Have you ever heard of the Maurer Rose?

The Maurer Rose was demonstrated in 1987 by Peter Maurer and is created by connecting certain points on a rose curve. This creates petal-like patterns, caused by the oscillation of a sine curve.

So, how are these created? A "rose curve" is created in polar coordinates with the equation sin(nt) for a (positive integer) value of n.  To create the Maurer Rose, straight line segments are drawn connecting points on the curve at incrementing angle values.  The size of this increment (called d in our examples) leads to different patterns of lines across the curve.

This can be done in Maple Learn! One example of the Maurer Rose already exists, complete with a full interactive visualization and a more detailed overview of the Maurer Rose.

Play around with it and look below at some of the different shapes that can be created using this document! The first is created with an n value of 31 and a d value of 65, with blue and red. The second uses an n value of 4 and a d value of 133, and purple and green.

Are there any other concepts you’d like to see represented in Maple Learn’s document gallery? Please let us know in the comments below!

An example of uniform motion along a generalized coordinate using the Draghilev method. (This post was inspired by school example in one of the forums.)
The equations used in the program are very simple and, I think, do not require any special comments. DM is a procedure that implements the Draghilev method with "partial parameterization".
DM_V.mw

When K = 1, parameterization is carried out by changing the angle of rotation of the wheel. That is, uniform rolling is carried out.

For K = 4, the coordinate corresponding to the position of the slider is parametrized.

When K = 6, the slider moves with acceleration, according to a given equation. Hence, we have carried out the parameterization with respect to “time”.

With the help of such techniques, we can obtain the calculation of the kinematics of both lever mechanisms and various types of manipulators.

Have you heard of Maple Scripting before? Do you want to extend your Maple Learn documents with your Maple knowledge? Scripting is the process of using Maple to create Maple Learn documents. If you’re already used to Maple, this may be a piece of cake for you, but we wanted to start from the basics for anyone who wants to extend their Maple Learn and Maple knowledge. This process can be used for many different types of documents, from quizzes to intensive 3D visualizations.

So, let’s get started! All Maple Learn document scripting needs the DocumentTools:-Canvas package. The canvas, as you know, is that white space in a Maple Learn document. Therefore, this package is the core content of a scripted document! Always put:

with(DocumentTools:-Canvas):

At the top of your code, or put

uses DocumentTools:-Canvas:

At the start of your procedures.

Now that we’ve told Maple to use the DocumentTools:-Canvas, we need to create a canvas.

Canvases are created as variables, using the command NewCanvas. Inside NewCanvas, you will add a square-bracket list of all the content you want to see inside. For now, just know that you can add text cells with Text(“YOUR TEXT”) and a math cell with Math(YOUR MATH). On the next line, make sure to put either ShareCanvas(YOUR CANVAS VARIABLE) or ShowCanvas(YOUR CANVAS VARIABLE).  ShareCanvas creates a Maple Learn sharelink, while ShowCanvas shows the canvas directly in Maple. Note that ShowCanvas does not have every Maple Learn feature, but makes quick work of fast error checking.

canvas := NewCanvas([Text(“My first canvas”), Math(3*x+2*y)]):

ShareCanvas(canvas);

There are two more things I want to show you in this post: How to make a group have multiple cells (instead of just the one), and how to position your items on the canvas. Let’s start with group making.

To create a group with multiple cells, use the Group() command within the NewCanvas command, and separate the cells with commas, in a list. You don’t need to specify Text() or Math() when using Group().

canvas := NewCanvas([Group([“This is the first cell…”, “The second….”, “and the third.”])]):

At the end of any command/canvas element, within the brackets, you can define position=[x,y] to specify where on the canvas the object should go. You can adjust the precision pixel by pixel until you are happy with the layout.

When we put all these together, we get code that looks like this:

with(DocumentTools:-Canvas):

canvas := NewCanvas([

Group(["This is the first cell…", "The second…", "and the third."], position=[200,200]),

Math(3*x+2, position=[100,100]),

Text("This is text!", position=[400,400])]):

ShareCanvas(canvas);

And in the end, your scripted document looks like this.

We hope this helps you get started with Maple Scripting. There will be another post on even more of what we can do with Maple Scripting, and how we can make these documents even more interactive. Let us know if there’s anything specific you want to see in that post!

We've just released Maple Flow 2022.2. The update enhances the user experience in many areas, including user interaction, performance, and the interface.

Performance is a signficant focus.

• Maple Flow prioritizes the evaluation of the math you see on screen, giving you faster calculation updates for the part of the worksheet you’re working on, with more math being evaluated as you scroll down.
• We also have more users developing larger documents. Adding white space to large documents, and interacting with sections is now more response and snappier.

In response to many user requests for faster interaction, a new optional evaluation method lets you simply hit equals to evaluate math and display results.

We've also refreshed the in-product Application Gallery with a new look and many new applications (this includes a library of section properties).

You can also optionally restrict printing to the left-most column of pages, allowing you to have off-screen supporting calculations not displayed in the final report.

You'll find a complete list of enhhacements here, and you can download the update here.

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

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

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

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

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

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

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

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

Image: Andrea Greengard/Mindful Living Network

Eggs:

Image: Andrea Greengard/Mindful Living Network

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

Image: Andrea Greengard/Mindful Living Network

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

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

Image: Maplesoft

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

Download Vectorial_ODEs_and_integration_constants.mw

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft

It seems to me that Draghilev's method can be applied quite successfully to the solution of Diophantine equations. Here is a simple example where we find two solutions at the intersection line of two ellipsoids:
  x1^2-x1*x2+x2^2+x2*x3+x3^2-961=0;
  (x1-3)^2+10*x2^2+x3^2-900=0;
Solutions: (11, -4, -26) and (10, 1, 29).
 

Based on the text of the program, it is possible to solve various examples with Diophantine equations.
3d_1.mw

Explanations.
f3 is an auxiliary equation for finding the starting point, NPar is a procedure that implements the Draghilev method, the red color of the text is the place where the integer values of the points on the integral curve are filtered.

 Can be compared with the solution of the isolve function
 

 restart:
  f1 := x1^2-x1*x2+x2^2+x2*x3+x3^2-961;
  f2 := (x1-3)^2+10*x2^2+x3^2-900;
  isolve({f1, f2})

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

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

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

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

Algebra: Double Vertical Asymptote Slider Graph

Graph Theory: Dijkstra’s Algorithm for Shortest Paths

Economics: Increase in Demand in a Market

Chemistry: Combined Gas Law Examples

Biology: Dihybrid Cross Punnett Squares

Physics: Displacement, Velocity, and Acceleration

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

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

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

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

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

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

Have you heard the news yet? Maple Learn has had a major update! You may be wondering what this means, and what all the shiny new features are. Let’s go through them together.

First, as with many updates, we’ve improved performance with Maple Learn. Longer documents will load and perform faster, requiring less computing power for operations, and as a result your browser will be more responsive. Performance on Chromebooks is also improved.

Operations that previously would have needed to be refreshed now automatically calculate. Up until now, if you performed a menu operation on an expression and then changed the value of the expression, the result would turn orange to warn you that the result was no longer valid. You would then have to refresh manually. Now, this is no longer the case, the orange refresh button has been removed from Maple Learn, and results are never out of date.

The plot window, inline plots, and the context panel are all resizable now. This means that, for example, if you’re presenting using Maple Learn, you can enlarge the plot window to be the focus of the presentation, and shrink the context panel out of the way. Take a look at the difference, with our animation of it in action!

Sliders are also more flexible now! Bounds for sliders can be expressed in terms of variables or symbols like π. As well, you can now animate sliders, animating the graph. This allows for more interactivity in documents. See the old view on the left, and the new view on the right! Make sure to take a look at an example of the animated slider below the views as well. 

You can also now snap groups to a grid, allow them to automatically adjust their position as other groups adjust. This ensures better alignment of groups. It also allows you to easily rearrange elements of your documents.

Next, Maple Learn could handle 3D plots before, but now Maple Learn supports 3D parametric plots!

Finally, Maple Learn now has printing! This means you can print out your Maple Learn documents, with two options: to print just the canvas, or to print just the plot. This was requested by many users.

Multiple selection is also possible, allowing you to select multiple cells in a group by holding down the Ctrl/Command key while clicking and dragging.

That’s all for the updates in this version, but keep an eye out for our other updates! For more details, please take a look at our What’s New In Maple Learn page. We hope you enjoy our new features, and let us know if there are any more features you’d like to see in Maple Learn below.

 This interactive electronic textbook, in the form of Maple worksheets, is released in its sixth edition, 2021 August.  This book has two major divisions, mathematics for chemistry -- the mathematics that any instructor of a course in chemistry would wish a student thereof to understand and to be able to implement, and mathematics of chemistry, in the sense of the classic volumes by Margenau and Murphy -- mathematical treatments of particular topics in chemistry from an introductory post-secondary level to a post-graduate level. The content, which includes not only chapters in previous editions that have been revised but also additional chapters on quantum mechanics, molecular spectrometry and advanced chemical kinetics, has been collected during two decades, with many contributions from other authors, acknowledged in particular locations.  Each chapter includes not only explanatory treatments but also illuminating examples and exercises with chemical applications where practicable.

Mathematics for chemistry      0  introduction to Maple commands

                                                 1  numbers, symbols and elementary functions

                                                 2  plotting, geometry, trigonometry and functions

                                                 3  differential calculus

                                                 4  integral calculus

                                                 5  multivariate calculus

                                                 6  linear algebra

                                                 7  differential and integral equations

                                                 8  probability, statistics, regression and optimisation

Mathematics of chemistry       9  chemical equilibrium

                                                10  group theory

                                                11  graph theory

                                                12  quantum mechanics in three parts -- models, atoms and molecules

                                                13  molecular spectrometry

                                                14  Fourier transforms

                                                15  advanced chemical kinetics

                                                16  dielectric and magnetic properties

The content freely available at https://www.maplesoft.com/applications/view.aspx?SID=154267 includes also a published report on teaching mathematics with symbolic software and an interactive periodic chart that yields information about particular chemical elements and their isotopic variants.

            The nature of this electronic interactive textbook makes it applicable with an instructor in a traditional setting, or computer laboratory, for which the material of mathematics for chemistry could be reasonably covered in three or four semesters, but even for self study.  The chapters on quantum mechanics and Fourier transforms are available as separate textbooks in the same format.

Here is the link of my paper.  Great pleasure to hear advice from you. Abel_equation(9).pdf

Mathematical visualizations are beautiful representations of technical phenomena.  From the visual “perfection” of the golden spiral to the pattern generation of fractals, so many works of art can be boiled down to formulas and equations.  Such is the case with N.G. de Bruijn’s medallion and frieze patterns.  Given two starting values, two lines of mathematical formulae produce a recursive sequence of complex numbers.  We can associate these numbers with the four cardinal directions, following the steps on a plot to produce beautiful patterns.  The patterns are of two different types, the closed medallion or repeating frieze, depending on the starting values.

When you need a complex math visualization, Maple is a perfect place to go.  A demonstration of medallion and frieze patterns is available in the Maple Application Center, in which you can vary the starting values and watch the outcome change, along with more detailed background information.  However, there’s an even simpler way to explore this program with the help of Maple Learn.  Maple Learn has the same computational power as Maple, streamlined into an easy-to-use notebook style.  

Maple Learn includes many core features, and anything missing can be ported in through Maple.  This is done using Maple’s DocumentTools:-Canvas package.  The package contains the necessary procedures to convert Maple code into a “canvas”, which can be opened as a Maple Learn sheet.  This makes the whole document look cleaner and allows for easy sharing with friends.

The medallion and frieze document, along with the additional contextual information, is now also available in Maple Learn’s Document Gallery, home to over one thousand example documents covering calculus, geometry, physics, and more.

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

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

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

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

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

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

Download New_arbitrary_constants_and_functions.mw

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft