DG in Mathematica
Osculating Plane r[t_] = {t Cos[t], t Sin[t], t}; r1[t_] = D[r[t], t]; r2[t_] = D[r[t], {t, 2}]; p[t_] = r[t] + u r1[t] + v r2[t]; ut[t_] = Normali…
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Conjugate Direction and its Properties
Let \( S:\vec{r}=\vec{r}( u,v )\) be a surface. Also let \( \Gamma \) and \( \Gamma' \) be tangent plane…
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Fundamental Equation of Surface Theory
The fundamental equations of surface theory describe how a surface bends and stretches in three-dimensional…
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Asymptotic Lines and related Theorems
Let \( S:\vec{r}=\vec{r}( u,v )\) be a surface. Then curves on the surface whose directions are self-con…
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Line of Curvature and its Properties
Let \(S: \vec{r}=\vec{r}(u,v)\) be a surface. Then there are two principal directions (tangent to principal se…
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Minimal Surface
A minimal surface is a type of surface in differential geometry that has minimal area for a given boundary. Ma…
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Developable Surface Unit 5
In differential geometry, a developable surface is a special type of surface that can be flattened onto a plan…
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