It’s been a hot week at the Maplesoft office, but we’re back with another fun example! In school, you probably learned how to calculate volume of simple shapes: Cubes, prisms, things like that. However, something I never understood was complex shapes. I struggled to separate it into smaller shapes, plus I had trouble understanding ratios!

Thankfully, Maple Learn has documents on almost anything. I love looking through them when making these posts, just to see what more I can learn. In this case, I found a really interesting example on Changing Dimensions and Effects on Volume, which taught me a lot. Let’s take a look at it, and hopefully it will help you too!

The document begins with a statement, saying “For a 3D object, if one or more dimensions (length, width, height) are changed, then the volume of the object is scaled by a factor equal to the product of all scale factors of changed dimensions”. If you’re not a math person, like me, this statement can be quite confusing at first glance. Let’s break it down.

The first part of the statement is easy to understand. We know what a 3D object is, and we know what dimensions changing means. We also know what the volume of an object is, as a concept. However, what is all this about scale factors?

Looking at the example, it starts to make a lot more sense. The solid has dimensions of 4x10x6. To find the scale factor, we first need to decide on an “original” solid. In this case, a 2x2x2 cube. The number of those cubes is found by dividing each dimension of the full shape by the dimensions of the original shape. This gives us 30. That means the new solid is 30 times larger than the cubes.

From there, the document has a fun, interactive example that lets you play around with sliders.

When you change a, b, and c you are changing the scale factors. This lets you see the final volume, and how it changes with those factors.

We hope this example helped you understand a concept you may have never been directly taught, as I know it helped me! Let us know if you’d like to see any more example walkthroughs.

Happy Friday everyone, and welcome to our third post about how you can use Maple Learn in non-math disciplines! Today, we’re going to talk about the Biology collection in Maple Learn. This was a recent addition to the Maple Learn document gallery.

Of course, there are too many documents in the Biology collection to talk about all of them. We’re going to talk about three documents today, and I’ll link to them as we go. Are you excited? I am!

First, let’s talk about the Introduction to Alleles and Genotype document. The current focus of our Biology collection is genetics. This document is therefore important to start with as it lays the foundation for understanding the rest of the documents. Using a visualization of a sperm cell and an egg cell, this document clearly explains what alleles and genotypes are, and how this presents in humans and other diploid organisms.

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Next is the Introduction to Punnett Squares. Punnett squares are used to predict genotypes and the probability of those genotypes existing in an organism. They can be pretty fun, once you get the hang of them, and are simple to understand using this document. We use the table feature in Maple Learn to display the Punnett squares, which is quite a handy feature for visualizations.

Finally, although there are other introductory documents (Phenotypes, Dihybrid crosses), let’s take a look at the Blood Typing document! As you may know, there are four main blood types (when you exclude the positive or negative): A, B, AB, and O. However, there are only three alleles, due to codominance and other factors. Come check out how this works, and read the document yourself!

Our Biology collection is still growing, and we’d love to hear your input. Let us know in the comments of this post if there are any other document topics you’d like to see!

Last week, we took a look at the Chemistry documents in Maple Learn. After writing that post, I started thinking more about the types of documents we have in the document gallery. From there, I realized we’d made several updates to the Physics collection, and added a Biology collection, that I hadn’t written about yet! So, this week, we’ll be talking about the Physics collection, and next week, we’ll have a discussion about the Biology collection. Without further ado, let’s take a look!

First, let’s talk Kinematics. This collection has been around for a while now, and if you’ve looked at the Physics documents, you’ve likely seen it. We have documents for Displacement, Velocity, and Acceleration, Equations 1 to 4 for Kinematics, 1D motion, and 2D motion. Let’s take a look at the 2D motion example, shall we?

In this document, we explore projectile motion. You can use sliders to change the initial velocity and the height of a projectile, in order to see how they affect the object’s motion. Then, in group two, you can adjust the number of seconds after an object has been released in order to see how the velocity changes. The resulting graph is shown above this paragraph.

Next, we also have documents on Energy, Simple Harmonic Motion, and Waves (interference and harmonics). These documents were added over the last few months, and we’re excited to share them! Opening the document used as an example for wave harmonics (link provided again here), we’re immediately given a description of the important background knowledge, and then a visualization, shown below. This allows you to see how waves change based on the harmonics and over time.

Finally, we have documents on Electricity and Magnetism, Dynamics, and some miscellaneous documents, like our document on the inverse square law applied to Gravity. Within these document collections, we have quizzes, information, and many more visualizations!

The Physics collection is quite an interesting collection, we hope you enjoy! As with the Chemistry documents, please let us know if there’s any topics you’d like to see in our document gallery.

We are happy to announce that we released MapleSim 2022 today.

The MapleSim 2022 family of products offers improvements in modeling and connectivity, including many that are in direct response to customer requests. Improvements include:

• Reduce diagram clutter by using “wireless” To-From blocks for a larger variety of signals
• Easily create, customize, and fine-tune control valves with new components and tools in the hydraulics library
• Expand modeling scope with improvements to several specialized libraries and toolboxes, including the MapleSim add-on products for Battery, Heat Transfer, and Web Handling
• New productivity and connectivity features in MapleSim Insight,  a standalone product in the MapleSim family that gives machine builders powerful simulation-based debugging and 3-D visualization capabilities that connect directly to your automation tools

See What’s New in MapleSim 2022 for more information about these and other improvements.

Hello Maple Learn enthusiasts, of all disciplines! Do any of you study Chemistry, or simply enjoy it? Well, you’re in luck. We’re released a new collection of documents in the document gallery, all focused on Chemistry. Remember, Maple Learn isn’t just for math fields. We also have documents on Biology, Physics, Finance, and much more!

First, we have our new gas laws documents. These documents focus on Boyle’s law, Charles’ law, Gay-Lussac’s law, and Avogadro’s law. We also have documents on the Combined Gas law and the Ideal Gas law. Many of these laws also have example questions to go along with them, for your studying needs.

We also have documents on molar and atomic mass. One example for atomic mass teaches you to use the proper formulas (No spoilers for the answer here, folks!) using the material Hafnium and its five isotopes. Don’t know the approximate masses of the isotopes without looking them up? No worries, I don’t either! It’s in the question text, as a hint.

Finally, let’s take a look at the dilution documents. We have documents discussing the calculations, and some examples. In this document, there are both an example walking you through the steps, and a practice question for you to try yourself. Of course, the solution is included at the bottom of the document, but we encourage you to try the problem yourself first.

We hope you’re just as excited as us for the Chemistry collection! Like our other collections, the Chemistry collection is constantly being added to. If you have any ideas for future documents, or even just topics you’d like to see, let us know in the comments below.

Today is a very exciting day at Maplesoft! Yesterday, we released Sumzle on the Maple Calculator app. Of course, this might not mean anything to you yet, because, well, what is Sumzle? Don’t worry, we know you’re asking. So, without waiting any longer, let’s take a look.

Sumzle is a math game, inspired by the Wordle craze, where you attempt to guess an equation. Each guess:

• Must include an equal sign
• Must include up to two operators
• May include a blank column

Sumzle’s interface looks like this:

After each guess, the tile’s colors change to reflect how correct the guess was. Green means that the tile is in the right spot, yellow means the tile is in the equation but the wrong spot, and grey means that it is not in the equation. Let me show you the progression of a game, on the Fun difficulty.

Sumzle can be played once a day on the free tier. For unlimited games, you can subscribe to Maple Calculator Premium or ask your friends to challenge you!

Math games are for everyone, and Sumzle has three levels of difficulty. Are you interested in the history of Sumzle? I sure am!

Sumzle was originally designed by Marek Krzeminski, a MapleSim developer. He had called it Mathie and showed the game to his colleagues here at Maplesoft. Well, we loved it!

After a few months of discussion and development, we tweaked the game to create Sumzle. Honestly, the hardest part was naming the game! We had so many great suggestions, such as Mathstermind and Addle. Eventually, we put it to a vote, and Sumzle rose above the rest.

We hope you enjoy the game, because Math not only matters, but is fun. Don’t forget to update your Maple Calculator app in order to receive that game, as otherwise you won’t be able to find it. Next time you need a break, we challenge you to a game of Sumzle!

Have you ever wanted to create practice problems and quizzes that use buttons and other features to support a student making their way to an answer, such as the following?

• Is this a function?
• Total Mass practice quiz
• Vector Operations quiz
• Steps Document – Matrix Eigenvalues

Let’s take a look at how you can use Maple 2022 to create documents like these that can be deployed in Maple Learn. I know I’ve always wanted to learn, so let’s learn together. All examples have a document that you can use to follow along, found here, in Maple Cloud.  

The most important command you’ll want to take a look at is ShareCanvas. This command generates a Maple Learn document. Make sure to remember that command, instead of ShowCanvas, so that the end result gives you a link to a document instead of showing the results in Maple. You’ll also want to make sure you load the DocumentTools:-Canvas subpackage using with(DocumentTools:- Canvas).

If you take a look at our first example, below, the code may seem intimidating. However, let’s break it down, I promise it makes sense!

with(DocumentTools:-Canvas);
cv := NewCanvas([Text("Volume of Revolution", fontsize = 24), "This solid of revolution is created by rotating", f(x) = cos(x) + 1, Text("about the y=0 axis on the interval %1", 0 <= x and x <= 4*Pi), Plot3D("Student:-Calculus1:-VolumeOfRevolution(cos(x) + 1, x = 0 .. 4*Pi, output = plot, caption=``)")]);
ShareCanvas(cv);

The key command is Plot3D. This plots the desired graph and places it into a Maple Learn document. The code around it places text and a math group containing the equation being graphed. 

Let’s take a look at IntPractice now. The next example allows a student to practice evaluating an integral.

with(Grading):
IntPractice(Int(x*sin(x), x, 'output'='link'));

 This command allows you to enter an integral and the variable of integration, and then evaluates each step a student enters on their way to finding a result. The feedback given on every line is incredibly useful. Not only will it tell you if your steps are right, but will let you know if your last line is correct, i.e if the answer is correct.

Finally, let’s talk about SolvePractice.

with(Grading):
SolvePractice(2*x + 3 = 6*x - 9, 'output' = 'link');

This command takes an equation, and evaluates it for the specified variable. Like the IntPractice command, this command will check your steps and provide feedback. The image below shows how this command looks in Maple 2022.

These commands are the stepping stones for creating practice questions in Maple Learn. We can do so much more in Maple 2022 scripting than I realized, so let’s continue to learn together!

Some other examples of scripted documents in the Maple Learn Document Gallery are our steps documents, this document on the Four Color Visualization Theorem, and a color by numbers. As you can see, there’s a lot that can be done with Maple Scripting.

 Let us know in the comments if you’d like to see more on Maple 2022 scripting and Maple Learn.

We’ve just released Maple Flow 2022!

The name of the product – Flow - references a psychological concept known as the flow state. You might know it as being in the zone. That’s when you’re so immersed in your present task that outside distractions melt away, your problem solving skills are firing on all four cylinders, and feel-good neurochemicals flood your brain.

Maple Flow supports a mathematical flow state through a simple design that productively guides the loosely structured and somewhat haphazard way that most people work.

Since Maple Flow's release a year ago, we've regularly added new features through updates, and we're commited to maintaining that momentum. These updates are driven by user feedback, so keep sending your comments and requests my way.

Here’s what we have lined up for you in Flow 2022.

Flow 2022 features a new in-product help system - see it in action here:

In addition to copying & pasting equations and expressions from a help page, you can open entire help pages as worksheets. The nature of Flow means that the help pages have a certain immediacy that becomes very tangible once you start working with them.

You can change the background colour of containers to highlight important results or draw the reader's attention to specific groups of containers.

Prior versions of Flow were a toolbox that needed to be installed on top of Maple.

Now, Flow 2022 is completely standalone, and does not require an existing installation of Maple.This makes managing an installation of Flow far simpler.

A new options menu let you specify how you want worksheet hyperlinks to open – in the same application window, or in a new application window.

We've also made many other quality-of-life changes to Flow. Head on over to the Maple Flow website to learn more or download an evaluation.

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!

Bon vendredi à tous! Je suis de retour avec un autre article de mise à jour détaillant les nouveautés que nous avons apportés à Maple Learn cette semaine. Bonne lecture!

Tout d'abord, nous avons ajouté des permutations et des combinaisons, ainsi que la notation binomiale, à Maple Learn ! Gardez l’œil à l’affût des documents utilisant ces nouvelles fonctionnalités et consultez nos exemples ici et ici. Les opérations se trouvent dans la palette des fonctions. Nous espérons que cela permettra de rendre votre création de document avec Maple Learn encore plus agréable !

Nous avons également mis à jour la syntaxe des graphiques paramétriques pour utiliser l'opérateur tel que. Veuillez consulter notre page d’instruction pour plus de détails (ici). Remplacez simplement la virgule de l'ancienne syntaxe par le |. À partir de là, placez vos restrictions et le tour est joué ! Un graphique paramétrique utilisant l'opérateur tel que.

Enfin, quelques changements mineurs à Maple Learn. Nous avons ajusté la taille de police par défaut à une police de taille 20. De plus, nous avons fait en sorte qu'il remplace automatiquement <= ou >= par le symbole ≤ ou ≥.

J'espère que ces nouvelles fonctionnalités sont tout aussi intéressantes pour vous qu'elles le sont pour moi ! Faites-nous savoir ce que vous pensez dans les commentaires ci-dessous.

Happy Friday everyone! I’m back with another update post detailing the new changes we’ve made to Maple Learn this week. Just keep reading, and we’ll get right into them.

First, we’ve added permutations and combinations, along with binomial notation, to Maple Learn! Keep an eye out for documents using these new features, and check out our examples here and here.  The operations can be found in the functions palette. We hope that this allows even more fun with documents on Maple Learn!

We’ve also updated the syntax for parametric plots to use the such that operator. Please see our how-to page for more detail (here). Simply replace the comma from the old syntax with the |. From there, place your restrictions, and voila! A parametric plot using the such that operator.

Finally, some minor changes to Maple Learn. We’ve adjusted the default font size to 20 point font. As well, we’ve made it automatically change <= or >= to the ≤ or ≥ symbol.

I hope these new features are just as exciting to you as they are to me! Let us know what you think in the comments below.

Probability is a field of mathematics that sees extensive use outside of academics.  Whether one’s checking the likelihood of rain on a weather app or the odds of winning the lottery, probability is everywhere.  My favorite application of probability is dice games like Dungeons and Dragons.  The game can be played very simply (choose to attack a monster, roll a 20-sided-die, try to exceed a certain number) or with a complexity that rivals high school math courses.  There are spells and abilities that modify one’s dice rolls, such as adding additional rolls to the total or rerolling the die and using the higher result.  A good player regularly asks themself when to activate certain buffs and how likely they are to succeed with or without them.

All of these questions boil down to the basics of probability.  Things that one learns in an introductory statistics course extend into countless applications.  Currently, I’m adding some of that knowledge to the Maple Learn document gallery, and I’m here to give a sneak peek.

First, I’ve built tree diagrams in Maple Learn.  Tree diagrams are a way to map probability across multiple events occurring in sequence.  Each branching path represents a series of events that have a specified probability of occurring.

Here’s an example: one morning I flip a coin to decide if I buy a lottery ticket.  If it’s heads, I do.  If I buy the ticket, I have a one in a million chance of winning the cash prize.  Drawn as a tree diagram…

I drew this using Maple Learn line, point, and label operations.

My new D&D-themed documents are a bit more exciting.  In the first, we explore a tree diagram with variable probabilities.  A brave hero makes their way into a dungeon, attacking any random monster they see.  How likely are they to land an attack?  Adjust the details of the question and watch the diagram change.

In the second, I used Maple program scripting to add a live randomized dice roller.  Many probability techniques are at play to analyze which of two buffs will do more good for a dice-rolling adventurer.

I plan on making more documents like these; keep your eyes on the Document Gallery probability collection for updates.

Les probabilités sont  un domaine des mathématiques largement utilisé en dehors des universités. Que l'on vérifie la probabilité de l’apparition de la pluie sur une application météo ou les chances de gagner à la loterie, les probabilités sont partout. Mon application des probabilités préférée est les jeux de dés comme Donjons et Dragons. Le jeu peut se jouer très simplement (choisir d'attaquer un monstre, lancer un dé à 20 faces, essayer de dépasser un certain nombre) ou avec une complexité qui rivalise avec les cours de mathématiques du lycée. Il existe des sorts et des capacités qui modifient les lancés de dés, comme ajouter des lancés supplémentaires au total ou relancer le dé et utiliser le résultat le plus élevé. Un bon joueur se demande régulièrement quand activer certains « buffs » et quelle est la probabilité qu'ils réussissent avec ou sans eux.

Toutes ces questions se résument aux bases des probabilités. Les choses que l'on apprend dans un cours d'introduction aux statistiques s'étendent à d'innombrables applications. Actuellement, j'ajoute certaines de ces connaissances à la galerie de documents Maple Learn je voulais vous en donner un aperçu.

Tout d'abord, j'ai construit des arbres de probabilité avec Maple Learn. Ceux-ci permettent de représenter graphiquement la probabilité de plusieurs événements se produisant en séquence. Chaque chemin de branchement représente une série d'événements qui ont une probabilité de se produire spécifique.

Voici un exemple : un matin, je lance une pièce pour décider si j'achète un billet de loterie. Si c'est face, je le fais. Si j'achète le billet, j'ai une chance sur un million de gagner l’argent. Dessiné sous forme d'arbre de probabilité…

J'ai dessiné ceci en utilisant les fonctionnalités ligne, point et étiquette de Maple Learn.

Mes nouveaux documents sur le thème de D&D sont un peu plus intéressants. Dans le premier, nous explorons un arbre de probabilités variables. Un héros courageux se rend dans un donjon, attaquant n'importe quel monstre aléatoire qu'il voit. Quelle est la probabilité qu'ils lancent une attaque ? Ajustez les détails de la question et regardez le diagramme changer.

Dans le second, j'ai utilisé la fonction script de Maple pour ajouter un lanceur de dés aléatoire en direct. De nombreuses techniques de probabilité sont en jeu pour analyser lequel des deux « buffs » fera le plus de bien à un aventurier qui lance les dés.

Je prévois de faire plus de documents comme ceux-ci; gardez un œil sur la catégorie de probabilités dans la galerie de documents Maple Learn pour les mises à jour.

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!