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edited Oct 12, 2014 at 21:13

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Update for space curescurves

curvature[f_] := With[{d1 = D[f, u], d2 = D[f, {u, 2}]}, Norm[Cross[d1, d2]] / Norm[d1]^3 // Simplify] loxodromes[a_, b_] := { 2 a E^(b u) Cos[u], 2 a E^(b u) Sin[u], a^2 E^(2 b u) - 1 } / (1 + a^2 E^(2 b u)) cur = curvature[loxodromes[1, 0.1]]; plo = Plot[cur, {u, -4 Pi, 4 Pi}, PlotRange -> All]

range = Last[PlotRange /. AbsoluteOptions[plo, PlotRange]]; Show[ ParametricPlot3D[loxodromes[1, 0.1], {u, -4 Pi, 4 Pi}, ColorFunction -> Function[{x, y, z, u, v}, ColorData["Rainbow"][Rescale[cur, range]]], ColorFunctionScaling -> False, PlotStyle -> Thickness[0.01]], Graphics3D[{Opacity[0.2], Sphere[]}], ImageSize -> 500 ]500]

Update for space cures

curvature[f_] := With[{d1 = D[f, u], d2 = D[f, {u, 2}]}, Norm[Cross[d1, d2]]/Norm[d1]^3 // Simplify] loxodromes[a_, b_] := { 2 a E^(b u) Cos[u], 2 a E^(b u) Sin[u], a^2 E^(2 b u) - 1 }/(1 + a^2 E^(2 b u)) cur = curvature[loxodromes[1, 0.1]]; plo = Plot[cur, {u, -4 Pi, 4 Pi}, PlotRange -> All]

range = Last[PlotRange /. AbsoluteOptions[plo, PlotRange]]; Show[ ParametricPlot3D[loxodromes[1, 0.1], {u, -4 Pi, 4 Pi}, ColorFunction -> Function[{x, y, z, u, v}, ColorData["Rainbow"][Rescale[cur, range]]], ColorFunctionScaling -> False, PlotStyle -> Thickness[0.01]], Graphics3D[{Opacity[0.2], Sphere[]}], ImageSize -> 500 ]

Update for space curves

curvature[f_] := With[{d1 = D[f, u], d2 = D[f, {u, 2}]}, Norm[Cross[d1, d2]] / Norm[d1]^3 // Simplify] loxodromes[a_, b_] := { 2 a E^(b u) Cos[u], 2 a E^(b u) Sin[u], a^2 E^(2 b u) - 1 } / (1 + a^2 E^(2 b u)) cur = curvature[loxodromes[1, 0.1]]; plo = Plot[cur, {u, -4 Pi, 4 Pi}, PlotRange -> All]

range = Last[PlotRange /. AbsoluteOptions[plo, PlotRange]]; Show[ ParametricPlot3D[loxodromes[1, 0.1], {u, -4 Pi, 4 Pi}, ColorFunction -> Function[{x, y, z, u, v}, ColorData["Rainbow"][Rescale[cur, range]]], ColorFunctionScaling -> False, PlotStyle -> Thickness[0.01]], Graphics3D[{Opacity[0.2], Sphere[]}], ImageSize -> 500]

added 991 characters in body

edited Oct 12, 2014 at 15:05

84.7k
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Update for space cures

curvature[f_] := With[{d1 = D[f, u], d2 = D[f, {u, 2}]}, Norm[Cross[d1, d2]]/Norm[d1]^3 // Simplify] loxodromes[a_, b_] := { 2 a E^(b u) Cos[u], 2 a E^(b u) Sin[u], a^2 E^(2 b u) - 1 }/(1 + a^2 E^(2 b u)) cur = curvature[loxodromes[1, 0.1]]; plo = Plot[cur, {u, -4 Pi, 4 Pi}, PlotRange -> All]

enter image description here

range = Last[PlotRange /. AbsoluteOptions[plo, PlotRange]]; Show[ ParametricPlot3D[loxodromes[1, 0.1], {u, -4 Pi, 4 Pi}, ColorFunction -> Function[{x, y, z, u, v}, ColorData["Rainbow"][Rescale[cur, range]]], ColorFunctionScaling -> False, PlotStyle -> Thickness[0.01]], Graphics3D[{Opacity[0.2], Sphere[]}], ImageSize -> 500 ]

enter image description here

A nice novel about Gauss

A nice novel about Gauss

Update for space cures

curvature[f_] := With[{d1 = D[f, u], d2 = D[f, {u, 2}]}, Norm[Cross[d1, d2]]/Norm[d1]^3 // Simplify] loxodromes[a_, b_] := { 2 a E^(b u) Cos[u], 2 a E^(b u) Sin[u], a^2 E^(2 b u) - 1 }/(1 + a^2 E^(2 b u)) cur = curvature[loxodromes[1, 0.1]]; plo = Plot[cur, {u, -4 Pi, 4 Pi}, PlotRange -> All]

enter image description here

range = Last[PlotRange /. AbsoluteOptions[plo, PlotRange]]; Show[ ParametricPlot3D[loxodromes[1, 0.1], {u, -4 Pi, 4 Pi}, ColorFunction -> Function[{x, y, z, u, v}, ColorData["Rainbow"][Rescale[cur, range]]], ColorFunctionScaling -> False, PlotStyle -> Thickness[0.01]], Graphics3D[{Opacity[0.2], Sphere[]}], ImageSize -> 500 ]

enter image description here

A nice novel about Gauss

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edited Oct 7, 2014 at 19:32

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A must-read about those jolly times: http://en.wikipedia.org/wiki/Sophie_Germain

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edited Oct 7, 2014 at 19:03

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edited Oct 7, 2014 at 18:47

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edited Oct 7, 2014 at 12:54

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edited Oct 7, 2014 at 0:28

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answered Oct 6, 2014 at 18:14

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