We are happy to announce another Maple Conference this year, to be held October 26 and 27, 2023!

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 work you've been doing with Maple and Maple Learn. There are two ways to do this.

First, 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 11, 2023.

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

The second way in which to share your work is through our Maple Art Gallery and Creative Works Showcase. Details on how to submit your work, due September 14, 2023, are given on the Web page.

Registration for attending the conference will open later this month. 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 attendee!

Paulina Chin
Contributed Program Chair

Happy Pride Month, everyone! June is a month for recognizing and celebrating the LGBT+ community. It was started to mark the anniversary of the Stonewall riots, which were a landmark event in the fight for LGBT+ rights. We celebrate Pride Month to honour those who have fought for their rights, acknowledge the struggles the LGBT+ community continues to face to this day, and celebrate LGBT+ identities and culture.

This Pride Month, I want to give a special shoutout to those in the math community who also identify as LGBT+. As a member of the LGBT+ community myself, I’ve noticed a fair amount of stigma against being queer in math spaces—and surprisingly often coming from within the community itself. It’s one thing for us to make jokes amongst ourselves about how none of us can sit in chairs properly (I don’t even want to describe how I’m sitting as I write this), but the similar jokes I’ve heard my LGBT+ friends making about being bad at math are a lot more harmful than they might realize. And of course it isn’t just coming from within the community—many people have a notion (whether conscious or unconscious) that all LGBT+ people are artistically inclined, not mathematical or scientific. Obviously, that’s just not true! So I want to spend some time celebrating queerness in mathematics, and I invite you to do the same.

One of the ways we’re celebrating queerness in math here at Maplesoft is with new Pride-themed Maple Learn documents, created by Miles Simmons. What better way to celebrate Pride than with trigonometry? This document uses sinusoidal transformations to mimic a pride flag waving in the wind. You can adjust the phase shift, vertical shift, horizontal stretch, and vertical stretch to see how that affects the shape of the flag. Then, you can watch the animation bring the flag to life! It’s a great way to learn about and visualize the different ways sinusoidal waves can be transformed, all while letting your colours fly!

For more trigonometry, you can also check out this fun paint-by-numbers that can help you practice the sines, cosines, and tangents of special angles. And, as you complete the exercise, you can watch the Pride-themed image come to life! Nothing like adding a little colour to your math practice to make it more engaging.

If you’re looking for more you can do to support LGBT+ mathematicians this Pride Month, take a look at Spectra, an association for LGBT+ mathematicians. Their website includes an “Outlist” of openly LGBT+ mathematicians around the world, and contact information if you want to learn more about their experiences. The Fields Institute has also hosted LGBT+Math Days in the past, which showcases the research of LGBT+ mathematicians and their experiences of being queer in the math community. Blog posts like this one by Anthony Bonato, a math professor at Toronto Metropolitan University, and interviews like this one with Autumn Kent, a math professor at the University of Wisconsin-Madison, can also help allies in mathematics to understand the experiences of their queer colleagues and how to best support them. Math is everywhere and for everyone—so let’s make sure that the systems we use to teach and explore math are for everyone too!

Happy Pride! 🏳️‍🌈

We've just launched Maple Flow 2023!

The new release offers many enhancements that help you calculate and write reports faster, resulting in polished technical documents. Let me describe a few of my favorite new features below.

You can now change the units of results inline in the canvas, without taking your hands off the keyboard. You can still use the Context Panel, but the new method is faster and enhances the fluid workflow that Flow exemplifies.

You can also enter a partial unit inline; Flow will automatically insert more units to dimensionally balance the system.

This is useful when results are returned in base dimensions (like time, length and mass) but you want to rescale to higher-level derived units. For an energy analysis, for example, you might guess that the result should contain units of Joules, plus some other units, but you don't know what those other units are; now, you can request that the result contains Joules, and Flow fills the rest in automatically.

The new Variables Palette lists all the user-defined variables and functions known to Flow at the point of the cursor. If you move your grid cursor up or down, the variables palette intelligently removes or adds entries.

You can now import an image by simply dragging it from a file explorer into the canvas.

This is one of those small quality-of-life enhancement that makes Flow a pleasure to use.

You can now quickly align containers to create ordered, uncluttered groups.

We've packed a lot more into the new release - head on over here for a complete rundown. And if you're tempted, you can get a trial here.

We have a lot more in the pipeline - the next 12 months will be very exciting. Let me know what you think!

On this day 181 years ago, Christian Doppler first presented the effect that would later become known as the Doppler effect. In his paper “On the coloured light of the binary stars and some other stars of the heavens”, he proposed (with a great deal of confidence and remarkably little evidence) that the observed frequency of a wave changes if either the source or observer is moving. Luckily for Doppler, he did turn out to be right! Or at least, right about the effect, not right about supernovas actually being binary stars that are moving really fast. The effect was experimentally confirmed a few years later, and it’s now used in a whole variety of interesting applications.

To learn more about how the Doppler effect works, take a look at this Maple MathApp. You can adjust the speed of the jet to see how the frequency of the sound changes, and add an observer to see what they perceive the sound as. You can even break the sound barrier, although the poor observer might not like that so much!

For Maple users, you can also check out the MathApp on the relativistic Doppler effect. You’ll find it in the Natural Sciences section, under Astronomy and Earth Sciences. Settle in to watch those colours come to life!

But wait, I mentioned interesting applications, didn’t I? And don’t worry, I’m not just here to talk about sirens moving past you or figuring out the speed of stars (although admittedly, that one is pretty interesting too). No, I’m talking about robots. Some robots make use of the Doppler effect to help monitor their own speed, by bouncing sound waves off the floor and measuring the frequency of the reflected wave. A large change in frequency means that robot is zooming!

The Doppler effect is also used in the medical field—Doppler ultrasonography uses the Doppler effect to determine and visualize the movement of tissues and body fluids like blood. It works by bouncing sound waves off of moving objects (like red blood cells) and measuring the result. The difference in frequency tells you the speed and direction of the blood flow, in accordance with the Doppler effect! Pretty neat, if you ask me.

And like any good scientific phenomena, the Doppler effect can be used for both work and pleasure. The Leslie speaker is a type of speaker invented in the 1940s that modifies the sound by rotating a baffle chamber, or drum, in front of the loudspeakers. The change in frequency dictated by the Doppler effect causes the pitch to fluctuate, creating a distinct sound that I can only describe as “woobly”. The speaker can be set to either “chorus” or “tremolo”, depending on how much woobliness the user wants. It was typically used with the Hammond organ, and you can hear it in action here!

You know who else uses the Doppler effect? Bats. Since they rely on echolocation to get around, they need some way to account for the fact that the returning sound waves won’t be at the same pitch that they were sent out at. This fantastic video explains it far better than I ever could, and involves putting bats on a swing, which I think should be enough of a recommendation all on its own.

That’s it for our little foray into the Doppler effect, although there’s still a lot more that could be said about it. Try checking out those Maple MathApps for inspiration—who knows, maybe you’ll find a whole new use for this fascinating effect!

Probability distributions can be used to predict many things in life: how likely you are to wait more than 15 minutes at a bus stop, the probability that a certain number of credit card transactions are fraudulent, how likely it is for your favorite sports team to win at least three games in a row, and many more. 

Different situations call for different probability distributions. For instance, probability distributions can be divided into two main categories – those defined by discrete random variables and those defined by continuous random variables. Discrete probability distributions describe random variables that can only take on countable numbers of values, while continuous probability distributions are for random variables that take values from continuums, such as the real number line.

Maple Learn’s Probability Distributions section provides introductions, examples, and simulations for a variety of discrete and continuous probability distributions and how they can be used in real life. 

One of the distributions highlighted in Maple Learn’s Example Gallery is the binomial distribution. The binomial distribution is a discrete probability distribution that models the number of n Bernoulli trials that will end in a success.

This distribution is used in many real-life scenarios, including the fraudulent credit card transactions scenario mentioned earlier. All the information needed to apply this distribution is the number of trials, n, and the probability of success, p. A common usage of the binomial distribution is to find the probability that, for a recently produced batch of products, the number that are defective crosses a certain threshold; if the probability of having too many defective products is high enough, a company may decide to test each product individually rather than spot-checking, or they may decide to toss the entire batch altogether.

An interesting feature of the binomial distribution is that it can be approximated using a different type of distribution. If the number of trials, n, is large enough and the probability of success, p, is small enough, a Poisson Approximation to the Binomial Distribution can be applied to avoid potentially complex calculations. 

To see some binomial distribution calculations in action and how accurate the probabilities supplied by the distribution are, try out the Binomial Distribution Simulation document and see how the Law of Large Numbers relates to your results. 

You can also try your hand at some Binomial Distribution Example Problems to see some realistic examples and calculations.

Visit the Binomial Distribution: Overview document for a more in-depth explanation of the distribution. The aforementioned Probability Distributions section also contains overviews for the geometric distribution, Poisson distribution, exponential distribution, and several others you may find interesting!

2-dimensional motion and displacement are some of the first topics that high school students learn in their physics class. In my physics classes, I loved solving 2-dimensional displacement problems because they require the use of so many different math concepts: trigonometry, coordinate conversions, and vector operations are all necessary to solve these problems. Though displacement problems can seem complicated, they are easy to visualize.
For example, below is a visualization of the displacement of someone who walked 10m in the direction 30^o North of East, then walked 15m in the direction 45^o South of East:

From just looking at the diagram, most people could identify that the final position is some angle Southeast of the initial position and perhaps estimate the distance between these two positions. However, finding an exact solution requires various computations, which are all outlined in the Directional Displacement Example Problem document on Maple Learn.

Solving a problem like this is a great way to practice solving triangles, adding vectors, computing vector norms, and converting points to and from polar form. If you want to practice these math skills, try out Maple Learn’s Directional Displacement Quiz; this document randomly generates displacement questions for you to solve. Have fun practicing!

In March of 2023, two high school students, Calcea Johnson, and Ne’Kiya Jackson, presented a new proof of the Pythagorean Theorem at the American Mathematical Society’s Annual Spring Southeastern Sectional Meeting. These two young women are challenging the conventions of math as we know it.
The Pythagorean Theorem states that in a right angle triangle, the sum of the squares of the legs is equal to the square of the hypotenuse: 

The theorem has been around for over two thousand years and has been proven hundreds of times with many different methods. So what makes the Johnson-Jackson proof special? The proof is one of the first to use trigonometry.
For years, mathematicians have been convinced that a trigonometric proof of the Pythagorean Theorem is impossible because much of trigonometry is based upon the Pythagorean Theorem itself (an example of circular reasoning).
That said, some results in trigonometry are independent of the Pythagorean Theorem, namely the law of sines, and the sine and cosine ratios; the latter is a result that 12-year-old Einstein used in his trigonometric proof of the theorem.
Though all the details of the Johnson-Jackson proof have not been made public, there was enough information for me to recreate the proof in Maple Learn. The idea of the proof is to construct a right angle triangle with an infinite series of congruent right angle triangles (the first of which has side lengths a, b, and c). Then, using the sine ratio, solve for the hypotenuse lengths of each small congruent triangle. To explore this construction see Johnson and Jackson’s Triangle Construction on Maple Learn.