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Paras31

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2 years, 20 days
Agricultural University of Athens
PhD Candidate

Social Networks and Content at Maplesoft.com

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Teacher of Mathematics with a proven track record of working in education management. Proficient in Ease of Adaptation, Course Design, and Instructional Technology. Holds a Bachelor's degree in Mathematics from the University of the Aegean and a Master's in Applied Mathematics at the Hellenic Open University, focusing on Ordinary and Partial Differential Equations. His enthusiasm lies in the application of mathematical models to real-world contexts, such as epidemiology and population growth. Aside from his passion for teaching, Athanasios enjoys football, basketball, and spending time with his dogs.

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These are questions asked by Paras31

Exploring the Mapping of Vertical Lines ...

Paras31 240 Maple 2025
complex plotting conformal
April 10 2025
2 0

In the transformation w = e^z, vertical lines in the complex z-plane of the form Re(z)=a are mapped to circles of radius e^a in the w-plane.

Can I create a Maple visualization that does the following:

  1. Displays the result side by side, showing each vertical line in the z-plane and its corresponding mapped circle in the w-plane.

  2. Does it use a different color and style for each line and its image (e.g., dashed, dotted, solid, or different colors)?

> 

restart; interface(imaginaryunit = 'i')
> 

z := 2+2*I

2+2*I

 (1)
> 

with(plots); point1 := pointplot([[Re(z), Im(z)]], symbol = solidcircle, color = blue, axes = normal, labels = ["Re(z)", "Im(z)"], title = "Complex Number Plot")

 
> 

mod_z := abs(z)

2*2^(1/2)

 (2)
> 

vector1 := arrow([0, 0], [Re(z), Im(z)], color = red, shape = double_arrow, width = 0.5e-1, border = false, head_width = .1, head_length = .1); vector2 := arrow([0, 0], [0, Im(z)], color = green, shape = double_arrow, width = 0.5e-1, border = false, head_width = .1, head_length = .1); vector3 := arrow([0, 0], [Re(z), 0], color = yellow, shape = double_arrow, width = 0.5e-1, border = false, head_width = .1, head_length = .1)
> 

display([vector1, point1, vector2, vector3], axes = normal, labels = ["Re(z)", "Im(z)"], view = [0 .. 3, -1 .. 4], scaling = constrained, title = "Modulus of complex number")

 
> 

w := 2+3*I

2+3*I

 (3)
> 

z+w

4+5*I

 (4)
> 

z-w

-I

 (5)
> 

z.w

-2+10*I

 (6)
> 

z/w

10/13-(2/13)*I

 (7)
> 

restart
> 

with(plots); a := 2; complexplot(a+I*t, t = -Pi .. Pi, title = "Vertical Line Re(z)=2")

 
> 

A := [-3, -1, 0, 1, 2]; P := [seq(complexplot(x+I*y, y = -10 .. 10, color = red), `in`(x, A))]; display(P, title = "Multiple Vertical Lines in Complex Plane")

 
> 

with(plots); B := [-3, -1, 0, 1, 2]; H := [seq(complexplot(x+I*y, x = -10 .. 10, color = blue), `in`(y, B))]; display(H, title = "Multiple Horizontal Lines in Complex Plane")

 
 

NULL

Download operations.mw

Plotting Julia sets with Maple...

Paras31 240 Maple 2025
fractal julia plotting
April 07 2025
2 2

I am studying the Julia sets. I have tried the following two codes to generate Julia Sets. The first one I found in Maple Help, and the second one from http://ftp.informatik.rwth-aachen.de/maple/mfrjulfn.htm. I am wondering if there exists another code to generate the Julia set. My question is just for educational purposes, because those two codes work fine.
 

> 

with(Fractals:-EscapeTime); with(ImageTools); bl, ur := -2.0-1.5*I, 2.0+1.5*I; c := -1; J := Julia(700, bl, ur, c, cutoff = 4, iterationlimit = 6000, output = layer1); Embed(J)
> 

restart; julfn_zsqrd := proc (x, y) local c, z, m; c := evalf(0); z := evalf(x+I*y); for m from 0 to 50 while abs(z) < 2 do z := -z^2+z end do; m end proc; plot3d(0, -1.0 .. 2.0, -2.0 .. 2.0, style = patchnogrid, orientation = [-90, 0], grid = [250, 250], scaling = constrained, color = julfn_zsqrd)

 
> 

NULL


 

Download Julia_Sets.mw

Finding and plotting the 6th roots of un...

Paras31 240 Maple 2025
complex roots plotting
March 31 2025
3 0

I was reading a book on complex analysis, and I tried to answer some questions like "Find and plot the sixth roots of unity on Maple."  I tried the following code, which works. Is there any other way to solve and plot the same question?

> 

with(plots); interface(imaginaryunit = 'I'); s := [seq(exp(2*I*Pi*k*(1/6)), k = 0 .. 5)]; X := [seq(Re(s[k]), k = 1 .. 6)]; Y := [seq(Im(s[k]), k = 1 .. 6)]

[1, 1/2+((1/2)*I)*3^(1/2), -1/2+((1/2)*I)*3^(1/2), -1, -1/2-((1/2)*I)*3^(1/2), 1/2-((1/2)*I)*3^(1/2)]

  

[1, 1/2, -1/2, -1, -1/2, 1/2]

  

[0, (1/2)*3^(1/2), (1/2)*3^(1/2), 0, -(1/2)*3^(1/2), -(1/2)*3^(1/2)]

 (1)
> 

UnitCircle := plot([cos(t), sin(t), t = 0 .. 2*Pi], color = gray, linestyle = dash); RootsPlot := pointplot([X, Y], symbol = solidcircle, color = blue, symbolsize = 10); display(UnitCircle, RootsPlot, scaling = constrained, title = "6th Roots of Unity")

 
> 

NULL


 

Download 6th_roots_of_unity.mw

Understanding PDEs' Initial Condition ...

Paras31 240 Maple 2024
syntax pde pdsolve
March 20 2025
2 4

All three expressions define the same initial velocity condition in different notations.
ic1 := u(x, 0) = f, D[2](u)(x, 0) = g
ic2 := u(x, 0) = f, diff(u(x, 0), t) = g;
ic3 := u(x, 0) = f, u__t(x, 0) = g;  

Why does only ic1 work while ic2 and ic3 do not? Should I use another way?

wave_equation_1D.mw

How to Create a Better Plot for Shaded ...

Paras31 240 Maple 2024
filled plotting
March 05 2025
2 1

Hi everyone,

I am trying to visualize the integral of x3 over the interval x=−1 to x=1. I tried using:

with(plots):
display(
   plot(x^3, x = -1 .. 1, color = black, thickness = 2),
   shadebetween(x^3, 0, x = -1 .. 1, color = cyan)
);

This works, but I wondered if there’s a better or more elegant way to visualize definite integrals. For example:

  • Can I add transparency to the shaded region?
  • Is there a built-in function that directly plots definite integrals with shading?
  • Any tips for improving the aesthetics of such plots?

Thanks in advance for any help!

Download εμβαδόν_χωρίου.mw

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