Maplesoft Blog

The Maplesoft blog contains posts coming from the heart of Maplesoft. Find out what is coming next in the world of Maple, and get the best tips and tricks from the Maple experts.

Maple Learn is an incredibly powerful tool for math and plotting, but it is made even more powerful when used in combination with Maple! Using scripting tools in Maple, we can make use of hundreds of commands that can solve complex problems for us. In the example of the Lagrange calculator, we are able to use the Maple command LagrangeMultipliers to generate a plot of the two functions and the critical points, even including text feedback about the points.


Something like this seems like it would take hours and a lot of coding knowledge to create, but a simple Maple command generates the entire plot for us! Then, all we had to do was use a button to update the plot. Give it a try yourself in Maple, run the following command with two functions f and g of your choosing:

That’s all there is to it! We now have a complex 3D plot showing the Lagrange problem, something that can be difficult to visualize in multivariate calculus. If we want detailed feedback about the Lagrange problem values, simply change output to detailed from plot:



Check out the entire Maple document (.mw file) to see how the Learn page was generated and to try things out for yourself. This entire document uses the LagrangeMultipliers command, but Maple has hundreds more to experiment with, so the possibilities are virtually limitless!

Share your creations here on MaplePrimes and tag us in your posts.

Maple Learn Document: 
https://learn.maplesoft.com/doc/lagrange-multipliers-calculator-1biue2ben9

Maple .mw file: https://maple.cloud/app/6546482431000576/LagrangeCalc

Maple Learn has a new face! We’ve changed our homepage to the document gallery, which some of you may have already noticed. This is a huge change, and we’re excited for it, as it places content front and center: the goal of Maple Learn. Don’t worry, getting to a blank document is still easy. There is a large orange button on the top right of the document gallery which says “start creating now”. This button will take you to a blank Maple Learn Document.

                                                                        

The most important reason for this change is to help new users get started. Seeing a blank document can sometimes be terrifying! With this new homepage, users can immediately begin looking through premade content, and get inspiration for their own documents.

 

The first document collection a user sees in the document gallery is still the same: Our featured collection. From there, we have the Maple Learn how-to documents, and then it’s into documents sorted by the overarching subject. Two examples of overarching subjects are Functions and Biology. And, if a user is interested in some of the more artistic sides of Maple Learn, we have our art collection available as well. There’s something for everyone in our gallery!

                             

Now that we’ve explained the largest change, let’s talk about some smaller ones too. Tables now can have row and column headings, allowing for a greater range of data to be represented. Along with that, we’ve added a correlation command to the context panel. Some bugs have also been fixed: Special characters now appear properly in the French and German galleries and scrollbars work over 3D plots.

 

We hope you enjoy the changes we’ve made. Please continue to report bugs and telling us about features you’d like to see!

Hi Maple Users

As I hope you have already heard, Maplesoft is having our Maple Conference again this fall. And that means that

Last year we had many great submissions and you can still read about them in detail on the 2021 conference site. Some of the featured works were excellent Maple visualizations, including a special prize for a student contribution by Avek Dongol (center).

But we also featured a number of impressive physical works, including the people's choice winning wood carving by Paul DeMarco (left), and the judges' choice winning cross stitch by Bridjet Lee and Curtis Bright (right).

This year, we are again looking to fill our virtual exhibition with all types of mathematical art, ranging from computer graphics and animations, to needlework, geometrical sculptures, or almost anything you can come up with. Surprise us!

The full announcement can be found at the Maple Conference Art Gallery page. We would like to have all submissions by September 22nd so that we can review and finalize the gallery before the conference begins November 2nd.

I can't wait to see what everyone sends in this year!

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?

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.

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