Recently, ChatGpt has gained a lot of attention and there are mixed reviews about it. Some people think highly of its capabilities, while others are more critical. Regardless, it has been an interesting  topic on assistant programming.

I'm going to give two examples to illustrate what's interesting and what's lacking.

First, I want ChatGpt to write a Maple code for the enumeration of all prime numbers up to 100. Then it writes:

primes:= proc(n)
   local i, j, primes;
   primes:= [2];
   for i from 3 to n do
      for j from 2 to i-1 do
         if i mod j = 0 then break;
      end do;
      if j = i then primes:= [op(primes), i]; end if;
   end do;
   return primes;
end proc;

primes(100);

I copy and paste this code, maple shows an error: Error, reserved word `do` unexpected

I report the error to it:

this code cannot run since "Error, reserved word `do` unexpected"

Then it gives: I apologize for the error in the previous code. Here is a corrected version of the code that can be run in Maple:

primes:= proc(n)
   local i, j, primesList;
   primesList:= [2];
   for i from 3 to n do
      for j from 2 to i-1 do
         if i mod j = 0 then 
            break;
         end if;
      end do;
      if j = i then 
         primesList:= [op(primesList), i]; 
      end if;
   end do;
   return primesList;
end proc;

primes(100);

Ok, It's tediously written code, but at least it's correct. 

Furthermore, I ask:

Is there a more concise approach that utilizes maple's built-in functions.

It tells me:

Yes, there is a more concise approach that utilizes Maple's built-in functions. Here's an example:

primes := [seq(i, i=2..100)]; primes := [op(select(isprime, primes))];

The seq function generates a list of numbers from 2 to 100. The select function filters out all non-prime numbers using the isprime function, which tests the primality of a number. The result is stored in the primes array.

Ok, this answer meets my expectations.

Another example is the generation of all 6th order non-isomorphic graphs, which pops up as:

# Load the GraphTheory package
with(GraphTheory):

# Generate a list of all non-isomorphic graphs with 6 vertices
graphs := NonIsomorphicGraphs(6):

# Print the list of non-isomorphic graphs
print(graphs);

But NonIsomorphicGraphs(6) as we know is the number  of non-isomorphic graphs but  not graphs  themselves.

So I say:

in the above codes, NonIsomorphicGraphs need the options output = graphs, outputform = graph

ChatGpt gives :

Here is a revised version of the code that takes into account the options output = graphs and outputform = graph:

# Load the GraphTheory package
with(GraphTheory):

# Generate a list of all non-isomorphic graphs with 6 vertices
graphsList := NonIsomorphicGraphs(6, output = graphs, outputform = graph):

# Print the number of non-isomorphic graphs
print("Number of non-isomorphic graphs: ", nops(graphsList));

# Print each non-isomorphic graph in the list
for i in 1 to nops(graphsList) do
  print("Graph ", i, ": ", graphsList[i]);
end do

It still has syntax errors. I made some artificial adjustments.

# Load the GraphTheory package
with(GraphTheory):

# Generate a list of all non-isomorphic graphs with 6 vertices
graphsList := [NonIsomorphicGraphs(6, output = graphs, outputform = graph)]:

# Print the number of non-isomorphic graphs
print("Number of non-isomorphic graphs: ", nops(graphsList));

# Print each non-isomorphic graph in the list
for i from 1 to nops(graphsList) do
  print("Graph ", i, ": ", graphsList[i]);
end do;

I pulled a wry face when  it builds a lot of codes  that do not exist in Maple.. Here's a little tidbit of my conversation with it.

This software still needs more work. I'm not sure how far it can go, but maybe programming becomes easier. Maybe more interesting examples will be found.

This year, for Christmas, my children^* got a Valve Steam Deck under the Christmas tree.  It's a pretty cool device that looks a little  like a monsterous Nintendo Switch, but it can run an impressive subset of the Steam video game catalog, games mostly designed to run on Windows PCs.  It manages this by sporting a custom x86_64 processor by AMD and running a customized version of Arch Linux that uses Wine via Valve's Proton tool.  The key point here, is that it is a tiny x86_64 compatible computer running Linux. So, of course, I needed to install Maple on it. So, I just paired a bluetooth keyboard, rebooted it into desktop mode and with a few small trick, bam, Maple on the Steam Deck:

There were a few small hiccups that required some work. I had absolutely no problems getting the Maple installer onto the device via a USB drive and no problems running it. I only ran into problems durring license activation:

Fortunately, I talked to our crack technical support team and they were able to identify this as a problem with Arch Linux not having full LSB 3.0 support installed by default. The process for fixing that is documented on the Arch Linux Wiki and involves just installing the ld-lsb package via pacman -- with the small additional wrinkle that you need to take the Steam Deck operating system out of 'read-only' mode in order to do that. But once that was done, I had a full version of Maple running well (albeit at 1280x800 resolution on a 7" display).

Since this device is designed for gaming, I was curious how fast it is compared to some other machines I work on. I chose an arbitrary benchmark of exactly solving a random linear system with integer coefficients.

restart;
N := 400;
A := LinearAlgebra:-RandomMatrix(N, N):
b := LinearAlgebra:-RandomVector(N):
v := [seq(cat(v__, i), i = 1 .. N)]:
sys := LinearAlgebra:-GenerateEquations(A, v, b):
CodeTools:-Usage(SolveTools:-LinearSolvers:-Rational(`~`[lhs - rhs](sys), v, dense = false)):

which it solves in decent time:

For comparison, this is 30% faster than the 32 core Xeon e5 workstation I do most of my work on, and only 5% slower than my notebook computer with an 8th gen Intel i7.  Not bad for a toy! (please don't make me sad by telling me how much faster this is on a Mac M1 or M2)

Let me know in the comments if you have other benchmarks you want me to run on the Steam Deck. Also, please let me know if you manage to get your employer to buy you a Steam Deck to do scientific computing.

^*Okay, maybe it was a gift for me. Shhhh, don't tell.

Hello,

  2022 was a wonderful year of progress in using Maple/MapleSim for almost everything my mathematical world.     

I just wanted to wish all the Maplesoft user community a very productive and Happy New Year for 2023.   I look forward to continue to find great nuggets of capability and insider techniques for using Maple in my endeavors.

Kindest Regards to ALL.
Happy New Year - 2023.
Bill

I have been making animated 3d plots recently; the last time was perhaps three years ago, and I had some problems then.  If I recall correctly, I couldn't make an animated 3d plot that was plotted in non-Cartesian coordinates.

I am very happy to report that this works very smoothly now in Maple 2022, and it's pretty fast, too.  I have a fairly complex function to plot, involving piecewise polynomials on a tensor product grid in the xi and eta variables (actually, I let plot3d pick out the grid; it seems happier to do so) and then plot them on an elliptical base, in coordinates x = d*cosh(xi)*cos(eta) and y=d*sinh(xi)*sin(eta)  (d is just a numerical constant, giving the location of the foci at (d,0) and (-d,0)), for 0 <= xi <= xi[0] (the outer elliptical boundary) and 0 <= eta <= 2Pi.  The straightforward command works, and building a sequence of plots and using plots[display] works.  I put option remember into my procedure w(xi,eta) and because the sample points are consistent for the time-dependent function exp(I*omega*t)*w(xi,eta) the xi-eta grid needs only to be done once and then one can compute (basically) as many frames as one wants in rapid succession.

Works great.  Thanks, folks!

for k to nplots do
    t := evalf(2*Pi*(k - 1)/nplots);
    plts[k] := plot3d([(xi, eta) -> focus*cosh(xi)*cos(eta), (xi, eta) -> focus*sinh(xi)*sin(eta), (xi, eta) -> Re(exp(omega*t*I)*w(xi, eta))], 0 .. xi[0], 0 .. 2*Pi, colour = ((xi, eta) -> Re(exp(omega*t*I)*w(xi, eta))), style = surfacecontour, lightmodel = "none");
end do;
plots[display](seq(plts[k], k = 1 .. nplots), insequence = true);
 

With the winter solstice speeding towards us, we thought we’d create some winter themed documents. Now that they’re here, it’s time to show you all! You’ll see two new puzzle documents in this post, along with three informative documents, so keep reading.

Let’s start with the tromino tree!

First, what’s a tromino? A tromino is a shape made from three equal sized squares, connected to the next along one full edge. In this puzzle, your goal is to take the trominos, and try to fill the Christmas tree shape.

There’s a smaller and larger tree shape, for different difficulties. Try and see how many ways you can fill the trees!

Next, we’ll look at our merry modulo color by numbers.

In this puzzle, your goal is to solve the modulo problems in each square, and then fill in the square with the color that corresponds to the answer. Have fun solving the puzzle and seeing what the image is in the end!

Snowballs are a quintessential part of any winter season, and we’ve got two documents featuring them.

The first document uses a snowball rolling down a hill to illustrate a problem using differential equations. Disclaimer: The model is not intended to be realistic and is simplified for ease of illustration. This document features a unique visualization you shouldn’t miss!

Our second document featuring snowballs talks about finding the area of a 2-dimensional snowman! Using the formula for the area of a circle and a scale factor, the document walks through finding the area in a clear manner, with a cute snowman illustration to match!

The final document in this mini-series looks at Koch snowflakes, a type of fractal. This document walks you through the steps to create an iteration of the Koch snowflake and contains an interactive diagram to check your drawings with!

I hope you’ve enjoyed taking a look at our winter documents! Please let us know if there’s any other documents you’d like to see featured or created.

Greetings, fellow educators, researchers, engineers, students, and folx who love mathematics! 

I believe in the importance of mathematics as a structure to our society, as a gateway to better financial decision making, and as a crucial subject to teach problem solving. I also believe in the success of all students, through self-discovery and creativity, while working with others to create their own knowledge. Consequently, I’ve designed my examples in the Maple Learn gallery to suit these needs. Many of my documents are meant to be “stand-alone” investigations, summary pages, or real-world applications of mathematical concepts meant to captivate the interest of students in using mathematics beyond the basic textbook work most curricula entail. Thus, I believe in the reciprocal teaching and learning relationship, through the independence and creativity that technology has afforded us. The following is an example of roller coaster track creation using functions. Split into a five part investigation, students are tasked to design the next roller coaster in a theme park, while keeping in mind the elements of safety, feasibility, and of course fun!

Common elements we take for granted such as having a starting and ending platform that is the same height (since most coasters begin and end at the same location), boarding the coaster on a flat surface, and smooth connections between curves translate into modeling with functions. 

Aside from interning with Maplesoft, I am an educator, researcher, student, financial educator, and above all, someone who just loves mathematics and wishes to share that joy with the whole world. As a practicing secondary mathematics and science teacher in Ontario, Canada, I have the privilege of taking what I learned in my doctorate studies and applying it to my classrooms on a daily basis. I gave this assignment to my students and they really enjoyed creating their coasters as it finally gave them a reason to learn why transformations of quadratics, amongst other functions, were important to learn, and where a “real life” application of a piecewise function could be used. 

Having worked with the Ontario and International Baccalaureate mathematics curricula for over a decade, I have seen its evolution over time and in particular, what concepts students struggled to understand, and apply them to the “real world.” Concurrently, working with international mathematics curricula as part of my collaboration with Maplesoft, I have also seen trends and emergent patterns as many countries’ curricula have evolved to incorporate more mathematical literacy along with competencies and skills. In my future posts, you will see Maple Learn examples on financial literacy since working as a financial educator has allowed me to see just how ill prepared families are towards their retirement and how we can get lost amongst a plethora of options provided by mass media. Hence, I have 2 main goals I dedicate to a lifelong learning experience; financial literacy and greater comprehension of mathematics topics in the classroom. 

Welcome back to another Maplesoft blog post! Today, we’re looking at how math appears in nature. Many people know that there’s math within the mysteries of nature, but don’t know exactly what’s going on. Today we’ll talk about some of the examples but remember that there’s always more.

Let’s start with a well-known example: The Fibonacci sequence! This is a recursive sequence, made by adding the previous two terms together to make the next term. The Fibonacci sequence starts with 0, then 1. So, when modelling this sequence, you get “0, 1, 1, 2, 3, 5, 8,” and so on.

Now, where can this sequence be seen? Well, the sequence forms a spiral. This spiral can be seen in fingerprints:

Image: Andrea Greengard/Mindful Living Network

Eggs:

Image: Andrea Greengard/Mindful Living Network

And, in some cases, spiral galaxies. For more examples of the Fibonacci sequence, check out a blog on examples of the Fibonacci Sequence by Andrea Greengard!

Image: Andrea Greengard/Mindful Living Network

Another interesting intergalactic math fact is that celestial bodies are typically spherical, such as stars and planets. As well, orbits tend towards spherical, often being ellipses. It’s fascinating to see how many spheres there are in nature!

Moving away from spirals in nature, another example of math in nature, although there are many more, is the Hardy-Weinburg Equilibrium.  When in Hardy-Weinburg Equilibrium, a population’s allele and genotype frequencies, in the absence of certain evolutionary factors, stay constant through generations. The Hardy-Weinburg Equilibrium is used to predict genotypes from phenotypes of certain populations, as one example. Come check out our documents on this topic for more details, both on the Hardy-Weinburg Equilibrium and some practice examples.

Image: Maplesoft

In the end, math is incredibly ingrained in nature. We can use mathematical formulas and patterns to predict how plants will grow, or population genetics, and much more! Please let us know if there’s any examples you’d like to see in more depth, and we can see if writing a blog post on it is possible, or even a Maple Learn document for the gallery!

Welcome back to another Maple Learn blog post! We know it is midterm season, and we’re here to help. Maple Learn can be used to study in many different ways, and I’m sure you’ve already tried some of them. One way is making your notes in Learn, or making your own examples, but have you taken a look at our document gallery? We have a wide range of subjects and types of documents, so let’s take a look at some documents!

I’m going to start by talking about the documents in the gallery which are content learning focused, then move into practice problems and a special document for studying.

First, let’s look at some calculus content learning documents! The calculus collection is our largest, reaching over 250 documents and still counting. The two documents I’ve picked from this category are our documents on the Fundamental Theorem of Calculus and a Visualization of Partial Derivatives. See a screenshot of the visualisations for each document below!

Are there other subjects you’d like to look at? Well, take a look at our list below!

Algebra: Double Vertical Asymptote Slider Graph

Graph Theory: Dijkstra’s Algorithm for Shortest Paths

Economics: Increase in Demand in a Market

Chemistry: Combined Gas Law Examples

Biology: Dihybrid Cross Punnett Squares

Physics: Displacement, Velocity, and Acceleration

We have many other subjects for documents, of course, but they wouldn’t fit in this post! Take a look at our entire document gallery for the others.

Another class of documents we have are the practice problems. Perfect for studying, we have practice problems ranging from practicing the four color theorem, to practicing mean, median, and mode, to even practicing dihybrid cross genotypes!

Now for, in my opinion, our most useful document for the midterm season: A study time calculator!

This document allows you to put in the amount you want to study each class over the day or week, and breaks down visually what that would look like.  

This allows you to make sure you’re taking enough time for breaks and sleep, and not overloading yourself. Feel free to customise the document to make it work better for you and your study style!

We hope you enjoyed this post, and that we could help you study! Let us know below if there’s anything else you’d want to see to support you during midterms and exams.

Who else likes art?  I love art; doodling in my notebook between projects and classes is a great way to pass the time and keep my creativity sharp.  However, when I’m working in Maple Learn, I don’t need to get out my book; I can use the plot window as my canvas and get my drawing fix right then and there.

We’ve done a few blog posts on Maple Learn art, and we’re back at it again in even bigger and better ways.  Maple Learn’s recent update added some useful features that can be incorporated into art, including the ability to resize the plot window and animate using automatically-changing variables.

Even with all the previous posts, you may be thinking, “What’s all this?  How am I supposed to make art in a piece of math software?”  Well, there is a lot of beauty to mathematics.  Consider beautiful patterns and fractals, equations that produce surprisingly aesthetically interesting outputs, and the general use of mathematics to create technical art.  In Maple Learn, you don’t have to get that advanced (heck, unless you want to).  Art can be created by combining basic shapes and functions into any image you can imagine.  All of the images below were created in Maple Learn!

There are many ways you can harness artistic power in Maple Learn.  Here are the resources I recommend to get you started.

1. I’ve recently made some YouTube videos (see the first one below) that provide a tutorial for Maple Learn art.  This series is less than 30 minutes in total, and covers - in three respective parts - the basics, some more advanced Learn techniques, and a full walkthrough of how I make my own art.
2. Check out the Maple Learn document gallery art collection for some inspiration, the how-to documents for additional help, and the rest of the gallery to see even more Maple Learn in action!

Once you’re having fun and making art, consider submitting your art to the Maple Conference 2022 Maple Learn Art Showcase.  The due date for submission is October 14, 2022.  The Conference itself is on November 2-3, and is a free virtual event filled with presentations, discussions, and more.  Check it out!

Have you ever wondered about the people behind the scenes at Maplesoft? What about the students who help design the products?

This week, we thought we’d introduce ourselves. We are some of the co-op students at Maplesoft, who in between studying believe that Math Matters.

I’ll go first. My name is Pleiades, I’m 21 and my pronouns are they/them. I am a product management intern at Maplesoft, working with Maple Learn and Maple Calculator. I'm not a math student, but my favorite thing about math is how expressive its language is. Mathematical equations and symbols can be used to express incredibly complex ideas, and even if you don't understand the sense, you can still read the "words". My favorite thing about working for Maplesoft is the flexibility. I have many different types of tasks, and I’m able to learn so many different things.

Keep reading, and find out more about my fellow students below!

Quality Assurance:

Hello, my name is Matilda (she/her)! I am 19 years old, studying physics and astronomy at the University of Waterloo. I am part of the QA team here at Maplesoft, working as a quality assurance analyst co-op. I find math fascinating as it is a broad field that can be challenging, but also invokes a lot of creativity. As I am a new addition at Maplesoft, I am excited to work with the various Maple products.  I am looking forward to meeting new students and individuals, and to help grow not only myself but the company further. 

My name is Kat, I’m 20 and my pronouns are she/her. In my spare time, I enjoy reading and rock climbing. I am a QA analyst at Maplesoft, mostly working on Maple 2023. I am a student at UW studying mathematical physics and I would like to also minor in astronomy/astrophysics. My favorite thing about math is the objectivity of it, how there is a set structure and logical solution to any problem. I especially like calculus and trigonometry. I’m excited to be at Maplesoft because I will be learning everything about Maple from the inside perspective, which is used in many 300 and 400-level applied math courses that I will be taking at UW. I also really like the office environment and my coworkers.

Development:

Hey, my name is Paul C, I am 22 years old, and I am working as a Web and Mobile developer with Steve Metzger for the next 4 months. At the University of Waterloo, I study Mathematical Physics, though, I love the Computational Mathematics courses I’ve taken at UWaterloo. As for the world of Mathematics, I have always been fond of how everything can be thoroughly proven through basic arguments and logic. I am very excited to be working at Maplesoft, as I have for a long time been intrigued as to how Maple, Symbolab, and WolframAlpha function. So, this position is finally giving me the opportunity to truly explore how such software is developed.

Sales:

My name is Robin, I’m 21 years old and my pronouns are he/him. I am currently working as a Business Operations Analyst at Maplesoft, working with the sales department. I am a candidate of Bachelors of Business Administration at Wilfrid Laurier University with a minor in Economics and a specialization in Finance. My favorite thing about math is how it is present everywhere. Numbers help us understand world and Math helps us understand the number. My favorite part about working at Maplesoft is the extremely positive culture that we work in. Rather than competing with other people in the department, sales team has a very healthy approach towards work and are always there to help out each other.

Content Creation:

My name is Nikolas (he/him), I’m 20 years old and I’m an undergraduate physics student at the University of Waterloo. I’m part of the math content team at Maplesoft, focussing on creating new content for Maple Learn. The thing I like most about math is that while it may be a very objective discipline, it still involves an incredible amount of creativity. My favourite part of working at Maplesoft is the chance to share what I’ve learned about physics and math through Maple Learn content.

Good morning, afternoon, or evening!  I'm Miles (age 23, he/him), and I'm a UW mathematics student majoring in combinatorics and optimization and minoring in biology.  This term at Maplesoft, I work in content development for Maple Learn, which involves creating examples for the Maple Learn Document Gallery, working on special requests for users, and more.  My favorite thing about math is the fact that it is the analytical backbone of so many other areas of research.  You may think of biological research as performing experiments or medical trials, but behind the scenes, data entry and analysis are key to finding valuable conclusions and discoveries.  Biology is my particular favorite, of course, but there are countless fields of study with these mathematical aspects.

I'm looking forward to expanding my skillset and repertoire of tasks at Maplesoft.  This is my second term working here; last term I got my bearings as a content developer and am looking forward to so much more.  More advanced documents and workshops/presentations are on the horizon! :D

Paulina Chin of Maplesoft and I are pleased to annouce Maple Transactions Volume 2 Issue 1, the Proceedings of the 2021 Maple Conference.

Articles can be found at mapletransactions.org

Some articles are written directly in Maple and are published via the Maple Cloud.  There is also a Demo Video by Michael Monagan of his new GCD code.  There are articles on Math Education, on Applications of Maple, on software, and on mathematics research.  We draw particular attention to the article by Veselin Jungic, 3M Teaching Fellow at SFU and a Fellow of the Canadian Math Society, on Indigenising mathematics.  We hope that, as members of the Maple Community, you find much of interest.

Best wishes,

Rob Corless, Editor-in-Chief

Maple Transactions

If you do as much math as I do, you’ll likely agree that it’s important to take breaks from intensive work.  However, sometimes one wants to keep one’s mind stimulated with math.  This makes mathematical puzzles and games a perfect respite.  Alternatively, even if you don’t do as much math professionally, math puzzles are a fun and easily-accessible way to keep your mind sharp.  Games like sudoku and Rubik’s cubes are incredibly popular for good reason.

My personal favourite math puzzle is the nonogram, sometimes called hanjie, picross, or picture cross.  The game presents players with a blank grid of squares and clues indicating which ones should be colored in.  When the puzzle is solved, the colored squares depict a simple image.  You can read more thorough instructions here.

Nonograms are now available in Maple Learn!  These documents are coded using Maple scripts which can be viewed online in Maple Learn.  The document collection has pre-made puzzles and randomly-generated puzzles, and now you can create your own!  Use this document to create an image, and follow the instructions therein to generate the interactive puzzle.  Once you’ve created your own Maple Learn nonogram, use the sharelink to send it to friends!  Also keep your eye on the entire Maple Learn games collection for more in the future!

Récemment, j’ai assisté à une présentation sur comment utiliser Maple Learn pour créer des documents artistiques et aujourd’hui  je vous écris pour vous donner mes conseils sur ce sujet. Maple Learn a beaucoup de fonctionnalités permettant de créer des documents visuels tout en étant un outil parfait pour faire vos devoirs.

Caractéristique 1 : Les formes

 Le premier document artistique de cette collection, le « Pi Pie » a été créé en utilisant la palette géométrie de Maple Learn. Elle fournit des modèles pour tracer des formes géométriques de façon plus simple. Le plus important dans ce document est l’utilisation de « Polygon() » pour créer le symbole pi. Insérez le nombre de points que vous voulez entre les parenthèses et le graphique connectera les points dans l’ordre entre eux. J’ai dessiné le symbole de pi sur un papier graphique et j’ai copié les points dans Maple Learn. C’est beaucoup d’effort, mais je pense que l’effet créé en vaut la peine.

Caractéristique 2 : Les fonctions

Ce personnage se nomme Milo je l’ai créé au lycée. Avec Maple Learn je l’ai reproduit en utilisant avec uniquement des fonctions. Voyons cela plus en détails :

• La tête et les cheveux sont des fonctions paramétriques. Les personnes  se souvenant de leur cours de maths savent que (x, y) = (cos(t), sin(t)) est la formule d’ un cercle unitaire. Nous pouvons modifier l ‘étendue de t, les coefficients avant sin(t) et cos(t) et additionner ou soustraire les constantes pour créer des cercles partielles ou des ellipses.
• Les yeux grisés sont fait avec des inégalités. Maple Learn permet de griser des régions d’inégalités automatiquement.
• Le sourire de Milo est l’équation d’un cercle limité par “| y < -0.5”. L’opérateur barre  « such that » vous permet de limiter le domaine et l’étendue d’une fonction.
• Le cœur vient d’une formule trouvée en ligne. Les mathématiciens ont découvert beaucoup d’équations incrédules de ce type !

Caractéristique 3 : L’animation

Mon document artistique final permet de voir germer une jolie fleur lorsque l’on utilise le curseur de la barre de défilement.  Après avoir défini une variable dans Maple Learn, la barre de défilement apparait et permet l’ajustement de la valeur de la variable. Par exemple :

• Associez les coordonnées d’un point avec une variable. Évaluez une fonction à un point correspondant à cette variable et voyez comment lorsque la variable change, le point se déplace.
• Associez l’étendue  d’une fonction paramétrique à une variable. Quand la variable change la fonction s’étend ou se contracte.
• Utilisez une variable avec une fonction par morceaux. Quand la variable est dans la gamme lui correspondant vous pouvez la visualiser.

Les mathématiques sont une belle langue et chaque type d’expression peut ajouter un plus à votre toile. Mes techniques ne sont que le début de belles pièces d’arts dans Maple Learn. Montrez-nous vos documents artistiques ou vos techniques dans les commentaires !

It’s been a few months since the previous blog post on Maple Learn art, and the possibilities keep on growing.  I recently took part in a presentation on art in Maple Learn, and am here to pass on some tips and tricks to you, dear blog reader.  Maple Learn has a huge capacity for both creativity and ingenuity, and is the perfect program for doing your homework or exploring the world of mathematical art.  Check out the art I made here, and soon even more will be added to the Maple Learn Example Gallery!

Feature 1: Shapes

The first drawing in the batch, the “Pi Pie” (happy Pi Day!) was created using Maple Learn’s geometry palette.  The palette provides templates for plotting geometric shapes easily.  Most notably in this art is the use of Polygon() to create the pi symbol.  Insert as many points as you want between the brackets, and the plot will connect each one in order.  I drew pi on graph paper and copied down all the coordinates into Maple Learn.  A lot of work, but the effect was worth it.

Feature 2: Functions

This is Milo, a character I made in high school.  In Maple Learn, he is built entirely out of functions.  Let’s take a deep dive into what’s going on:

• The head and hair are parametric functions.  Folks who’ve taken a math class that includes parametrics know that (x, y) = (cos(t), sin(t)) is the formula for a unit circle.  We can modify the range of t, coefficients in front of sin(t) and cos(t), and add or subtract constants to create partial circles and ellipses.

• The shaded eyes are done with inequalities; Maple Learn shades inequality areas automatically.

• Milo’s big smile is the equation of a circle with the added detail “| y < -0.5”.  The bar is the “such that” operator, which allows users to limit the domain and range of the function.

• The body is a piecewise function: positive slope for x-values on the left side, negative slope for x-values on the right, and nothing in between.

• The heart shape came from a formula found online.  Mathematicians have discovered some incredible equations!

Feature 3: Animation

By final piece sprouts into a beautiful flower as one moves a slider.  After defining a variable in Maple Learn, a slider appears to adjust it.  This can be used for interactive explorations of graphs and animations.  For example:

• Associate the coordinates of a point with the variable or a function evaluated at the variable.  As the variable changes, the point will move.

• Associate the range of a parametric function with the variable.  As the variable changes, more or less of the function will appear.

• Use the variable in the conditions of piecewise functions.  When the variable is in the correct range, the shapes or functions you defined in the piecewise will appear.

Mathematics is a beautiful language, and every type of expression can add more to your canvas.  These techniques are just the beginning of beautiful Maple Learn art.  Feel free to share your own art or your favorite tips in the comments! 

In computer science, the Towers of Hanoi (Wiki) are considered a prime example of a problem that can only be solved recursively (or iteratively). The time for calculating a certain position n thus grows exponentially with O(2ⁿ). In this article an explicit solution is presented with which one can compute any position n with the same computing time O(1). This explicit solution is used in all animations.

Explicit solution