Assignment 1

Posted   20150713;  due  ??

Problems by Branko Ćurgus

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Problem 1: When I was an undergraduate sudent

On August 8, 2013, I posted about a problem that I was assigned as an undergraduate student. Read this post and replicate as much of it as you can.

Problem 2: Is a torus in a way

Consider the torus

ParametricPlot3D[(2+Cos[s])(Cos[θ]{1,0,0}+Sin[θ]{0,1,0})-Sin[s]{0,0,1},{θ,0,2 Pi},{s,0,2 Pi},PlotStyle-> {Opacity[0.6]},PlotRange->{{-5,4},{-4,4},{-4,4}}]

This torus is opaque. It is not transparent. I pictured it transparent for a nicer picture.

Also consider the following three points:

pA={1,(5/2),(13/8)};pB={(1/4),-4,-(5/2)};pC={-(35/8),1,(1/2)};

Show[ParametricPlot3D[(2+Cos[s])(Cos[θ]{1,0,0}+Sin[θ]{0,1,0})-Sin[s]{0,0,1},{θ,0,2 Pi},{s,0,2 Pi},PlotStyle-> {Opacity[0.6]},PlotRange->{{-5,4},{-4,4},{-4,4}}],Graphics3D[{{PointSize[0.02],Cyan,Point[{pA,pB,pC}]},{Text["A",pA],Text["B",pB],Text["C",pC]}}]
]

Explore visability of these points from each other. That is, answer whether the point A is visable from the point B, whether the point B is visable from the point C and whether the point C is visable from the point A. Please be detailed in your answer.  State the all relevant facts that you find out.  Illustrate with Mathematica plot.

Problem 3: Just replicate

Problem 4: Length of an ellipse