Dr. Sarah's Maple File for Homework 3General Maple items LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVElJnBpO0YnLyUnaXRhbGljR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRic= and its decimal approximation, exponential function in Maple: Pi; evalf(%); exp(t);Maple for Question 1 Part b) on Exercise 1.4.7:Modify the equation of the curve in the curve1 command to match the curve in 1.4.7. Be sure to use exp(t) in the curve1 command!with(VectorCalculus):
curve1:= <r*cos(t), r*sin(t), h*t>;
TNBFrame(curve1,t) assuming t::real;
simplify(Curvature(curve1,t));
simplify(Torsion(curve1,t));Maple for Question 3 Part b) on the Osculating Circle:Modify the constants in the equation of the osculatingcircle command for the center of the circle and the radius-squared to mesh with your by-hand work. If you like, you can also modify the domain and range -1/2 .. 1/2 and -1 .. 1 in the osculatingcircle command:with(plots):
osculatingcircle := implicitplot((x-1/4)^2+(y-1/4)^2-1/4, x = -1/2 .. 1/2, y = -1 .. 1):
curve2plot:=plot(x^2, x = -2..2):
display(curve2plot, osculatingcircle);Note that I defined the plots and used a colon to surpress their output and then used the display command with a semi-colon to show them on the same graph.(Optional) Maple for Question 5 on the Strake:If you choose to use Maple in Question 4, then you can modify the equation of the curve in the curve4 command and in the innerhelix and outerhelix commands to match the strake (modify 5 and 3and 5.1 and 3.1)with(VectorCalculus): with(plots):
curve4:= <5*cos(t), 5*sin(t), 3*t>;
simplify(Curvature(curve4,t), trig);
ArcLength(curve4, t = -10 .. 10);
Cylinder := implicitplot3d(x^2+y^2 = 1, x = -1 .. 1, y =-1 .. 1, z = 0 .. 10):
innerhelix:= spacecurve({[5*cos(t), 5*sin(t), 3*t, t = 0 .. 7]}):
outerhelix:= spacecurve({[5.1*cos(t), 5.1*sin(t), 3.1*t, t = 0 .. 7]}):
display({Cylinder, innerhelix,outerhelix});