## Two cones: A puzzle and an animation

Maple

Some years ago I taught a calculus course for especially talented students. I made up the following problem as an interesting challenge.

Take a circular disk made of paper. Cut out a sector of some angle α from the disk. Roll each of the resulting two pieces into cones. Let V(α) be the sum of the volumes of the two cones. Find the α that maximizes V(α).

Here is an animated statement of the problem, produced in Maple.

## Maple Learn and Desmos and GeoGebra, Oh My!

by: Maple Learn

The most frequent question I get asked when presenting Maple Learn is: “How is Maple Learn different from Desmos?”  The second most frequent question is: “How is Maple Learn different from GeoGebra?”. And they are great questions! Why invest time in learning and introducing students to something new if it works and behaves exactly like something you already use? I certainly wouldn’t bother, and I can’t imagine that anyone else would either. So, in this post, I will do my best to articulate the differences as succinctly as possible, and we’ll be happy to arrange a demo for anyone who is interested in learning more.  Are you ready for another top 3 list!?

Disclaimer: Before we dive in, I’d like to start by saying that Desmos and GeoGebra are great tools. This post is not intended to disparage them. Rather my goal is to highlight the things that make Maple Learn unique.

So without further ado:

1. Maple Learn is the equivalent to doing math on paper, just better!

Maple Learn is akin to a digital math notebook. The canvas gives students the same feeling as solving a math problem on paper – the ability to work through a problem line by line, with explanations, notes, and additional calculations wherever they want them on the page – only with extras. Students can also use Maple Learn to perform tedious intermediate steps, see a graph to get a better sense of the problem, vary parameters to explore the effect on graphs and results, do a quick side calculation to double-check an individual step, and verify the final result.

2. Maple Learn takes a more holistic approach to learning

Where other tools focus predominately on visualization and getting the final answer, the Maple Learn environment supports much more of the teaching and learning experience.  Students can articulate their thought processes and mathematical reasoning using a combination of text, math, plots and images that can be placed anywhere on the canvas. Teachers can devise lessons in Maple Learn that focus not just on solving problems, but on developing skills in mathematical thinking, communication, and all the competencies and standards outlined in the curriculum. For example, instead of having your students work through the minutia of solving for x from two equations, you can create a document that focuses on having them set up the problem correctly, and then let them use the content panel to get the solution. Or you can use interactive supports, such as Algebra Tiles, to allow them to explain the concept of Completing the Square. Or give them an equation, and ask them to jot down features of the equation. The questions you can pose and the discussion that arises as a result is what sets Maple Learn apart from the rest. Because ultimately, the study of mathematics and science is about understanding, not the final answer.

3. Maple Learn is about math not commands

Maple Learn is an environment for learning math and math-based subjects, not about learning commands. So how do you perform an operation in Maple Learn? Easy! Maple Learn’s intelligent context-sensitive panel offers students a list of relevant operations to choose from, based on the mathematical equation or expression in question. This feature was first introduced in Maple over two decades ago, and it’s one of the most beloved features of students, teachers, and new Maple users, so of course we included it in Maple Learn. The context panel means that you and your students can focus on learning math not commands.

And here’s a bonus for making it all the way through:

4. You can pull math into Maple Learn really easily using the Maple Calculator

Let’s face it, for now at least, there will always be students who will feel more comfortable doing math on paper. It’s like tomato soup and grilled cheese – some things are meant to go together. So to make the transition from paper to digital easier, students can take a picture of their problem, or even their completed handwritten solution and bring them into Maple Learn instantly. That way, they can have the comfort of paper, AND the advantages of the digital environment. (I’d say something about having their cake and eating it too, but all this talk of food is making me hungry!)

## Hello, Algebra Tiles! Where were you when I was...

by: Maple Learn

One of the things I love most about my job is working and collaborating with math teachers across the globe. Every discussion leads to additional insights into the challenges facing teachers today, and new ideas on how to make Maple and Maple Learn better. And sometimes, I even learn some math I thought I already knew!

A few months ago, I introduced Maple Learn to a friend of mine who teaches high school math in Kingston, Ontario. I showed her how she could use Maple Learn to teach many concepts during our call, including Completing the Square. I walked her through Maple Learn’s free-form canvas and explained how her students could work through a problem line-by-line just as they would in their notebooks. I highlighted the live plot window and showed how her students could graphically verify that their solution was equivalent to the initial expression. And, I demonstrated the power of Maple Learn’s intelligent context panel and how her students could check their answers algebraically. I thought I had done a good job, until she said: “Karishma, that’s not how we teach Completing the Square anymore!”. Huh! I was floored. What I had shown was the way I had learned the concept so many years ago. I was surprised to learn that there was a new way.

My friend then introduced me to Algebra Tiles and how she used it to teach Completing the Square. Once we went through a few examples, I realized that I had never fully appreciated what I was doing when I completed the square. I had memorized a series of steps without really understanding what I was trying to do. The progression of our discussion naturally led to the inevitable question: “Karishma, does Maple Learn include Algebra tiles? Because that would be a game-changer for my students. Currently, we use physical tiles, but with remote learning, we need something digital.” At that time, my answer was ‘not yet’; however, with the introduction of image support last week, I’m happy to announce that Maple Learn can support algebra tiles and other interactive supports.

Here is the Maple Learn document I created on Completing the Square using Algebra Tiles.

Feel free to change the expressions listed in the document and share it with your students. To see algebra tiles in action inside Maple Learn, take a look at the short video that I created.  If you have any suggestions for improving this application, please feel free to let me know.

## Suggestion: improvement of help pages in future...

by: Maple

A simple suggestion...

I would appreciate being able to open multiple help pages simultaneously instead of just one.
This seems to me particularly interesting when you have to browse back and forth between several related items.

## Waterfall Chart

Maple

In the plotting guide I didn't see a waterfall chart so I created a procedure.
If anyone has a more efficent, better or alternate way please feel free to add.

 (1)

## Maple Learn - Now with Images!

by: Maple Learn

Yes, that’s right! You can now add images to your Maple Learn documents! Whether you’re adding a diagram to help visualize a physics concept, inserting the logo or your school or organization, or just adding a cute selfie so that everyone knows how great you looked while making this document, you can add any image you’d like using the image icon on the toolbar. You’ll need to be logged in to access this new feature, but luckily making an account is completely free!

To insert the image, just click the image icon and select the image you want from your computer or tablet. To resize it, highlight the image and click the image icon again. You can also turn the image into a hyperlink by highlight the image and clicking the link button! Now, not only will your document look snazzy, but it can take you anywhere you’d like.

Images aren’t the only exciting new feature in Maple Learn. If you were excited by all the circles in the last set of updates, then you’re going to love this one, because we’ve introduced the Circle command! Just plug in the centre of the circle and the radius, and bam, circle. What’s more, you can easily turn your circle into an arc by adding the angle measures of the two endpoints of the arc. Infinitely customizable round objects, right at your fingertips. To learn more, check out the How-To documents Using the Circle Command and Plotting Arcs.

Ancient Greek mathematicians thought that there was nothing that couldn’t be constructed with only a compass and a straightedge. A wise math professor once tasked my class with using these same tools to draw a pretty picture. With Maple Learn’s Circle function and ability to graph straight lines, you have all the tools you need to complete this same task! We look forward to seeing the results.

## VII National Meeting of Physics Didactics

Maple 2021

Universidad Metropolitana de Ciencias de la Educación
Santiago de Chile

Derivative operator on vectors of real variable (R3): applied to curvilinear motion with Maple and MapleSim

In the present work it will be demonstrated how the derivative operator acts in functions of real variable in the movement of a particle that performs a curvilinear trajectory; using the scientific software of the Maplesoft company known by the names Maple and MapleSim, because nowadays most university teachers (higher education) do not visualize the movement of the particle in real time as well as the results of the calculations of speed and acceleration simultaneously. The objectives achieved are to use the vector operator with the help of these programs. As a theoretical tool we will use the three-dimensional vector spaces of real variable with Newton's notation. The methodology we have used was native syntax and embedded components using block diagrams. For the case of particle motion we use the graphical programming proposed by MapleSim. Viable results were achieved for motivational effects and time reduction in complex calculations without neglecting innovation in physical sciences, for teachers in higher education and university students. This work is self-sustaining via Maple Cloud.

Lenin Araujo Castillo

## Comparing Units

by: Maple

Guys, this is still the most painful thing i Maple for me, and I hope this gets a high priority for future development.

It is still not possible to compare variables, when one of them could become zero.

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 (2)

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 >

## Maple Conference starts tomorrow!

by: Maple Maple Calculator Maple Learn Maple Flow

This is my second try---my previous post about the Maple Conference  https://www.maplesoft.com/mapleconference/2021/ seems to have vanished into thin electrons.

Anyway!  The conference opens tomorrow!  There are many really interesting prerecorded talks, three live plenaries, two excellent panels, and registration is free!  See the above link.

I look forward to "seeing" you tomorrow.

Rob Corless, co-Chair of the Program Committee

on behalf of the organizers

## New Application Center - Beta

by: MaplePrimes

As many of you are aware, the Maple Application Center is a very important resource for Maple users. It is a place for authors to share their Maple work, and for users to have access to a rich collection of over 2,500 curated Maple documents covering a wide array of topics and disciplines.

I am very pleased to announce that we have been hard at work on a new version of the Application Center, and it’s at a state where we’re ready to open it up to the public for testing. You can access the new site here: https://www.maplesoft.com/applications_beta . We are looking for feedback, so please give it a try, and let us know what you think!

Here are a few of my favorite features of the new site:

Updated Look & Feel
The interface of the current version of the Application Center has not changed in many years, and it was time for a new paint job. I think you’ll find that the new site is cleaner, modern, and more enjoyable to use.

Easier to Find the Documents you Want
The updated Application Center provides multiple new ways to find content that is relevant for you. Browse user-made collections of documents or use tags (the same tags used in MaplePrimes) to find documents for the topics you are interested in. Alternatively, you can use the search bar to quickly find documents, tags or authors.

If you are logged-in when using the Application Center, you will be able to customize what you see by pinning your favorite collections, authors or tags to your home page.

Community Moderation & Reputation
As with MaplePrimes, the strength of the Application Center comes from the amazing community of individuals who contribute to it. In addition to submitting your own content to the Application Center, users can now edit tags and create collections of content that others can use. Similar to MaplePrimes, community moderation is restricted to members who have a sufficient reputation score. Speaking of reputation, quality contributions to MaplePrimes will now be reflected in your reputation score. When someone likes one of your submissions, your reputation will increase by 5.

There are many other great new features as well, and we have a roadmap of future updates planned that will make it even better.

I invite you to take a look at the new site and play with it. Browse some content, search, look through tags, and create some collections. Most importantly, I’m really hopeful that you will then use the comments section below to let us know what you think. Did you discover any bugs or issues? What do you like? What do you dislike? What other features would you like to see?

We are hoping to run the Beta for a period of a few weeks, and I’m looking forward to hearing and reading your thoughts. Hope you enjoy it!

https://www.maplesoft.com/applications_beta

Bryon

## MaplePrimes as a source for Maple Transactions

Dear all,

The November issue of Maple Transactions is now up (we will be adding a few more items to that issue over the course of the month).  See https://mapletransactions.org/index.php/maple/index for the articles.

More importantly, Maple Primes seems to have a great many interesting posts, some of which could well be worked up into a paper (or a video).  Maple Transactions accepts worksheets (documents, workbooks) for publication, as well, although we want a high standard of readability for that.  I invite you to contribute.

The next issue of Maple Transactions will be the Special Issue that is the Proceedings of the Maple Conference 2021 (see my previous post :)

-r

## Concerning Chromebooks and Calculations

by: Maple Learn

Do you have a Chromebook?  Are you a student or a teacher looking for the mighty power of Maple, but find yourself limited by your web-only computer? Well, have no fear, because Maple Learn is here!

As a web-based application, Maple Learn is fully supported by Chromebooks. You can create graphs, perform and check calculations, and share documents all within the comfort of your own browser. No need to download any kind of software—just go to learn.maplesoft.com to get started!

Students, if you’re looking for some use for your school-provided Chromebook and wondering how it can help you learn instead of just weighing down your backpack, Maple Learn can help. It’s the perfect, all-inclusive tool to help you learn, visualize, and check your math. And, if you’re looking to brush up on all that math you forgot over the summer, you can check out the Maple Learn Example Gallery, home to hundreds of examples and explanations of a wide variety of math concepts. And it’s all accessible on your Chromebook!

## Excellent book

by: Maple

Hi to all,

Dr. Lopez's "Advanced Engineering Mathematics with Maple" is just excellent... I strongly advise...

That book is my most favorite and Dr. Lopez is my favorite teacher :)

## Check out Engineering Matters Podcast #127 - Tools...

by: Maple Maple Flow

Here's a podcast that covers a few topics that get discussed on MaplePrimes.

We all like finding the right tool for the job. In the Sep 2021 episode of the Engineering Matters Podcast “#127 – Tools for Thinking” you can discover how far engineers have come in their quest for better tools.

It features contributions from several members of the Maplesoft team as they discuss how the user experience shapes the adoption of engineering software tools.

The hosts have fun describing some early calculation hacks - from early Sumerian farmers using their fingers as tally counters, to the paper calculus notebooks of the 1850s used by historical engineering figures like Isambard Kingdom Brunel. What starts as a necessity gets improved over time to save them mental effort – all driven by the way users interact with the tool.

This episode gives a behind-the-scenes look at some of the decisions that shaped the engineering product that is now Maple Flow from its roots in Maple. Maplesoft CEO Laurent Bernardin describes the spark of innovation in the late 1970s, when two professors at the University of Waterloo developed Maple. “The two professors got together, realising that there was a need in math education for a tool to help with calculations and setting out to create that tool. And Maple was born quickly, was adopted across universities around the globe.”

As engineers typically work in ways far removed from the regular academic setting, Product Manager Samir Khan weighs in on the shift that comes from a different user base: “Different tools have different design intents,” says Khan. “Some tools are designed for programmers such as code development environments, like Visual Studio. Some environments are aimed at mathematicians, people who need precise control over the mathematical structure of their equations, and some environments are designed for engineers who simply want to throw down a few equations on a virtual whiteboard and manipulate them and get results.”

The conversation also touches on the design of the GUI itself. Margaret Hinchcliffe, Maple’s Senior GUI Developer expresses the importance of smoothing the user experience - drilling down and taking “the typical tasks that people want to do the most, and make those the most immediate. So really focusing on how many keystrokes do they need to do this task?”.

Ironically the idea of the paper notebook still has features that are desirable. Khan muses on the idea that Maplesoft has “taken the first step with having a virtual whiteboard, but Maple Flow still relies on keyboard and mouse input”. He offers suggestions for what may be next in the industry: “It’d be interesting to see if we can take advantage of modern advances in deep learning and AI to imitate what humans are doing and interpreting handwritten mathematics.”

You can listen to the entire podcast (~30 min) here: https://engineeringmatters.reby.media/2021/09/30/the-evolution-of-tools-for-thinking/

## A Chebyshev Flower

by: Maple

From a tweet by Tamás Görbe : plotting Chebyshev polynomials in polar coordinates leads to some interesting pictures.  Screenshot here, link to the worksheet (and some perhaps interesting puzzles) at the end.

ChebyshevRose.mw

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