(*^ ::[ Information = "This is a Mathematica Notebook file. It contains ASCII text, and can be transferred by email, ftp, or other text-file transfer utility. It should be read or edited using a copy of Mathematica or MathReader. If you received this as email, use your mail application or copy/paste to save everything from the line containing (*^ down to the line containing ^*) into a plain text file. On some systems you may have to give the file a name ending with ".ma" to allow Mathematica to recognize it as a Notebook. The line below identifies what version of Mathematica created this file, but it can be opened using any other version as well."; FrontEndVersion = "Macintosh Mathematica Notebook Front End Version 2.2"; MacintoshStandardFontEncoding; fontset = title, nohscroll, center, bold, L0, 24, "Times New Roman"; fontset = subtitle, nohscroll, center, bold, L0, 18, "Times New Roman"; fontset = subsubtitle, nohscroll, center, italic, L0, 14, "Times New Roman"; fontset = section, nohscroll, grayBox, bold, L0, 18, "Times New Roman"; fontset = subsection, nohscroll, blackBox, bold, L0, 14, "Times New Roman"; fontset = subsubsection, nohscroll, whiteBox, bold, L0, 12, "Times New Roman"; fontset = text, nohscroll, L0, 12, "Times New Roman"; fontset = smalltext, nohscroll, L0, 10, "Times New Roman"; fontset = input, nowordwrap, bold, L-4, 12, "Courier New"; fontset = output, nowordwrap, L-4, 12, "Courier New"; fontset = message, nowordwrap, R32768, L-4, 12, "Courier New"; fontset = print, nowordwrap, L-4, 12, "Courier New"; fontset = info, nowordwrap, B32768, L-4, 12, "Courier New"; fontset = postscript, nowordwrap, L0, 12, "Courier New"; fontset = name, nohscroll, italic, L0, 10, "Arial"; fontset = header, L0, 12, "Times New Roman"; fontset = leftheader, L2, 12, "Times New Roman"; fontset = footer, center, L0, 12, "Times New Roman"; fontset = leftfooter, L2, 12, "Times New Roman"; fontset = help, nohscroll, L0, 10, "Times New Roman"; fontset = clipboard, nohscroll, L0, 12, "Times New Roman"; fontset = completions, nohscroll, L0, 12, "Times New Roman"; fontset = special1, nohscroll, L0, 12, "Times New Roman"; fontset = special2, nohscroll, L0, 12, "Times New Roman"; fontset = special3, nohscroll, L0, 12, "Times New Roman"; fontset = special4, nohscroll, L0, 12, "Times New Roman"; fontset = special5, nohscroll, L0, 12, "Times New Roman"; currentKernel; ] :[font = title; inactive; preserveAspect; plain; bold; italic; fontColorBlue = 65535; fontName = "Times"; startGroup] Live Graphics Workshop :[font = text; center; plain; italic; fontSize = 14; fontName = "Times"] Original by W. Shaw © 1993-1996 :[font = section; inactive; Cclosed; preserveAspect; fontName = "Times"; startGroup] Minimal Surfaces :[font = input; preserveAspect; fontName = "Times"] MiniCartPlot[f_, {a_, b_}, {c_, d_}, n_:15] := Module[{x, y, z, u, v, comppoint, paracomppoint, realpoint}, x[w_] := (w^2 - 1) D[f, {w, 2}] - 2 w D[f, w] + 2 f; y[w_] := I ((w^2 + 1) D[f, {w, 2}] - 2 w D[f, w] + 2 f); z[w_] := 2 w D[f, {w, 2}] - 2D[f, w]; comppoint = Evaluate[{x[w], y[w],z[w]}]; paracomppoint = comppoint /. w -> u + I v; realpoint[u_, v_] = Expand[ComplexExpand[Re[paracomppoint]]]; ParametricPlot3D[Evaluate[ realpoint[u, v]], {u, a, b}, {v, c, d}, PlotPoints -> n, Axes -> False] ] :[font = input; preserveAspect; fontName = "Times"] enneper = MiniCartPlot[w^3, {-4, 4}, {-4, 4}] :[font = input; preserveAspect; fontName = "Times"] LinkWrite[live, enneper] (or) ThreeScript["enneper.ts", enneper] :[font = input; preserveAspect; fontName = "Times"] MiniPolarPlot[f_, {a_, b_}, {c_, d_}, n_:15] := Module[{x, y, z, u, v, comppoint, paracomppoint, realpoint}, x[w_] := (w^2 - 1) D[f, {w, 2}] - 2 w D[f, w] + 2f; y[w_] := I ((w^2 + 1) D[f, {w, 2}] - 2 w D[f, w] + 2 f); z[w_] := 2 w D[f, {w, 2}] - 2D[f, w]; comppoint = Evaluate[{x[w], y[w],z[w]}]; paracomppoint = comppoint /. w -> Exp[u + I v]; realpoint[u_, v_] = Expand[ComplexExpand[Re[paracomppoint]]]; ParametricPlot3D[Evaluate[realpoint[u, v]], {u, a,b}, {v, c, d}, PlotPoints -> n, Axes -> False] ] :[font = input; preserveAspect; fontName = "Times"] catenoid = MiniPolarPlot[w*Log[w], {-2, 2}, {0, 2 Pi}] :[font = input; preserveAspect; fontName = "Times"; endGroup] LinkWrite[live, catenoid] (or) ThreeScript["catenoid.ts" catenoid] :[font = section; inactive; Cclosed; preserveAspect; fontName = "Times"; startGroup] Knots :[font = text; inactive; preserveAspect; fontName = "Times"] Be sure to load the definitions in the knots NoteBook Before attempting these! :[font = input; preserveAspect; fontName = "Times"] plotknot[p_, q_, col_:.5] := Show[tube[ {Cos[t] (1 + .5 Cos[(q/p) t]), Sin[t] (1 + .5 Cos[(q/p) t]), .5 Sin[(q/p) t]}, {t, 0, 2 Pi p, 50}, 8, .1], ViewPoint -> {0, 0, 1}, Boxed -> False, LightSources -> {{{0, 0, 1}, RGB[col, 1-col, col/2]}}] :[font = input; preserveAspect; fontName = "Times"] myknot = plotknot[2, 5] :[font = input; preserveAspect; fontName = "Times"; endGroup] LinkWrite[live, myknot] (or) ThreeScript["myknot.ts", myknot] :[font = section; inactive; Cclosed; preserveAspect; fontName = "Times"; startGroup] Discontinuous Function :[font = input; preserveAspect; fontName = "Times"] Z[r_, t_] := Which[r <= 0.0001, 0, True, Sin[2 t]/2]; :[font = input; preserveAspect; fontName = "Times"] discont = ParametricPlot3D[{r Cos[t], r Sin[t], 2*Z[r, t]}, {r, 0, 2}, {t, 0, 2 Pi}, PlotPoints -> {20, 30}] :[font = input; preserveAspect; fontName = "Times"; endGroup] LinkWrite[live, discont] (or) ThreeScript["discont.ts", discont] :[font = section; inactive; Cclosed; preserveAspect; fontName = "Times"; startGroup] Non-differentiable function :[font = input; preserveAspect; fontName = "Times"] nondiff = ParametricPlot3D[{r Cos[t], r Sin[t],W[r, t]}, {r, 0, 2}, {t, 0, 2 Pi}, PlotPoints -> {20, 30}] :[font = input; preserveAspect; fontName = "Times"; endGroup; endGroup] LinkWrite[live, nondiff] (or) ThreeScript["nondiff.ts", nondiff] :[font = section; fontName = "Times"; startGroup] For further information, advice or suggestions please contact :[font = text; cellOutline; fontName = "Times"; endGroup] Email: support@milohedge.com Post: Milo Hedge Limited, 6 The Isis Business Centre, Pony Road, Oxford, OX4 2RD WWW: http://www.milohedge.com/mathlive/ ^*)