## Surface of revolution starting from an arbitrary 2...

Suppose I want to revolve the curve given in the (X,Y)-plane by the set of parametric equations

x(t) = cos(t) + t sin(t)

y(t) = sin(t) - t cos(t)

for t in [0,Pi/2] around the X-axis. How can I plot the given surface of revolution? Similarly, the same question for

x(t) = exp(t)*cos(t)

y(t) = exp(t)*sin(t)

for t in [0,Pi/2]

## AFactor doesn't factor a (supposedly) reducible po...

I have the following Polynomial F. Computing the genus shows that this curve has negative genus and thus is reducible. But using AFactor doesn't produce a factorization. Any ideas?

```with(algcurves):
F := z^9+(-3/2+(3/2*I)*sqrt(3))*y^3*z^6+(-3/2-(3/2*I)*sqrt(3))*x^3*z^6+(-3/2-(3/2*I)*sqrt(3))*y^6*z^3+(-3/2+(3/2*I)*sqrt(3))*x^6*z^3+y^9+(-3/2-(3/2*I)*sqrt(3))*x^3*y^6+(-3/2+(3/2*I)*sqrt(3))*x^6*y^3+x^9-3*(x*y*z)^3:
z:=1:
genus(F, x, y);
evala(AFactors(F));
```

## Tangent to a curve in maple...

A family of curves has polar equation r=cos^n (theta/n), 0<=theta,n*pi, where n is a positive even integer.

Previously Using t = theta as the parameter and finding  a parametric form of the equation of the family of curves it was shown that

dy/dx = (sin(t)sin(t/n)-cos(t)cos(t/n)) /( sin(t)cos(t/n)+cos(t)sin(t/n)).

Is it possible to show on Maple with a program that there are n+1 points where the tangent to the curve is paralell to the y axis?

## Distance Between 2 curves...

i got 2 curves
a := abs(x);
b := (3/4)*x^2+1/4;

how can i get the max distance between them from x = -1 until x =1?

heeeeeeeeeelp

## Find angle between curves...

How to get tangent angle between two curves?

example for these : f(x)=((x^4+5)^(1/2))/(sinx+5) and g(x)=cosx^2   ; x>0

thanks :)

## Curve fitting for function and experimental data...

Hi

friend i want fit a curve regarding some data and fnction and how we can find the values of a,b,c and d for the following

f=1-(8*a*b+6*c*d/(b*k*x))/(2*a*b+c*b*(1/(b*k*x)))

X := Vector([200, 210, 220, 230, 240, 250, 260, 270, 280, 290])

Y := Vector([.4172, .3030, .4668, .3317, .1276, .1303, .1733, .1451, .3466, .4125])

## Parallel curves on surfaces

by: Maple 15

Parallel curves on surfaces. The distance between the points of the curves is measured along the curves of intersection of the surface and perpendicular planes.
(According to tradition, it also does not make sense.)

equidistant_curve_surface_MP.mw

## nonlinear curve fit...

Dear Community,

I've made a nonlinear curve fit with the Minimize routine (see attachment). What would be an easy and elegant way to rerun the model (Model) with the fitted values of a, b, c and plot the result together with the measured points in the same chart? I'm stuck here.

best regards

Andras

BroSzem_Data.xlsx

Nonlin_Curve_Fit.mw

## how to calculate implicit Cartesian equation from ...

from mathematica,

n = 5;
CalabiYau[z_, k1_, k2_] := Module[{z1 = Exp[2Pi I k1/n]Cosh[z]^(2/n), z2 = Exp[2Pi I k2/n]Sinh[z]^(2/n)}, {Re[z1], Re[z2], Cos[alpha]Im[z1] + Sin[alpha]Im[z2]}];
Do[alpha = (0.25 + t)Pi; Show[Graphics3D[Table[ParametricPlot3D[CalabiYau[x + I y, k1, k2], {x, -1, 1}, {y, 0, Pi/2}, DisplayFunction -> Identity, Compiled ->False][[1]], {k1, 0, n - 1}, {k2, 0, n - 1}], PlotRange -> 1.5{{-1, 1}, {-1, 1}, {-1, 1}}, ViewPoint -> {1, 1, 0}]], {t, 0, 1, 0.1}];

n := 5;

z1 := exp(2*3.14*I*k1/n)*cosh(z)^(2/n);
z2 := exp(2*3.14*I*k2/n)*sinh(z)^(2/n);

alpha = (0.25 + t)Pi;

xx := Re(z1);
yy := Re(z2);
uu := cos(alpha)*Im(z1) + sin(alpha)*Im(z2);

where k1, k2, alpha are variables

print([xx,yy,uu]);

i find algcurve has implicitize

how to use this implicitize to find 3d surface?

is there any other method to find?

i searched groebner basis can do this, but in mathematica is different from maple example

## How to plot this in Maple...

Hi,

I am having trouble in plotting the following surface (it is a quite complicated expression, but should be fine).

OwnSurface := [-Re(arctan(exp(I*Pi*(1/4))*(u^2+v^2)^(1/2)))-(1/2)*ln((1+(u^2+v^2)^2)^(1/2)), -arctan(1/((2*(u^2+v^2))^(1/2)-1))+7*Pi*(1/4), (1/8)*ln(u^2+v^2-(2*(u^2+v^2))^(1/2)+1)-(1/8)*ln(u^2+v^2+(2*(u^2+v^2))^(1/2)+1)-(1/4)*arctan(1/((2*(u^2+v^2))^(1/2)+1))+(1/4)*arctan(1/((2*(u^2+v^2))^(1/2)-1))];

plot3d(OwnSurface, u = -.4 .. .4, v = -.4 .. .4, labels = [x1, x2, x3]);

The only thing maple does is plotting a box with a diagonal line. How can I fix this?

## Plotting Szego curve...

I want to plot a curve of the form |z*e^(1-z)| = 1 (the Szego curve). I am not sure how to call complexplot() to make this happen. Just calling complexplot(abs(z*exp(1-z)) = 1) does not work, and I don't know what else to specify. Any help?

## Spiral around the curve

by: Maple 15

Spiral (equidistant) around the curve.  In this case, a spiral around the spiral.
So without any sense.
spiral_around_curve.mw

If we re-save the animation with the program Easy GIF Animator, its size is reduced by about 10 times, and sometimes much more.

## Catmull-Rom spline curves...

Hello,

I try to use a Catmull-Rom spline which has to match on several points.

I use a code extracted from the book "Geometry and curves with maple".

Here you can find an extract which is visible from google book :

I have slightly modified the initial procedure crom_2d. I didn't find the error in my procedure. May you help me to find the blocking point of my procedure ?

Here I attached my code:

CalculSplineMatmull-Rom.mw

## Plot of Implicitly Defined 3D Curve...

Suppose that we have the following curve on a unit sphere

r^2+z^2=1

phi=pi/3

-1<=z<=1

which is the implicit equation of a circle in "cylindrical coorinates" (r,phi,z) on the sphere.

How can I plot this curve without solving the implicit equation for r or z ?

Also, I don't want to make any parameterization.