Some texts distinguish between unary and binary negation signs, using short dashes for unary negation and a longer dash for binary subtraction. How important is this distinction to users of Maple?

Some earlier versions of Maple used to have short dashes for negation (in some places). Maple 2023 has apparently abandoned the short dash for unary negation, and all such signs are now a long dash.

How about math books? Do all texts make this short-long distinction? The typesetters for my 2001 Advanced Engineering Math book also opted for all long dashes and that book was set from the LaTeX exported from Maple 20+ years ago. But I also have texts in my library that use a short dash for unary negation, on the grounds that -a, the additive inverse of "a" is a complete symbol unto itself, the short dash being part of the symbol for that additive inverse.

Apparently, this issue bugs me. Am I making a tempest in a teapot?

We all know that math is beautiful in and of itself—but sometimes students might need a little convincing. What better way to do that then sprucing up your math with a little colour? With Maple Learn, plot colours are fully customizable. We have several colour palettes to choose from—want your document to evoke the delicate tones of springtime? Looking for a palette that’s colourblind friendly? Or maybe you’re just nostalgic for the colours of Maple V? All these options and more are available for making your graphs colourful and coordinated. But maybe you’re the kind of person who wants to go against the grain, and you laugh in the face of predetermined colour coordination. Don’t worry, we’ve got you covered too! With our colour selector, you can also choose your own custom colours. The full colour spectrum is right at your fingertips. To learn more about how to customize the colours on your document, check out this How-To guide.

And of course, the potential for colour inevitably leads to the potential for art. Our Maple Learn Art Gallery has plenty of fun and colourful works you can admire and contemplate (and maybe even draw inspiration from!). One of our most recent and most colourful additions is this document showcasing the history of the rainbow pride flag, in honour of June being Pride Month. You can use the slider to move through time, letting you see how the colours on the flag evolved and read about the meanings behind them. And, thanks to the colour selector, the colours match the precise shades used for the original flags! That’s the magic of hexadecimal colours for you.

Hold on—the magic of hexadecimal colours, I hear you ask? What an enticing concept. If only we had some kind of document, perhaps one made in Maple Learn, that explained how hexadecimal colours worked and included an interactive example so that you could easily see how the red, green, and blue colour values blend together to create any given colour… Too bad we don’t!

Just kidding. Of course we do.

If all these colours have inspired you, be sure to check out our Call for Creative Works for the upcoming Maple Conference! Maybe your colourful creation could be this year’s winner.

If you've seen Paulina's announcement then you know that we are once again holding a virtual Maple Conference this year.  As well, we are once again going to have a virtual gallery featuring artwork and creative projects submitted by the Maple community!

Last year we had a number of great submissions to our Maple Art Gallery and our Maple Learn Creative Showcase.  These were our excellent prize winners.

From left to right we have A visualization of all the primitive roots of 10037 created by Simon Plouffe, winner of the Judge’s Choice, Mother’s Day Rose created with Maple plots by Greg Wheaton, winner of the People’s Choice, and Mona Lisa in Maple Learn created by Paul DeMarco (with help from Leonardo DaVinci), the winner of the People’s Choice for the Maple Learn Showcase.

This year we are expanding the Gallery into two collections to encourage more people to submit.  They are

• The Art Gallery - A small gallery to highlight high effort, mathematically interesting works (with stricter criteria)

• The Creative Works Showcase - A larger showcase for nearly any interesting visual works created with Maplesoft products like Maple Learn and Maple

Feel free to submit nearly anything cool for the Creative Works Showcase, if we find it particularly impressive we might even ask you to let us consider it for the gallery.  Also, do not be intimidated by the title "Art Gallery" we're looking for anything that has taken some artistic effort and tells a mathematical story.

For more information on critera and how to submit, please visit our Call for Creative Works.  The important deadline to know is the September 14th deadline for submission of works with virtual gallery reception and awards ceremony durring the conference October 26-27.

I look forward to seeing all the submissions for the Maple community again this year!

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. 

Next, find the side lengths of the large triangle (A and B) by evaluating an infinite sum (composed of the hypotenuse lengths of the small congruent triangles). Finally, apply the law of sines to the isosceles triangle made from the first 2 congruent triangles. After simplifying this expression, the Pythagorean relationship (c² = a² + b²) emerges.
 

To see more details of the proof, check out Johnson and Jackson’s Proof of Pythagorean Theorem on Maple Learn.
This new proof of the Pythagorean Theorem shows that discoveries in math are still happening and that young people can play a big role in these discoveries!

The most recent shift in education has seen countries adopting a more student-centered approach to learning. This approach involves enabling students to make sense of new knowledge by building on their existing knowledge. Many countries have embraced this approach in their educational systems. Teachers are no longer the sage on the stage, and gone are lectures and one-way learning. This new era of learning lends itself to the social constructivist framework of teaching and learning. 

Social Constructivism. Students adopt new knowledge through interacting with others to share past experiences and make sense of the learned concepts together. Perhaps the most well-known applications of social constructivist classrooms are Thinking Classrooms popularized by Peter Liljedahl in 2021 (the same age as Maple Learn!). In a Thinking Classroom, groups of students collaborate to discuss potential solutions to solve open-ended problems. Ideas are recorded on vertical surfaces so that all students, including those from different groups, have access to one another’s ideas. The teacher is hands-off in this type of classroom, with students asking each other questions if stuck or unsure. This approach facilitates the exchange of ideas and encourages collaboration among students. Sadly, this innovative idea was brought into the classroom at a peculiar time, at the height of the pandemic when less socialization was happening. 

Nevertheless, teachers were intrigued by this idea, and like any good idea, it spread like wildfire. For the first time, many teachers have reported that they observed their students engage in active thinking, rather than just mechanically plugging and chugging numbers into formulae, as was traditionally done in math education. This shift in approach has led to a deeper understanding of mathematical concepts and improved problem-solving skills among students. At the same time, students were more uncomfortable than ever before because they were not accustomed to the feeling of “not knowing.” The strongest students were often the most uncomfortable as they were conditioned to view mathematics as having only one correct answer. This discomfort is a natural part of the learning process, as it indicates that students are grappling with the new concepts and expanding their understanding. This new approach, which emphasized exploration and problem-solving over rote memorization, challenged their existing beliefs and required them to think in new ways. Over time, as they become more familiar with this approach, students develop greater confidence in their mathematical skills and improve their abilities to think critically and creatively.

Social Constructivism in Maple Learn. As a secondary math teacher, I’ve been using Maple Learn to support my students’ learning. I’ve mainly created projects and collections of financial literacy documents that are not only informative but also exploratory for students to engage with at their own pace. Here is where I see the potential of Maple Learn - not only to support teachers in the classroom but also to act in place of the teacher for asynchronous class work by being the guide on the side. 

The project-based ideas such as “Designing a roller coaster or slide,” “Exploring the rule of 72,” and open-ended questions such as “Designing a cake” and “Moving sofa” can lend themselves to creative discussions using mathematics. This is because Maple Learn offers its users the chance to visualize dynamic representations. Users can relate the algebraic, graphical, text-based, and/or geometrical representations of the same math concept. The convenience of having everything on one page encourages students to take away what they deem are the most important pieces of information as opposed to the teacher telling them what the major takeaways are. Due to their diverse backgrounds and unique mathematical identities, different students tend to focus on different aspects of a given concept. However, it is precisely these differences that can lead to a deeper understanding of the topic at hand. By sharing their perspectives and insights with one another, students can gain a more complete and nuanced understanding of mathematical concepts, and develop a broader range of problem-solving strategies. 

Source: Double angle identity. Illustration provides geometrical and algebraic representations side by side.  

In addition, the different functions that Maple Learn offers, allow students with varying mathematical backgrounds to have an equitable chance at learning. Some students may be better at manipulating equations, while others might be more visual. Maple Learn provides students with a blank canvas to explore mathematical concepts on their own, without the stress of mental calculations, the need to access different functions on a calculator, or the necessity to search for explanatory videos online. Maple Learn can also have embedded hyperlinks which can be important concepts or documents. These links can provide an easier learning platform for students to construct their own knowledge. An example can be found here. By removing these barriers, students are free to delve into the material and develop a deeper understanding of the underlying principles. This approach can further foster creativity, curiosity, and a passion for learning among students, while also equipping them with the tools they need to succeed in their future academic pursuits. 

Arguably the most difficult aspect of social constructivism to implement using Maple Learn is the “social” aspect of it all which requires a bit of creativity. The goal is not to eliminate the use of teachers, but rather have teachers present the material in a different light. The teacher still decides what students learn in the classroom (or maybe that’s already decided by  the government agency) but how they learn the material is up to the teacher. After interacting with Maple Learn and coming up with interesting solutions, students can trade their responses with their peers to evaluate one another’s responses, approaches, ideas, and solutions to a problem. Students definitely learn more from each other and I believe as teachers, we should capitalize on this aspect. With many jurisdictions around the world adopting a student-centered approach to learning, it is time we advance our teaching styles. Even with the recent advances in AI, we still need to teach our kids how to think, and to think deeply. Tech can definitely help in this regard. 

In summary, by emphasizing collaboration, critical thinking, and exploration, social constructivism encourages students to build their understanding of new concepts through interaction with others. Often seen as Thinking Classrooms, Maple Learn can supplement social constructivist classrooms by offering a blank canvas for students to explore mathematical concepts on their own, free from the limitations of traditional calculations and rote memorization. Together, these approaches can empower students to become active learners and critical thinkers, setting them on a path towards success in the classroom and beyond. Here are some “How-To” videos to help you get started with creating your own documents in Maple Learn. You can also browse the example gallery with thousands of existing examples here. Happy creating!

A geometric transformation is a way of manipulating the size, position, or orientation of a geometric object. For example, a triangle can be transformed by a 180^o rotation: 

Learning about geometric transformations is a great way for students, teachers and anyone interested in math to get comfortable using x-y coordinates in the cartesian plane, and mapping functions from R² to R². Understanding geometric transformations is also an essential step to understanding higher-level concepts like the Transformations of Functions and Transformation Matrices.
Check out the Geometric Transformations collection on Maple Learn to learn about this topic. Start out by playing with the Geometric Transformations Exploration document to build intuition about how objects are affected by each of the four transformation types: Dilation, Reflection, Rotation, and Translation. Once you are confident in your skills, try using the Single Geometric Transformation Quiz to test your knowledge.
For those looking to expand their understanding of geometric transformations, the Combined Transformations Exploration document will let you explore how multiple transformations and the order of said transformations affect the final form of an object. For example, the blue polygon can be transformed into 2 different pink polygons depending on whether the reflection or rotation is performed first:

Once you have the hang of combined transformations, try answering questions on the Combined Geometric Transformations Quiz. 

How Can Maple Learn Help Address Math Anxiety in Classrooms?

Math anxiety is referred to as negative behaviours such as uneasiness and general avoidance when asked to solve math problems. For teachers and teacher candidates, this can be due to various reasons such as previous negative experiences in math classes, learning styles that conflict with their math teacher, lack of self-confidence, low self-esteem, and stereotype issues related to the belief that math is for men only. Although it is commonly believed that math anxiety only exists in students, research has shown that math anxiety is present among elementary teacher candidates and elementary teachers, particularly women. Furthermore, research has shown that female teachers who suffer from math anxiety have a tendency to pass down their math anxious behaviours to students, particularly affecting more girls than boys. Since the majority of the elementary teaching staff are women, it is possible that a cyclic pattern will arise where teachers will pass down math anxiety to students, and these students will grow up dealing with math anxiety.

As a current PhD candidate, I have taught elementary teacher candidates basic math knowledge. It was clear to me from the first day, math anxiety was very present within the students I had. Many of these teacher candidates had candidly revealed that they have not taken any math classes since Grade 11, which is the final grade in Ontario where math is mandatory. With Maple Learn, because manyof the documents are created by educators, these documents can function as learning materials which a teacher can use for extra practice and guidance. 

One strategy to combat math anxiety in general is developing greater self-efficacy and confidence in their math skills. For example, using the Converting and Decimals to Fractions document, teachers and teacher candidates can use this as a tool to support their understanding and can help double-check their work. Unlike students, when learning about math concepts and skills in class, in addition to using online resources they also can ask teachers for help. Whereas for adult learning, it is possible that some may feel shy or embarrassed to seek help from others. On Maple Learn, there are multiple quizzes where a teacher can use as practice to further their understanding. In addition to the solution, these features also provide hints and a “check your work” button so that it can guide the teacher in solving such problems if stuck on a question. One of the cool features of these solutions is that they don’t just reveal the answer, but also include steps to solve the question whenever a teacher gets stuck.

Furthermore, additional visualizations could be a useful tool for visual learners and serve as another method to understand and solve such math problems rather than solely relying on algebra. 

The documents provided in the example gallery provide multiple different methods on understanding and solving math problems. For example, when multiplying fractions, one can either simplify before multiplying the fractions together or they can first multiply the fractions, then simplify.

The more practice one does, the better they become at solving math problems, and if interested, Maple Learn has many quizzes that one can use to improve their math skills. For more fractions documents, check out this page here!

Happy Springtime to all in the MaplePrimes Community! Though some in our community may not live in the northern hemisphere where flowers are beginning to bloom, many will be celebrating April holidays like Ramadan, Passover, and Easter.

One of my favorite springtime activities is decorating eggs. Today, the practice is typically associated with the Christian holiday of Easter. However, painted eggs have roots in many cultures.

For over 3,000 years, painting eggs has been a custom associated with the holiday of Nowruz, or Persian New Year, during the spring equinox. Furthermore, in the Bronze Age, decorated ostrich eggs were traded as luxury items across the Mediterranean and Northern Africa. Dipped eggs have also played an important role in the Jewish holiday of Passover since the 16th century.

To celebrate this tradition, I would like to invite all of the Maplesoft community to create a decorated egg of their own with the Easter Egg Art Maple Learn document. In this document, an ovoid egg equation is used to define the shape of an egg. 

The ovoid egg equation mimics the shape of a typical hen’s egg. Each bird species lays differently shaped eggs. For example, an ostrich’s egg is more oblong than an owl’s, and an owl’s egg is rounder than a goose’s. Surprisingly, every egg can be described by a single equation with four parameters:

Learn more about this equation and others like it with John May’s Egg Formulas Maple Learn document.

The Easter Egg Art document includes 9 different decorative elements; users can change the color, position, and size of each in order to create their own personal egg! The egg starts out looking like this:



In just a couple of minutes, you can create a unique egg. Have fun exploring this document and share a screenshot of your egg in the comments below!  Here’s one I made:

Several studies, such as “Seeing and feeling volumes: The influence of shape on volume perception”, have shown that people have a tendency to overestimate the volume of common objects, such as glasses and containers, that are tall and thin and underestimate those that are short and wide; this phenomenon is called “elongation bias”. 

Sue Palmberg, an instructor at Edwin O. Smith High School, created and shared with us a lab activity for students to design a glass in Maple and use volumes of revolution to determine the amount of liquid it can hold. This lab was then turned into this Maple Learn document: Piecewise Volumes of Revolution Activity.

Use this document to create your own glass or goblet shape and determine its volume. Simply create a piecewise function that will define the outside shape of your glass between your chosen bounds and another piecewise function to define the hollowed-out part of your creation. The document will graph the volumes of revolution that represent your glass and calculate the relevant volume integral for you.

Here is my own goblet-shaped creation: 

I used this piecewise function to define it:

After creating the outline of my goblet, I constructed a function for the hollow part of the goblet – the part that can actually hold liquid.

Using Context Panel operations and the volume integral provided by the document, I know that the volume of the hollow part of my goblet is approximately 63.5, so my goblet would hold around 63.5 units³ of liquid when full.

Create your own goblets of varying shapes and see if their volumes surprise you; elongation bias can be tricky! For some extra help, check out the Piecewise Functions and Plots and Solids of Revolution - Volume Derivation documents!