Maplesoft’s CEO, Dr. Laurent Bernardin, has written an opinion piece on Fostering Student Retention through Success in Mathematics. In it, he discusses ways to reduce university dropout rates by turning the technology shortcuts students are already using in their math courses into data-driven insights and interventions that promote student success.

You can read the whole article here:  Fostering Student Retention through Success in Mathematics

You will not be shocked to learn that Maplesoft plays a role in the strategy he proposes. 😊 (But this is a serious problem for a lot of schools, and we really would like to help!)

Hello everyone,

I am creating this post to begin a thread where I will share a series of worksheets on important topics in Complex Analysis, written as part of my notes for my classes. Complex_Analysis_Notes.pdf

The planned sections include:

• Section 1: Infinite Series

• Section 2: Power Series

• Section 3: The Radius of Convergence of a Power Series

• Section 4: The Riemann Zeta Function and the Riemann Hypothesis

• Section 5: The Prime Number Theorem

Each worksheet will include calculations, plots, and examples using Maple to illustrate key ideas.

✅ I plan to upload one worksheet every week to keep a steady pace and allow time for discussion and feedback between posts.

I hope this thread will be helpful both for learning and for deeper exploration.
Feel free to comment, suggest improvements, or ask questions as I post the materials.

Thank you!

Download infinite_series.mw

As a university-level math student, I am constantly working through practice problems. An issue I constantly face is that when I get a problem wrong, it can be challenging to find out which line I did wrong. Even if I use Maple Calculator or Maple Learn to get the full steps for a solution, it can be tedious to compare my answer to the steps to see where I went wrong.

This is why Check My Work is one of the most popular features in Maple Learn. Check My Work will check all the lines in your solution and give you feedback showing you exactly where you went wrong. I honestly didn’t know that something like this existed until I started here at Maplesoft, and it is now easy to see why this has been one of our most successful features in Maple Learn.

Students have been loving it, but the only real complaint is that it’s only available in Maple Learn. So, if you were working on paper, you'd either have to retype your work into Maple Learn or take a picture of your steps using Maple Calculator and then access it in Maple Learn. Something I immediately thought was, if I’m already on my phone to take a picture, I’d much rather be able to stay on my phone.

And now you can! Check My Work is now fully available within Maple Calculator!

To use Check My Work, all you need to do is take a picture of your solution to a math problem.

Check My Work will recognize poor handwriting, so there is no need to worry about getting it perfect. After taking the picture, select the Check My Work dropdown in the results screen to see if your solution is correct or where you made a mistake.

Check My Work will go through your solution line-by-line giving you valuable feedback along the way! Additionally, if you make a mistake, Maple Calculator will point out the line with the error and then proceed with checking the remainder of the solution given this context.  

For students, Check My Work is the perfect tool to help you understand and master concepts from class. As a student myself, I’ll for sure be using this feature in my future courses to double-check my work.

What makes Check My Work great for learning a technique is that it doesn’t tell you what mistake you made, but rather where the mistake has been made. This is helpful since as a student you don’t have to worry about the time-consuming task of finding the step with an error, but rather you can focus on the learning aspect of actually figuring out what you did wrong.

Once you have made corrections to your work on paper, take a new picture and repeat the process. You can also make changes to your solution in-app by clicking the “Check my work in editor” button in the bottom right, which runs Check My Work in the editor where you can modify your solution.

No other math tool has a Check My Work feature, and we are very proud to bring this very useful tool to students. By bringing it fully into Maple Calculator, we continue working towards our goal of helping students learn and understand math.

View the GIF below for a brief demonstration of how to use Check My Work!

We hope you enjoy Check My Work in Maple Calculator and let us know what you think!

Download New_in_Physics_2025.mw

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions

Download limits.mw

Hello everyone,

I have created a Maple worksheet titled "ΕΜΒΑΔΟΝ ΕΠΙΠΕΔΟΥ ΧΩΡΙΟΥ", designed to help my students prepare for their final exams as they qualify for university. This worksheet focuses on area calculations in plane geometry, using Maple to visualize and solve problems efficiently.

This worksheet is aimed at high school students preparing for university entrance exams, as well as teachers who want to integrate Maple into their teaching.

I would love to hear your thoughts and feedback!

Have you used Maple for similar exam preparation?
εμβαδόν_χωρίου.mw

Hi Maple lovers, and others,

I wrote up some simple Maple code that 
checks if an expression (a^3+2) is a prime number.

The output fits on one page of paper.
n_cubed_plus_2.mw

n_cubed_plus_2.pdf

Also, I have an account at mersenneforum.org

Kindest Regards,

Matt

PS Does this help?  The code works.

I'm happy to announce the publication of Volume 5, Issue #1 of Maple Transactions.  You can find it at

mapletransactions.org
 

We have a survey paper by Veselin Jungic and Naomi Borwein on teaching Experimental Mathematics courses as our Featured Contribution.  Many of you will find it interesting and useful.

In the refereed paper section we have a paper on Metaprogramming with Maple and C by Ilias Kotsireas; a paper on fast transposed Vandermonde solving by Hyukho Kwon & Michael Monagan; a paper by David Ulgenes (an honours student in Oslo) on Gamma, Pseudogamma, and Inverse Gamma functions; and a paper by John Campbell on applications of Gosper's nonlocal derangement identity (which, if you don't know that the word "derangement" has a technical mathematical meaning, may give you the wrong impression!).

As usual I've also written something, and I hope you like it: it's about Chladni figures and standing modes in an elliptical drum, and visualizing such in Maple.  It uses Mathieu functions in Maple and noodles a bit about zerofinding (but winds up using fsolve because that's so convenient).
 

Keep the papers coming.  This is the 12th issue of Maple Transactions, and I remind you that it has a "Diamond Class" designation, which means there are no page charges to authors, and the articles are free to read for everyone.  This means that there's some volunteer labour needed, of course: you have to write the articles, and what we want is that you write articles that people in the Maple community actually want to read.

I'd also like to thank the copyeditor, Michelle Hatzel, for her very hard work on this issue.  She's really made a difference, and I think you will be able to see it.   

In the book by W.G. Chinn, N.E. Steenrod "First Concepts of Topology" the another remarkable theorem was proved: any two flat bounded regions can be cut by a single straight line so that each of these regions is divided into two regions of equal area (the second  pancake problem). This is an existence theorem which does not provide any way to find this cut. In this post I made an attempt to find such cut for any 2 convex regions on the plane bounded by a piecewise smooth self-non-intersecting curves.
The Each_Into_2_Equal_Areas procedure returns a list of coordinates of 4 endpoints of the cutting segments. This procedure significantly uses my old procedures  Area  and  Picture , which can be found in detail at the link  https://mapleprimes.com/posts/145922-Perimeter-Area-And-Visualization-Of-A-Plane-Figure-  . The formal arguments of the Each_Into_2_Equal_Areas procedure are the lists  L1  and  L2 specifying the boundaries of the regions to be cut. When specifying  L1  and  L2 , the boundary can be passed clockwise or counterclockwise, but it is necessary that the parameter t (when specifying each link) should go in ascending order. This can always be achieved by replacing  t  with  -t  if necessary. The Pic procedure draws a picture of the source regions and cutting segments. For ease of use, the code for the  Area  and  Picture   procedure is also provided. It is also worth noting that the procedure also works for "not too" non-convex regions (see examples below).

restart;
Area := proc(L) 
local i, var, e, e1, e2, P; 
for i to nops(L) do 
if type(L[i], listlist(algebraic)) then 
P[i] := (1/2)*add(L[i, j, 1]*L[i, j+1, 2]-L[i, j, 2]*L[i, j+1, 1], j = 1 .. nops(L[i])-1) else 
var := lhs(L[i, 2]); 
if type(L[i, 1], algebraic) then e := L[i, 1]; 
if nops(L[i]) = 3 then P[i] := (1/2)*(int(e^2, L[i, 2])) else 
if var = y then P[i] := (1/2)*simplify(int(e-var*(diff(e, var)), L[i, 2])) else 
P[i] := (1/2)*simplify(int(var*(diff(e, var))-e, L[i, 2])) end if end if else e1 := L[i, 1, 1]; e2 := L[i, 1, 2]; 
P[i] := (1/2)*simplify(int(e1*(diff(e2, var))-e2*(diff(e1, var)), L[i, 2])) end if end if end do; 
abs(add(P[i], i = 1 .. nops(L))); 
end proc:

Picture := proc(L, C, N::posint := 100, Boundary::list := [linestyle = 1]) 
local i, var, var1, var2, e, e1, e2, P, Q, h; 
global Border;
uses plottools; 
for i to nops(L) do 
if type(L[i], listlist(algebraic)) then P[i] := op(L[i]) else 
var := lhs(L[i, 2]); var1 := lhs(rhs(L[i, 2])); var2 := rhs(rhs(L[i, 2])); h := (var2-var1)/N; 
if type(L[i, 1], algebraic) then e := L[i, 1]; 
if nops(L[i]) = 3 then P[i] := seq(subs(var = var1+h*i, [e*cos(var), e*sin(var)]), i = 0 .. N) else 
P[i] := seq([var1+h*i, subs(var = var1+h*i, e)], i = 0 .. N) fi else e1 := L[i, 1, 1]; e2 := L[i, 1, 2]; P[i] := seq(subs(var = var1+h*i, [e1, e2]), i = 0 .. N) fi; fi; od; 
Q := [seq(P[i], i = 1 .. nops(L))]; Border := curve([op(Q), Q[1]], op(Boundary)); [polygon(Q, C), Border] 
end proc:

Each_Into_2_Equal_Areas:=proc(L1::list, L2::list)
local D, n, m, L10, L20, S1,S2, f, L11, L21, i, j, k, s, A, B, C , sol;

f:=(X,Y)->expand((y-X[2])*(Y[1]-X[1])-(x-X[1])*(Y[2]-X[2]));
L10:=map(p->`if`(type(p,listlist),[[p[1,1]+t*(p[2]-p[1])[1],p[1,2]+t*(p[2]-p[1])[2]],t=0..1],p), L1);
L20:=map(p->`if`(type(p,listlist),[[p[1,1]+t*(p[2]-p[1])[1],p[1,2]+t*(p[2]-p[1])[2]],t=0..1],p), L2);
S1:=Area(L1); S2:=Area(L2);  
n:=nops(L1); m:=nops(L2);

for i from 1 to n do
for j from i to n do

for k from 1 to m do
for s from k to m do

if not ((nops({i,j})=1 and type(L1[i],listlist)) or (nops({k,s})=1 and type(L2[k],listlist))) then

A:=eval(L10[i,1],t=t1): 
B:=eval(L10[j,1],t=t2):
C:=eval(L20[k,1],t=t3): 
D:=eval(L20[s,1],t=t4):

L11:=`if`(j=i,[subsop([2,2]=t1..t2,L10[i]),[B,A]],`if`(j=i+1,[subsop([2,2]=t1..op([2,2,2],L10[i]),L10[i]),subsop([2,2]=op([2,2,1],L10[j])..t2,L10[j]),[B,A]], [subsop([2,2]=t1..op([2,2,2],L10[i]),L10[i]),op(L10[i+1..j-1]),subsop([2,2]=op([2,2,1],L10[j])..t2,L10[j]),[B,A]])):

L21:=`if`(s=k,[subsop([2,2]=t3..t4,L20[k]),[D,C]],`if`(s=k+1,[subsop([2,2]=t3..op([2,2,2],L20[k]),L20[k]),subsop([2,2]=op([2,2,1],L20[s])..t4,L20[s]),[D,C]], [subsop([2,2]=t3..op([2,2,2],L20[k]),L20[k]),op(L20[k+1..s-1]),subsop([2,2]=op([2,2,1],L20[s])..t4,L20[s]),[D,C]])):

sol:=fsolve(simplify({Area(L11)-S1/2,Area(L21)-S2/2,eval(f(A,B),[x=C[1],y=C[2]]),eval(f(A,B),[x=D[1],y=D[2]])}),{t1=op([2,2,1],L10[i])..op([2,2,2],L10[i]),t2=op([2,2,1],L10[j])..op([2,2,2],L10[j]),t3=op([2,2,1],L20[k])..op([2,2,2],L20[k]),t4=op([2,2,1],L20[s])..op([2,2,2],L20[s])});

if type(sol,set(`=`)) then  return eval([A,B,C,D],sol) fi;

fi;
od: od: od: od:
end proc:

Pic := proc(L1,L2,col1,col2,Size:=[800,400])
local P1, P2, P3, T, P;
uses plots, plottools;
P1, P2 := Picture(L1, color=col1), Picture(L2, color=col2):
P3 := line(Sol[1..2][],color=red,thickness=3), line(Sol[3..4][],color=red,thickness=3), line(Sol[1],Sol[4],linestyle=2,thickness=3,color=red):
T:=textplot([[Sol[1][],"A"],[Sol[2][],"B"],[Sol[3][],"C"],[Sol[4][],"D"]], font=[times,18], align=[left,above]);
P:=pointplot(Sol, symbol=solidcircle, color=red, symbolsize=10);
display(P1,P2,P3,T,P, scaling=constrained, size=Size, axes=none);
end proc: 

Examples of use.

local D:
L1:=[[[8,0],[6,7]],[[6,7],[2,5]],[[2,5],[0,2]],[[0,2],[0,0]],[[0,0],[8,0]]]:
L2:=[[[5*cos(t)+16,5*sin(t)],t=Pi/2..Pi],[[5*cos(t)+16,5*sin(t)/2],t=Pi..2*Pi],[[21,0],[16,5]]]:
Sol:=Each_Into_2_Equal_Areas(L1,L2): Points:=[A,B,C,D]:
seq(Points[i]=Sol[i], i=1..4);
Pic(L1,L2,"Yellow","LightBlue",[900,400]);

The specified regions may overlap:

L1:=[[[8,0],[6,7]],[[6,7],[2,5]],[[2,5],[0,2]],[[0,2],[0,0]],[[0,0],[8,0]]]:
L2:=[[[5*cos(t)+9,5*sin(t)],t=Pi/2..Pi],[[5*cos(t)+9,5*sin(t)/2],t=Pi..2*Pi],[[14,0],[9,5]]]:
Sol:=Each_Into_2_Equal_Areas(L1,L2):  Points:=[A,B,C,D]:
seq(Points[i]=Sol[i], i=1..4);
Pic(L1,L2,"Yellow","LightBlue");

If there is a solution for which the cutting segments intersect the boundary of each of the regions at 2 points, then the procedure also works for such non-convex regions:

L1:=[[[cos(t),sin(t)],t=Pi/3..2*Pi-Pi/3],[[cos(-t)+1,sin(-t)],t=-Pi-Pi/3..-Pi+Pi/3]]:
L2:=[[[cos(t)+2,sin(t)],t=-Pi/6..Pi+Pi/6],[[cos(-t)+2,sin(-t)-1],t=-5*Pi/6..-Pi/6]]:
Sol:=Each_Into_2_Equal_Areas(L1,L2): Points:=[A,B,C,D]:
seq(Points[i]=Sol[i], i=1..4);
Pic(L1,L2,"Yellow","LightBlue");

A number of other interesting examples can be found in the attached file.

Each_Into_2_Equal_Areas1.mw

After a long chat with ChatGPT I finally received a fully working code for a proc for a generalized Woodbury Identity for the inversion of the sum of two or more positive definite matrices.
I was inspired by a family member who is a trained professional programmer, who told me that in his professional work he uses ChatGTP for an initial draft of his program.  
I did find out that ChatGTP makes errors: from simple ones like writing 'Simplify' instead of 'simplify' to serious conceptual errors, for example in recursive loops. However, ChatGTP seems to 'understand' the error after given specific feedback. Although, this does not mean that the next proposal does not contain the same logical error. But after a long chat I received a nice proc that seems to work. 
My second surprise was that Gemini suggested a formula for the generalized Woodbury lemma that was unknown to me, and I was unable to find on Scholar Google or https://math.stackexchange.com. Based on a special case of that formula, I was able to write the second proc myself. 
In conclusion, to start working it can be helpful to collaborate with AI friend, a little patience may help, AI may not be astute as someone on Mapleprimes wrote, but neither am I. I am now retired, and it is fun to play with Maple and AI. 
By the way, the search term Woodbury did not give a single hit on Mapleprimes.With_a_little_help_from_my_friends.mw
kind regards,Harry 

 

Download blogpost-algebra.mw

In the excellent book by W.G. Chinn, N.E. Steenrod "First Concepts of Topology" the theorem is proved which states that any bounded planar region can be cut into 4 regions of equal area by 2 perpendicular cuts (the pancake problem). This is an existence theorem which does not provide any way to find these cuts. In this post I made an attempt to find such cuts for any convex region on the plane bounded by a piecewise smooth self-non-intersecting curve.
The Into_4_Equal_Areas procedure returns a list of coordinates of 5 points: the first 4 points are the endpoints of the cutting segments, the fifth point is the intersection point of these segments. This procedure significantly uses my old procedure Area , which can be found in detail at the link  https://mapleprimes.com/posts/145922-Perimeter-Area-And-Visualization-Of-A-Plane-Figure-  . The formal argument of the Into_4_Equal_Areas procedure is a list  L specifying the boundary of the region to be cut. When specifying  L, the boundary can be passed clockwise or counterclockwise, but it is necessary that the parameter t (when specifying each link) should go in ascending order. This can always be achieved by replacing  t  with  -t  if necessary. The Pic procedure draws a picture of the source region and cutting segments. For ease of use, the code for the  Area  procedure is also provided. It is also worth noting that the procedure also works for "not too" non-convex regions (see examples below).

restart;
Area := proc(L) 
local i, var, e, e1, e2, P; 
for i to nops(L) do 
if type(L[i], listlist(algebraic)) then 
P[i] := (1/2)*add(L[i, j, 1]*L[i, j+1, 2]-L[i, j, 2]*L[i, j+1, 1], j = 1 .. nops(L[i])-1) else 
var := lhs(L[i, 2]); 
if type(L[i, 1], algebraic) then e := L[i, 1]; 
if nops(L[i]) = 3 then P[i] := (1/2)*(int(e^2, L[i, 2])) else 
if var = y then P[i] := (1/2)*simplify(int(e-var*(diff(e, var)), L[i, 2])) else 
P[i] := (1/2)*simplify(int(var*(diff(e, var))-e, L[i, 2])) end if end if else e1 := L[i, 1, 1]; e2 := L[i, 1, 2]; 
P[i] := (1/2)*simplify(int(e1*(diff(e2, var))-e2*(diff(e1, var)), L[i, 2])) end if end if end do; 
abs(add(P[i], i = 1 .. nops(L))); 
end proc:

Into_4_Equal_Areas:=proc(L::list,N::symbol:='OneSolution', eps::numeric:=0)
local D, n, c, L1, L2, L3, f, L0, i, j, k, m, A, B, C, P, S, sol, Sol;
f:=(X,Y)->expand((y-X[2])*(Y[1]-X[1])-(x-X[1])*(Y[2]-X[2]));
L0:=map(p->`if`(type(p,listlist),[[p[1,1]+t*(p[2]-p[1])[1],p[1,2]+t*(p[2]-p[1])[2]],t=0..1],p), L);
S:=Area(L); c:=0;
n:=nops(L);
for i from 1 to n do
for j from i to n do
for k from j to n do
for m from k to n do
if not ((nops({i,j,k})=1 and type(L[i],listlist)) or (nops({j,k,m})=1 and type(L[j],listlist)))then
A:=convert(subs(t=t1,L0[i,1]),Vector): 
B:=convert(subs(t=t2,L0[j,1]),Vector):
C:=convert(subs(t=t3,L0[k,1]),Vector): 
D:=convert(subs(t=t4,L0[m,1]),Vector):
P:=eval([x,y], solve({f(A,C),f(B,D)},{x,y})):
L1:=`if`(j=i,[subsop([2,2]=t1..t2,L0[i]),[convert(B,list),P],[P,convert(A,list)]],`if`(j=i+1,[subsop([2,2]=t1..op([2,2,2],L0[i]),L0[i]),subsop([2,2]=op([2,2,1],L0[j])..t2,L0[j]),[convert(B,list),P],[P,convert(A,list)]], [subsop([2,2]=t1..op([2,2,2],L0[i]),L0[i]),L0[i+1..j-1][],subsop([2,2]=op([2,2,1],L0[j])..t2,L0[j]),[convert(B,list),P],[P,convert(A,list)]])):
L2:=`if`(k=j,[subsop([2,2]=t2..t3,L0[j]),[convert(C,list),P],[P,convert(B,list)]],`if`(k=j+1,[subsop([2,2]=t2..op([2,2,2],L0[j]),L0[j]),subsop([2,2]=op([2,2,1],L0[k])..t3,L0[k]),[convert(C,list),P],[P,convert(B,list)]], [subsop([2,2]=t2..op([2,2,2],L0[j]),L0[j]),L0[j+1..k-1][],subsop([2,2]=op([2,2,1],L0[k])..t3,L0[k]),[convert(C,list),P],[P,convert(B,list)]])):
L3:=`if`(m=k,[subsop([2,2]=t3..t4,L0[k]),[convert(D,list),P],[P,convert(C,list)]],`if`(m=k+1,[subsop([2,2]=t3..op([2,2,2],L0[k]),L0[k]),subsop([2,2]=op([2,2,1],L0[m])..t4,L0[m]),[convert(D,list),P],[P,convert(C,list)]], [subsop([2,2]=t3..op([2,2,2],L0[k]),L0[k]),L0[k+1..m-1][],subsop([2,2]=op([2,2,1],L0[m])..t4,L0[m]),[convert(D,list),P],[P,convert(C,list)]])):
sol:=fsolve({Area(L1)-S/4,Area(L2)-S/4,Area(L3)-S/4,LinearAlgebra:-DotProduct(D-B,C-A, conjugate=false)},{t1=op([2,2,1],L0[i])-eps..op([2,2,2],L0[i])+eps,t2=op([2,2,1],L0[j])-eps..op([2,2,2],L0[j])+eps,t3=op([2,2,1],L0[k])-eps..op([2,2,2],L0[k])+eps,t4=op([2,2,1],L0[m])-eps..op([2,2,2],L0[m])+eps}) assuming real:
if type(sol,set(`=`)) then if N='OneSolution' then return convert~(eval([A,B,C,D,P],sol),list) else c:=c+1; Sol[c]:=convert~(eval([A,B,C,D,P],sol),list) fi;
 fi; fi;
od: od: od: od:
convert(Sol,list);
end proc:

Pic:=proc(L,Sol)
local P1, P2, T;
uses plots, plottools;
P1:=seq(`if`(type(s,listlist),line(s[],color=blue, thickness=2),plot([s[1][],s[2]],color=blue, thickness=2)),s=L):
P2:=line(Sol[1],Sol[3],color=red, thickness=2), line(Sol[2],Sol[4],color=red):
T:=textplot([[Sol[1][],"A"],[Sol[2][],"B"],[Sol[3][],"C"],[Sol[4][],"D"],[Sol[5][],"P"]], font=[times,18], align=[left,above]);
display(P1,P2,T, scaling=constrained, size=[800,500], axes=none);
end proc: 

Examples of use:

L:=[[[0,0],[1,4]],[[1,4],[6,7]],[[6,7],[12,0]],[[12,0],[0,0]]]:
Sol:=Into_4_Equal_Areas(L);
Pic(L, Sol);

# Check (areas of all 4 regions)
Area([[L[1,1],Sol[4],Sol[5],Sol[1],L[1,1]]]),
Area([[Sol[4],Sol[5],Sol[3],L[4,1],Sol[4]]]),
Area([[Sol[5],Sol[2],L[3,1],Sol[3],Sol[5]]]),
Area([[Sol[5],Sol[2],L[1,2],Sol[1],Sol[5]]]);

L:=[[[1+cos(-t),1+sin(-t)],t=-3*Pi/2..-Pi],[[0,1],[-1,0]],[[cos(t),sin(t)],t=Pi..2*Pi]]:
Sol:=Into_4_Equal_Areas(L);
Pic(L,Sol);

# The boundary is the Archimedes spiral and the arc of a circle

L:=[[[t*cos(t),t*sin(t)],t=0..2*Pi],[[Pi+5*cos(-t),sqrt(25-Pi^2)+5*sin(-t)],t=arccos(Pi/5)..Pi-arccos(Pi/5)]]:
Sol:=evalf(Into_4_Equal_Areas(L));
Pic(L,Sol);

L:=[[[0,0],[2,0]],[[2,0],[1,sqrt(3)]],[[1,sqrt(3)],[0,0]]]:
Sol:=evalf[5](Into_4_Equal_Areas(L, AllSolutions, 0.1)); # All 3 solutions
plots:-display(<Pic(L, Sol[1]) | Pic(L, Sol[2])  | Pic(L, Sol[3])>, size=[300,300]);  

L:=[[[-t,-sin(-t)],t=-5*Pi/4..0],[[cos(t),sin(t)-1],t=Pi/2..3*Pi/2],[[t,cos(t)-3],t=0..3*Pi/2],[[3*Pi/2,-3],[5*Pi/4,sqrt(2)/2]]]:
Sol:=evalf(Into_4_Equal_Areas(L));
Pic(L,Sol);

More examples can be found in the attached file.

4_Equal_Area1.mw

[Edit]. The post has been edited. One inaccuracy in the code has been corrected, which could sometimes lead to errors. Two options have been added to the code of Into_4_Equal_Areas procedure. The first option is the formal argument  N . If N=OneSolution  (by default), the procedure returns one solution. If  N=AllSolutions , the procedure returns all solutions that it can find. The  eps  option has also been added (by default, eps=0). It is advisable to use it when we are looking for all solutions, and the ends of the cutting segments fall on the boundaries of intervals (this option slightly expands the boundaries of intervals, otherwise the  fsolve  command sometimes misses solutions). Two new examples have also been added.

Maple Transactions Volume 4 Issue 4 has now been published.

This issue has two Featured Contributions by people who have been plenary speakers at Maple Conferences in the past, namely Veselin Jungić and Juana Sendra. We hope you enjoy both articles.  There is an accompanying video by Professor Sendra, which we will add a link to when it becomes ready.

As usual, there is an article in the Editor's Corner, but this one is a bit different.  In this one, Michelle Hatzell (the new copyeditor for Maple Transactions, who is also a Masters' student working with me at Western) and I have written about a fun use of Maple's colour contour plots to make an image that might be used as the cover of an upcoming book, namely Perturbation Methods using backward error, which I'm just finishing now with Nic Fillion and which SIAM will publish next year.  So, while there's some math in that paper, it's more about Maple's utilities for colour plotting; so you might find it useful.  We also hope you like at least some of the images.  Some are more attractive than others!

We have several Refereed Contributions, not all of which are ready at this time of publication but which will be added as they are revised and sent in.  We have a nice paper on using continued fractions in a high school context, another on code generation, and another on using Digital Signal Processing in Engineering courses.

Finally we have a first publication in French, by Jalale Soussi.  Actually we have the paper also in English: we chose to publish both, in our Communications section, each with links to the other.  It is possible to publish in Maple Transactions solely in French, of course, but the author provided both, so why not?

Happy reading, and best wishes for 2025. 

Hello Maple enthusiasts,

I am excited to share a sample worksheet on Ordinary Differential Equations (ODEs), created as part of my ongoing project—a book I am writing for undergraduate students. This book is designed to teach ODEs using Maple, offering an interactive and intuitive approach to solving differential equations.

As far as I know, there aren’t many books available in the Greek language that combine ODEs with Maple. In fact, I believe there’s only one other such resource, which highlights the lack of materials in this niche. My goal is to fill this gap by providing students and educators with a resource that is both practical and accessible, leveraging Maple's powerful capabilities to deepen understanding and simplify complex concepts.

The worksheet I’m sharing includes:

• Step-by-step solutions to ODEs using Maple.
• Graphical representations to visualize solutions, which I believe are invaluable for fostering comprehension.

I hope this preview sparks your interest and provides insight into the teaching style and structure of the upcoming book. I would love to hear your thoughts, feedback, or suggestions for topics you think should be included.

Download separable_diff_equations.mw

Hello,

I present the rolling of an ellipse along a spatial curve and along curves placed on a surface, also along a Mobius surface.

Attached are the Maple source files.

Best regards.

Source_-_mw.zip