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!)

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!

I’m absolutely delighted to announce the launch of Maple 2025!

Although you see a new release every year, new features take anything from a few fast-paced weeks to develop, to months of careful cultivation.

Working on so many features in parallel, each with varying time scales, isn't easy! We have to fastidiously manage and track our work.

So it's easy to lose ourselves in the daily minutiae of software development. To help us maintain perspective, we constantly ask ourselves questions like:

• What user problem are we solving and how often does this problem occur?
• Can we validate our proposed solution with preliminary user feedback?
• Is this a solution to a problem that doesn't exist and will never exist, or are we pre-empting a future need?
• Are we offering value to our users?

Given the answers, we course-correct to make sure we stay on track for our central mission - to make you happy, and to keep you coming back year-after-year.

With Maple 2025, I think we've smashed that goal. We have many new features that'll appeal to many different types of users - from students, educators and mathematicians, to engineers, scientists and technical professionals

Let me walk you through some of my personal highlights.

It’ll be difficult for anyone to miss this - Maple 2025 has a new interface! It’s a ribbon-based UI that look clean and contemporary, and helps you find and discover tools more quickly than before.

You have large, meaningful icons.

Items are logically grouped.

The ribbons is contextual. If you click on a plot, you get new tabs for interacting with and drawing on the plot.

A new Education tab collects pedagogical resources that were scattered around the interface in prior releases.

This is the biggest visual overhaul to Maple in many years. We hope you like it! 

We also appreciate that changes in look and feel can be divisive. Please rest assured that we will refine and finesse the interface with each successive release; your comments and suggestions are most welcome.

The new interface is available on Windows and Linux, and as a technology preview on Mac.

The right arrow key on my keyboard is wearing out…and it’s all because of Maple. I’m knee deep in Maple nearly every day entering equations, and I’m always using right-arrow to move the cursor. It gets kind of tedious!

This anecdote reflects some investigative work we did. We comprehensively examined our internal library of thousands of Maple worksheets and discovered that these three input patterns are extremely common.

Previously, you’d use the right-arrow key to move the cursor out of the exponential, division or subscript.

Now, in Maple 2025, when you

• type ^, /, or enter a literal subscript with a double-underscore,
• followed by a number or symbol
• and then input another operator (such as +)

the operator is automatically inserted on the baseline (except when y = 1).

Of course, you can also make the cursor return to or stay in the exponent or denominator with a simple keystroke, when that is what is needed.

This is one of those little quality of life refinements that I’m very fond of - it’s a little visual and usability dopamine hit.

The sum command (and its typeset form) now indexes into vectors without you needing to spam unevaluation quotes all over your expression.

We’ve been integrating units deeper into the Maple system, release after release. Much of this is driven by our engineering users.

A few releases ago, we made int(numeric) compatible with units. With Maple 2025, you can now numerically differentiate  expressions and procedures that have units.

I’m a grizzled thermodynamics hack, so here’s an example in which I calculate the specific heat capacity of water by differentiating enthalpy with respect to temperature (and then confirm the result with the built-in value):

This is in addition to many other improvements to the units experience.

Although this is a part of Maple that I don’t touch often (my colleague Karishma takes point on the education side), I REALLY wish I’d had this when I was struggling with math.

You can now automatically generate unlimited variants of the same problem for students to solve with the Try Another feature, which has been added to Maple’s Check My Work tools (another feature I really could have used!). This is available for many common math principles, including factorization, simplification, integration and more.

This is just one of the improvements in Maple 2025 for teaching and learning.

 If you’ve ever found yourself going back and forth (and back and forth) between two large, almost identical-looking Maple expressions, trying to figure out how they are different, you’re going to love this one.  ExpressionTools is a new package that lets you compare the differences between two expressions.

I really like the use of color to highlight differences. Less squinting at the screen!

You can now run Maple Flow worksheets from Maple (you don’t need Maple Flow installed to do this). You can send parameters into the Flow worksheet and extract your desired results.

This means you can use the entire flexibility of Maple to analysis and manipulate your Flow worksheet. You could, for example:

• Attach a Flow worksheet to a Maple workbook and create an interactive application
• Carry out parameter studies of a Flow worksheet by evaluating it over many parameter sets in Maple
• Create an Excel interface for a Flow worksheet using the Maple add-in for Excel

Simplify is one of those functions that literally tens of thousands of people use each day. Every time we make an incremental improvement, the cumulative benefits across our entire user base are significant.

We’ve refined simplify in a number of critical ways. For example, simplify now recognizes when exponentials can be profitably converted to hyperbolic trig functions:

The analysis of many scientific phenomena result in Laplace transforms that do not have a symbolic inverse which can be expressed in terms of elementary functions. This includes applications in heat transfer, fluid mechanics, fractional diffusion processes, control systems and electrical transmission.

For example, this monster Laplace transform results from an analysis of voltage on a transmission line:

You can now numerically invert this transform courtesy of an enhancement to inttrans:-invlaplace - a fast quadrature method.

I’ve saved what I think has the most future potential for last.

I’m sure nearly all of you have experimented with the various AI tools. They’re an inevitable part of our present and future, whether we're comfortable with it or not.

This is something we've been mulling over for some time.

• In Maple 2019, the DeepLearning package made its debut. This package provides tools for machine learning, supporting operations such as classification and regression using neural networks.
• In Maple 2024, we introduced an AI-powered formula lookup feature.

In Maple 2025, we’re giving you an early-stage technology preview of AI-powered document generation.

You can automatically generate worksheet content by prompting an AI, and then gradually refine the content

If you’re an educator, you might want some content that describes applications of calculus. So you might ask the AI “How do I derive the formula for the area of a circle” by entering your prompt into this text box:

This is the worksheet content that may be returned:

If you’re structural engineer who wants to know how to calculate the hardness of concrete, you might ask the AI: “How do I calculate the compressive strength of slow hardening concrete as a function of time? Use the CEB-FIP Model Code 90. Include a worked example with Maple code”.

This worksheet content that could be generated (note the live Maple code):

We’re labelling AI-generated worksheet content as a technology preview. You might see

• text that might be misleading (but sounds plausible)
• code that doesn’t work (but looks plausible)
• or different results each time you click “Generate Document”

For the moment, I would not rely on AI-generated worksheet content without realistic expectations, a healthy dose of scepticism and a modicum of detached analysis. But AI models are rapidly growing in robustness, and we want to position ourselves to best exploit their future potential. The next few years will be VERY exciting.

We can never cover everything in a short blog post like this. So if you want to know more, head on over to the What’s New pages for Maple 2025!

After more than 25 years of leading research in areas such as differential equations, special functions, and computational physics, Edgardo's role with Maplesoft will shift at the end of 2024 as he returns to academic research. At Maplesoft, he will transition into the position of Research Fellow Emeritus. In this role, Edgardo will remain engaged with many of his cherished projects, though he will not have as much time to maintain the intense level of activity that characterized his work for so many years.

Many of you know Edgardo personally or have interacted with him here or on the Maple Beta Forum. I hope you'll join me in wishing him the very best as he begins this new chapter.

We’re thrilled to announce the launch of our new Student Success Platform! Over the past several months, our academic team has dedicated itself to understanding how we can better support institutions in addressing their concerns around student retention rates. The numbers tell a concerning story: In the U.S., nearly 25% of first-year undergraduates don’t complete their studies, and in STEM fields, the numbers are even higher. In both STEM programs and non-STEM programs with math gateway courses, struggles with math are often a key reason students do not, or cannot, continue their studies. This has a profound impact on both the students’ futures and the institution’s revenue and funding.

From what we’re hearing from institutions and instructors, one of the most pressing issues is the lack of readiness among first-year students, particularly in math courses. With larger class sizes and students arriving with varying levels of preparedness, instructors face challenges in providing the personalized support that is essential. Additionally, many students don’t fully utilize existing resources, such as office hours or TA sessions, which increases their risk of falling behind and ultimately dropping out.

Our new Student Success Platform is designed to tackle these issues head-on. It combines all of our existing tools with exciting new features to help students succeed on their own terms—without adding to instructors' already busy workloads. The early feedback has been fantastic, and we can’t wait for you to see the impact it can make.

You can read more about the Student Success Platform here: https://www.maplesoft.com/student-success-platform/

VerifyTools is a package that has been available in Maple for roughly 24 years, but until now it has never been documented, as it was originally intended for internal use only. Documentation for it will be included in the next release of Maple. Here is a preview:

VerifyTools is similar to the TypeTools package. A type is essentially a predicate that a single expression can either satisfy or not. Analogously, a verification is a predicate that applies to a pair of expressions, comparing them. Just as types can be combined to produce compound types, verifications can also be combined to produce compund verifications. New types can be created, retrieved, queried, or deleted using the commands AddType, GetType (or GetTypes), Exists, and RemoveType, respectively. Similarly in the VerifyTools package we can create, retrieve, query or delete verifications using AddVerification, GetVerification (or GetVerifications), Exists, and RemoveVerification.

The package command VerifyTools:-Verify is also available as the top-level Maple command verify which should already be familiar to expert Maple users. Similarly, the command VerifyTools:-IsVerification is also available as a type, that is,

VerifyTools:-IsVerification(ver);

will return the same as

type(ver, 'verification');

The following examples show what can be done with these commands. Note that in each example where the Verify command is used, it is equivalent to the top-level Maple command verify. (Also note that VerifyTools commands shown below will be slightly different compared to the Maple2024 version):

Download VerificationTools_blogpost.mw

Austin Roche
Software Architect
Mathematical Software
Maplesoft

Dear Maple Community,

It has been a year since the passing of Stefan Vorkoetter, who started contributing to the Maple project in the 80s and was a long term member of our development team. 

Here are a few recently published articles about Stefan, that I'd like to share with you:

https://mapletransactions.org/index.php/maple/article/view/18269
https://mapletransactions.org/index.php/maple/article/view/18681

we shall not forget

We are pleased to announce that the registration for the Maple Conference 2024 is now open.

Like the last few years, this year’s conference will be a free virtual event. Please visit the conference page for more information on how to register.

This year we are offering a number of new sessions, including more product training options and an Audience Choice session.
You can find an overview of the program on the Sessions page. Those who register before September 10th, 2024 will have a chance to vote for the topics they want to learn more about during the Audience Choice session.

We hope to see you there!

We are happy to announce another Maple Conference to be held October 24 and 25, 2024!

It will be a free virtual event again this year, and it will be an excellent opportunity to meet other members of the Maple community and get the latest news about our products. More importantly, it's a chance for you to share the work you've been doing with Maple and Maple Learn. 

We have just opened the Call for Participation. We are inviting submissions of presentation proposals on a range of topics related to Maple, including Maple in education, algorithms and software, and applications. We also encourage submission of proposals related to Maple Learn. 

You can find more information about the themes of the conference and how to submit a presentation proposal at the Call for Participation page. Applications are due July 17, 2024.

Presenters will have the option to submit papers and articles to a special Maple Conference issue of the Maple Transactions journal after the conference.

Registration for attending the conference will open in July.  Watch for further announcements in the coming weeks.

I encourage all of you here in the Maple Primes community to consider joining us for this event, whether as a presenter or an attendee!

Kaska Kowalska
Contributed Program Co-Chair

I’m excited to announce that we’ve just launched MapleSim 2024.

The new release has tools that are designed to drive innovation, and overall save you time when creating and developing simulations.

At Maplesoft we are looking to continually enhance our engineering software with new features based on customer feedback, and I’m pleased to share some of the fruits of that labor, and thank the developers, product management team, and  customers that contributed.

The new offering  helps engineers to

• Rapidly Tune Parameters
• Explore Design Concepts
• Expand Modeling Capabilities

For example, the new Rerun panel allows you to significantly cut the time between simulations as you quickly apply different parameter values, initial conditions and even simulation settings between runs. It does this by skipping the formulation steps when there are no structural changes made to the model, and you can even see the plots and results of the different iterations side by side.
You can see it in action in this short demo video.

There is now support for the latest Modelica feature set, so you can import Modelica Libraries that make use of MSL 4.0.0 features, and adds a range of new modeling components to the standard MapleSim libraries (electrical, 1-D mechanical, signal block and more).

MapleSim 2024 also includes more components in the Hydraulic library to support modeling of flow restrictions and adds a Scripting button to add and organize Maple worksheets.

We’ve also applied a whole series of updates to our MapleSim add-on products, including:

• The MapleSim Web Handling Library has new tools for modeling heavier webs, winding of multiple rolls on the same drum, and adding a Switching Nip Roller to swing the web contact points between rollers.
• The MapleSim Connector for FMI can now import and export FMI 3.0.
• The MapleSim CAD Toolbox supports recent software releases from NX™, SOLIDWORKS®, Solid Edge®, Parasolid®, and other CAD tools.
• The MapleSim Heat Transfer Library has gained a new T-junction component for the Water subpackage to improve flow/pressure-drop calculations for systems with branches.

We have an upcoming webinar for you to see the new 2024 features in MapleSim Web Handling Library – you can sign up to register here.

You can find out more about the other new features at the MapleSim What’s New web page, and as always, we are happy to hear your comments and product suggestions.

And if you are new to MapleSim and would like to try building and running a model yourself, you can request a free trial, or contact Maplesoft sales team with any questions.

We've just launched Maple Flow 2024!

You're in the driving seat with Maple Flow - each new feature has a straight-line connection to a user-driven demand to work faster and more efficiently.

Head on over here for a rundown of everything that's new, but I thought I'd share my personal highlights here.

If your result contains a large vector or matrix, you can now scroll to see more data. You can also change the size of the matrix to view more or fewer rows and columns.

You can resize rows and columns if they're too large or small, and selectively enable row and column headers.

If the vector or matrix in your result contains a unit, you can now rescale units with the Context Panel (for the entire matrix) or inline (for individual entries).

A few releases ago, we introduced the Variables palette to help you keep track of all the user-defined parameters at point of the grid cursor.

You can now insert variables into the worksheet from the Variables palette. Just double-click on the appropriate name.

Maple Flow already features command completion - just type the first few letters of a command, and a list of potential completions appears. Just pick the completion you need with a quick tap of the Tab key.

We've supercharged this feature to give potential arguments for many popular functions. Type a function name followed by an opening bracket, and a list appears.

In case you've missed it, the argument completion list also features (when they make sense) user-defined variables.

You can now link to different parts of the same worksheet. This can be used to create a table of contents that lets you jump to different parts of larger worksheets.

This page lists everything that's new in the current release, and all the prior releases. You might notice that we have three releases a year, each featuring many user-requested items. Let me know what you want to see next - you might not have to wait that long!

     Happy Easter to all those who celebrate! One common tradition this time of year is decorating Easter eggs. So, we’ve decided to take this opportunity to create some egg-related math content in Maple Learn. This year, a blog post by Tony Finch inspired us to create a walkthrough exploring the four-point egg. The four-point egg is a method to construct an egg-shaped graph using just a compass and a ruler, or in this case, Maple Learn. Here's the final product: 

     The Maple Learn document, found here, walks through the steps. In general, each part of the egg is an arc corresponding to part of a circle centred around one of the points generated in this construction. 

     For instance, starting with the unit circle and the three red points in the image below, the blue circle is centred at the bottom point such that it intersects with the top of the unit circle, at (0,1). The perpendicular lines were constructed using the three red points, such that they intersect at the bottom point and pass through opposite side points, either (-1,0) or (1,0). Then, the base of the egg is constructed by tracing an arc along the bottom of the blue circle, between the perpendicular lines, shown in red below.

     Check out the rest of the steps in the Maple Learn Document. Also, be sure to check out other egg-related Maple Learn documents including John May’s Egg Formulas, illustrating other ways to represent egg-shaped curves with mathematics, and Paige Stone’s Easter Egg Art, to design your own Easter egg in Maple Learn. So, if you’ve had your fill of chocolate eggs, consider exploring some egg-related geometry - Happy Easter!  

Attention Maple enthusiasts! It gives me great pleasure to announce Maple 2024! Maple 2024 brings together a collection of new features and enhancements carefully designed to enrich your mathematical explorations. Maple 2024 is the result of a lot of hard work by a lot of people, and there is far more in it than I can cover here. But I’d like to share with you some of my favorite features in this release.

AI Formula Assistant

The AI Formula Assistant in Maple 2024 is undoubtedly the feature that excites me the most, especially considering how often I’m asked the question: 'When will Maple include AI features?' This assistant serves as your new mathematical companion and will change the way you look up and enter formulas and equations. Driven by advanced AI technology, it presents a range of relevant options based on your search query. Alongside suggestions, you'll also receive detailed explanations for each formula and its parameters so you can select the one you need, and then you can insert the formula into your document at a click of a button, as a proper Maple expression.

NaturalLanguage Package

The Formula Assistant is built on top of the new NaturalLanguage package, which integrates powerful language models like GPT-4 and ChatGPT from OpenAI into Maple. With this feature, you can leverage large language models to process natural language within Maple. Ask the AI to explain concepts, provide additional details, find specific Maple commands, and more. Of course, since this is a Maple package, you can also use it as a basis to build your own AI-powered applications inside Maple. We’re really looking forward to seeing what you will do with it!

Argument Completion
We’ve had a lot of requests from people who wanted Maple’s command completion features to do even more, and I’m happy to say that Maple 2024 delivers. The new argument completion feature in Maple 2024 is poised to significantly enhance your experience with commands. For many users, including myself, not being aware of all the options a command takes is a challenge, often leading me to refer to help pages for clarification. With argument completion, that's no longer a concern. Just enter the command with the help of the existing command completion feature, then automatic argument completion takes over to guide you through the rest. Give it a try with the 'plot' command!

Check My Work

A personal favorite feature that's gotten even better in Maple 2024 is Check My Work. As someone who has tutored students, I vividly recall their stress before exams, often receiving emails and text messages from them seeking last-minute help. At the time, I found myself wishing the students had a way to check their work themselves, so we would all be less stressed! So I was super excited when we added the first Check My Work feature a couple of years ago, and am very happy that it gets better ever year. In Maple 2024, we’ve expanded its capabilities to support problems involving factoring, simplification, and limits.

Scrollable Matrices:
This feature will definitely resonate with many of the engineers in the Maple Primes community. If you're someone who works with worksheets containing large matrices, you've likely wished that you could scroll the matrices inside your document instead of having to launch a separate matrix browser. With Maple 2024, your wish has come true.

Color Bars

And finally, for those of you who appreciated the addition of color bars in Maple 2023 but wanted to see them extended to more 2D and 3D plots, you'll be delighted to know that this is exactly what we’ve done. We’ve also added new customization options, providing you with greater control over appearance.

This is just a partial glimpse of what's new in Maple 2024. For a comprehensive overview, visit What’s New in Maple 2024.

Time is running out for users of Mathcad^® 15 worksheets.
Engineers who need to retain their historical Mathcad project files are faced with a looming deadline to move the content to another file format.

The good news is that Mathcad 15 users can turn to Maple Flow as an effective replacement design calculation tool. Maple Flow is an advanced calculation tool with a free-form layout that makes it easy for engineers to brainstorm, develop, and document their project designs.

Maplesoft now has an efficient migration solution for moving critical Mathcad content to Maple Flow worksheets. This gives engineers a path to safeguard their critical reference designs, mathematical analyses, and engineering test results.

Why are engineers moving from Mathcad 15?
In 2025, some changes are expected that will severely restrict access to Mathcad 15 software. Here’s some background:

• PTC announced that Mathcad 15 is end-of-sale effective December 2021, restricting license activations for new users.
• Those existing Mathcad 15 customers who bought multiyear license extensions will see them expire by December 2025. After that, those with subscription licenses will not be able to open the app, and will not be able to access their historic design documents.
• One of the significant issues engineers are encountering is that the new version of the software is not directly compatible with their historical Mathcad documents. PTC no longer has the right to distribute software versions with a third-party component, and has opted to use a different symbolic calculation engine in Mathcad Prime® that cannot read and edit the legacy files.
• Another issue is that the Mathcad 15 software does not support Windows 11, so is typically run on Windows 10, a platform that Microsoft will not be supporting after October 2025.
• Without a reliable way to keep accessing their project work in the Mathcad 15 format, engineers are looking for an alternative design worksheet platform.

As a result, engineers with large repositories of these design files now face converting all the worksheets to a new format or risk losing access to valuable design reports, and the possible regulatory consequences.

Maple Flow as a replacement for Mathcad 15
Engineers who want a long-term stable environment for their critical project work can change their design workflow to use Maple Flow for everyday calculation tasks.

The advanced math features and formatting options in Maple Flow make it a good fit for creating (and updating) design documentation and hand calculations, where engineers combine mathematical equations and variables that change regularly, and show the results in a report.

Maple Flow has a short learning curve, and the range of example templates in the Application Center and the customized training all help users quickly get up to speed with Maple Flow commands and formatting features.

How can I migrate Mathcad 15 content to Maple Flow?
Maplesoft has created a series of migration strategies for users of Mathcad software to transition to Maple Flow for ongoing calculation needs or to meet compliance requirements.

For engineers with a handful of worksheets, or where the calculations only span a few pages, it is relatively quick to reenter the calculations directly in Maple Flow. Some steps will need to be updated to the equivalent Maple Flow function, and there is also the opportunity to use features that are not available in Mathcad 15 (or its successor Mathcad Prime), such as advanced signal processing tools, thermodynamic data, and functionality for the analysis of linear systems.

For engineering firms with large repositories of legacy Mathcad 15 files, Maplesoft has developed a convenient path to migrate batches of content into Maple Flow. Maplesoft Engineering Services guide customers through the migration process and apply an efficient Migration Assistant to move the equations, variable definitions, units, layout, and other supported features from Mathcad 15 worksheets to Maple Flow. The content is mapped to the equivalent Maple Flow functionality, so that calculations can be run and developed further. This allows project worksheets and templates to be recreated with the least investment in time.

This image shows a calculation section before and after batch migration into Maple Flow format:

Ongoing support from Maplesoft

Maple Flow was first launched in 2021 and was developed to give engineers a single tool that can perform mathematical analysis and present results in a professional-looking format. There is built-in support for natural mathematical notation and tracking units, and the development roadmap continues to follow a user-focused approach, so new usability enhancements are regular and relevant.

The current release of Maple Flow gives engineers a path to avoid losing legacy calculations and designs previously stuck in Mathcad 15 worksheets and reuse the content for ongoing project work.

If you would like assistance from Maplesoft with migrating large repositories of design worksheets, please contact Maplesoft Sales.

[This is a contributed article by Alex Beilby, Technical Marketing Mgr, Maplesoft]

The Lunar New Year is approaching and 2024 is the Year of the Dragon! This inspired me to create a visualization approximating the dragon curve in Maple Learn, using Maple. 

The dragon curve, first described by physicist John Heighway, is a fractal that can be constructed by starting with a single edge and then continually performing the following iteration process:  

Starting at one endpoint of the curve, traverse the curve and build right triangles on alternating sides of each edge on the curve. Then, remove all the original edges to obtain the next iteration. 

This process continues indefinitely, so while we can’t draw the fractal perfectly, we can approximate it using a Lindenmayer system. In fact, Maple can do all the heavy lifting with the tools found in the Fractals package, which includes the LSystem subpackage to build your own Lindenmayer systems. The subpackage also contains different examples of fractals, including the dragon curve. Check out the Maple help pages here: 

Overview of the Fractals Package  

Overview of the Fractals:-LSystem Subpackage 

Using this subpackage, I created a Maple script (link) to generate a Maple Learn document (link) to visualize the earlier iterations of the approximated dragon curve. Here’s what iteration 11 looks like: 

You can also add copies of the dragon curve, displayed at different initial angles, to visualize how they can fit together. Here are four copies of the 13th iteration: 

Mathematics is full of beauty and fractals are no exception. Check out the LSystemExamples subpackage to see many more examples. 

Happy Lunar New Year!