

What Math Equations Look Like in 3-D - fahrbach
http://www.wired.com/2014/06/math-equations-models/

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MrMeker
"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.

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ansjmels
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...](http://en.wikipedia.org/wiki/Singularity_\(mathematics\)#Algebraic_geometry_and_commutative_algebra)

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

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Grue3
Fixed headline: "This is what 3d graphs of math equations look like".

