example18.mws

> i1 := exp(t)*cos(t);

i1 := exp(t)*cos(t)

> j1 := exp(t)*sin(t);

j1 := exp(t)*sin(t)

> k1 := t;

k1 := t

> with(plots);

> path := spacecurve([i1,j1,t],t=-1..1, axes=normal, color=red, numpoints=100); point1 := PLOT3D(POINTS([1,0,0],SYMBOL(DIAMOND))); display3d({point1, path});

[Maple Plot]

> i2 := diff(i1,t);

i2 := exp(t)*cos(t)-exp(t)*sin(t)

> j2 := diff(j1, t);

j2 := exp(t)*sin(t)+exp(t)*cos(t)

> k2 := diff(k1, t);

k2 := 1

> D1 := simplify(i2^2 + j2^2 + k2^2);

D1 := 2*exp(2*t)+1

> i3 := diff(i2, t);

i3 := -2*exp(t)*sin(t)

> j3 := diff(j2, t);

j3 := 2*exp(t)*cos(t)

> k3 := diff(k2, t);

k3 := 0

> i22 := simplify(i2^2);

i22 := exp(2*t)*(cos(t)-sin(t))^2

> C1 := simplify(i2^2 + j2^2 + k2^2);

i22 := exp(2*t)*(cos(t)-sin(t))^2

> Ia := simplify( (i2 * k3) - (i3 * k2));

Ia := 2*exp(t)*sin(t)

> Ja := simplify( (j2 * k3) - (j3 * k2));

Ja := -2*exp(t)*cos(t)

> Ka := simplify( (i2 * j3) - (i3 * j2));

Ka := 2*exp(2*t)

> D2 := simplify(Ia^2 + Ja^2 + Ka^2);

D2 := 4*exp(2*t)+4*exp(4*t)

> K0 := simplify( (D2^(1/2))/(D1^(3/2)));

K0 := 2*(exp(t)^2*(1+exp(t)^2))^(1/2)/(2*exp(2*t)+1...

> Ksolve := evalf(subs( t=0, K0));

Ksolve := .5443310534

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