- #1

The Bill

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- 146

I've got sources for this already, but I'm not "allowed" to use them for this, I need a professionally published journal/textbook source for a citation.

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In summary, the speaker is looking for a professionally published journal or textbook source that provides a formula for the Gaussian curvature at a single point of an intrinsically defined Riemannian or Semi-Riemannian manifold, using the intrinsic metric tensor and/or Riemann tensor. They specify that the formula should be in traditional debauch-of-indices Ricci-style and should not use coordinate-free notation or methods. This is for a computational approach and the manifold will already have specific charts in place for the use of the algorithm.

- #1

The Bill

- 374

- 146

I've got sources for this already, but I'm not "allowed" to use them for this, I need a professionally published journal/textbook source for a citation.

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- #2

jedishrfu

Mentor

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- 9,478

- #3

The Bill

- 374

- 146

This is for a computational approach, too be read by people who just want to see the math they need to write an algorithm to crunch numbers with, nothing more. The manifold will be defined with specific choices of charts already there for the use of the algorithm, so coordinate-free methods are unnecessary.

The Gauss formula is a mathematical formula used to calculate the curvature of a surface at a specific point. It is closely related to Riemann's formula, which is used to calculate the curvature of a surface at any point along a given curve. Both formulas are important in the field of differential geometry.

The Gauss formula is derived from Riemann's formula by considering the curvature of a surface at a single point instead of along a curve. It involves taking the first and second derivatives of the surface at that point and using them to calculate the curvature.

No, the Gauss formula can be applied to surfaces of any dimension. However, it is most commonly used in 2-dimensional surfaces because it is easier to visualize and calculate.

The Gauss formula is significant in mathematics because it provides a way to measure the curvature of a surface at a specific point. This is important in many fields, including physics, engineering, and computer graphics.

Yes, the Gauss formula has many practical applications. It is commonly used in computer graphics to create realistic 3-dimensional surfaces, and it is also used in physics and engineering to analyze the curvature of objects and surfaces.

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