## 80 Reputation

12 years, 210 days

## Join two lines with a pair of spirals?...

Maple

This is what I have so far

S1:=unapply(u*FresnelS(u)+((1/Pi)*cos((1/2)*Pi*u^2))-(1/Pi),u);

C1:=unapply(u*FresnelC(u)-((1/Pi)*sin((1/2)*Pi*u^2)),u);

with(plottools);

with(plots);

u0:=sqrt(0.25);

e1:=evalf(FresnelC(u0)+FresnelS(u0)*cot((3*Pi)/8));

p1:=display(plot([FresnelC(u),FresnelS(u),u=0..u0]));

p2:=display(plot(x-e1,x=0..1,y=0..1,colour=black));

display(p1,p2);

## delete specific parts of my graph...

Maple

From this program

S1:=unapply(u*FresnelS(u)+((1/Pi)*cos((1/2)*Pi*u^2))-(1/Pi),u);

C1:=unapply(u*FresnelC(u)-((1/Pi)*sin((1/2)*Pi*u^2)),u);

R1:=1;

u1:=evalf(sqrt(0.4));

E1:=evalf(Pi*R1*S1(u1)+R1);

D1:=evalf(Pi*R1*C1(u1)+1);

a:=evalf(Pi*R1*(u1));

with(plottools);

with(plots);

c1 := circle([D1,0], R1);

display(c1);

plot([a*FresnelC(u),a*FresnelS(u),u=0..u1]);

p1:=plots[display](plot([1+a*FresnelC(u),a*FresnelS(u)-E1,u=0..u1]),c1,scaling=constrained);

## flip a graph about the x and y axis...

Maple

The following program produces a plot in the 4th quadrant.

S1:=unapply(u*FresnelS(u)+((1/Pi)*cos((1/2)*Pi*u^2))-(1/Pi),u);

C1:=unapply(u*FresnelC(u)-((1/Pi)*sin((1/2)*Pi*u^2)),u);

R1:=1;

u1:=evalf(sqrt(0.4));

E1:=evalf(Pi*R1*S1(u1)+R1);

D1:=evalf(Pi*R1*C1(u1));

with(plottools);

with(plots);

c1 := circle([D1, 0], R1);

a:=evalf(Pi*R1*u1);

p1:=plots[display](plot([1+a*FresnelC(u),a*FresnelS(u)-E1,u=0..u1]),c1,scaling=constrained);

p3:=plot(0,x=-1..0);

display(p1,p3);

## create a new axis at a specific point...

Maple

I have the above program

S1:=unapply(u*FresnelS(u)+((1/Pi)*cos((1/2)*Pi*u^2))-(1/Pi),u);

C1:=unapply(u*FresnelC(u)-((1/Pi)*sin((1/2)*Pi*u^2)),u);

R1:=1;

u1:=evalf(sqrt(0.4));

E1:=evalf(Pi*R1*S1(u1)+R1);

D1:=evalf(Pi*R1*C1(u1));

with(plottools);

with(plots);

c1 := circle([D1, E1], R1);

a:=evalf(Pi*R1*u1);

plot([a*FresnelC(u),a*FresnelS(u),u=0..u1]);

p1:=plots[display](plot([a*FresnelC(u),a*FresnelS(u),u=0..u1]),c1,scaling=constrained);

p3:=plot(0,x=-1..0);

display(p1,p3);

## combine 2 graphs...

Maple

From the program below

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