the sentence. Thank you, now I have something to read about for the next few hours.

Grue3• 12 years ago

Fixed headline: "This is what 3d graphs of math equations look like".

What Math Equations Look Like in 3-D

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