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Alfred Gray's Surfaces Properties

Source Notebook

Alfred Gray’s associated surfaces taken from his original notebooks of his book "Modern Differential Geometry of Curves and Surfaces with Mathematica"

Details

The surfaces properties include:
AreaElementarea element
AsymptoticCurvesasymptotic curves
FirstFundamentalFormCoefficientsfirst fundamental form coefficients
SecondFundamentalFormCoefficientssecond fundamental form coefficients
UnitNormalunit normal
GaussianCurvatureGaussian curvature
MeanCurvaturemean curvature
PrincipalCurvaturesprincipal curvatures
ParametricSurfaceTangentPlanetangent plane of a parametric surface at a point
FocalSetfocal set
Geodesicequations for geodesics
InversionSurfaceinversion surface
ParallelSurfaceparallel surface
PerpendicularSurfaceperpendicular surface
MovingOrthonormalFramethe moving orthonormal frame
RiemannTensorRiemann tensor
RicciCurvatureRicci curvature
RicciScalarRicci scalar
ShapeOperatorshape operator
WeingartenMatrixWeingarten matrix

Examples

Basic Examples

Retrieve the ResourceData:

In[1]:=
AlfredGraysSurfacesProperties = ResourceData[\!\(\* TagBox["\"\<Alfred Gray\[CloseCurlyQuote]s Surfaces Properties\>\"", #& , BoxID -> "ResourceTag-Alfred Gray's Surfaces Properties-Input", AutoDelete->True]\), "Association"];

Display a list of the available curves:

In[2]:=
Keys[AlfredGraysSurfacesProperties] // Short
Out[3]=

The total number of curves:

In[4]:=
AlfredGraysSurfacesProperties // Length
Out[5]=

Get a list of possible keys:

In[6]:=
Keys@AlfredGraysSurfacesProperties["rconoid"]
Out[6]=

Ask for values of a definite surface:

In[7]:=
AlfredGraysSurfacesProperties["rconoid"]["PedalSurface"]
Out[8]=

Some values can be very large:

In[9]:=
AlfredGraysSurfacesProperties["pseudosphere"][ "PrincipalCurvatures"] // Short
Out[9]=

Enrique Zeleny, "Alfred Gray's Surfaces Properties" from the Wolfram Data Repository (2022)  

Data Resource History

  • Date Created:

Source Metadata

  • Citation:
    • Gray, A., Modern Differential Geometry of Curves and Surfaces with Mathematica, 2nd ed. Boca Raton, FL: CRC Press, 1997.

See Also

Publisher Information

  • Prepared for the Wolfram Data Repository By: Alfred Gray
  • Publisher of Record: Enrique Zeleny