As AI becomes increasingly relevant in the tech world, Maplesoft has taken steps to integrate AI into our products. We recently launched two new features: Ask AI in Maple Learn and Word Problem Solver in Maple Calculator. 

Ask AI - Maple Learn

As a Math Content Creator at Maplesoft, sometimes I find myself in a creative rut. What documents would be engaging for students? How can I address certain math topics in a fun and interactive way?

I've had the pleasure of creating several collections during my time, including Extreme Value Theorem, Intermediate Value Theorem, and Polynomial Long Division. Nonetheless, each collection took a lot of storyboarding and creativity before I even began drafting them, and I've missed out on creating so many more collections because of this long idea generation process. Having a tool in my back pocket to reignite those creative juices would make it so much easier and faster to create new and exciting Maple Learn documents. 

Luckily, our new Ask AI feature in Maple Learn can help with that! 

Whenever you enter text into a Maple Learn document, a new Context Panel operation called "Ask AI" will pop up. Simply click that button to receive an AI response related to your prompt.

One of my favourite uses of Ask AI is to pick a random subject or phrase and see what the AI responds with. The Ask AI feature is designed to respond with a mathematics-centric answer so it will twist even the least mathematical of concepts into a math problem! The prompt "tacos" resulted in some formulas about sharing tacos with friends, and a prompt of "celebrity gossip" introduced statistical functions to compute the number of celebrity mentions per day. 

I also found that completing part of a tongue twister will result in some funny AI responses!

Here are a couple of my favorites below:

"She sells sea shells..."

Ask AI completes this tongue twister, then offers some formulas to compute the profit of selling S shells!

"How much wood..."

After relating that this tongue twister is not a mathematical problem, Ask AI then builds a simple formula for computing how much wood a woodchuck would (hypothetically) chuck.

There are many more applications of this feature, and I hope you all enjoy exploring them as you create documents on Maple Learn. If you're having trouble inputting text into your documents, or looking for a quick introduction to Maple Learn, check out the Walkthrough Tutorial. Beginner Tutorial (slide 8) addresses adding text to your document. Check out this blog post if you aren't sure how to access the Walkthrough Tutorial. 

Word Problem Solver - Maple Calculator

Maple Calculator now offers support for word problems by leveraging AI. Simply take a picture of your word problem and Maple Calculator will provide a solution generated by AI.

Here is a quick example:

I wrote on paper, “Alice and Bob have 17 apples total. Alice has double the number of apples as Bob plus two. How many apples does Bob have?”. Then I took a picture of this in Maple Calculator, and it gave me a breakdown of the problem using linear equations. See screenshots of my Maple Calculator below.

AI can be an amazing tool, but it can also make mistakes. We ensure that all our tools that incorporate AI clearly indicate its use, so that our users can know when AI is used and choose whether to use it. We're committed to remaining transparent about AI as our journey continues and we are always open to feedback. 

For our community of educators, a valuable exercise for students might be to show examples where AI makes mistakes and encourage students to find and explain the errors.

As an example, here is an algebra problem answered by Ask AI in Maple Learn – but it made a mistake! See if your students can spot where it went wrong and explain what should happen instead.

Building these skills will translate into good critical thinking skills that will benefit students inside and outside the classroom. For example, these exercises aim to help students identify their own mistakes in math and critically evaluate online sources. We would love to hear feedback about these exercises if you try them.

We hope these features will come in handy next time you use Maple Learn and Maple Calculator! 

I’m thrilled to introduce the updated Q&A Cards Creator! Michael Barnett had created the original Flash Cards Creator, inspired by the quiz creators in the Maple Learn gallery. I added some of the features (mentioned later in this post) that will help you use this tool to make more comprehensive quizzes. Students can use the creator to quiz themselves before a test, and instructors can integrate more practice quizzes into their lesson plans. One feature I particularly love is the ability to link full solutions to the back of each card, allowing users to understand the answers in depth (as shown in this document). Additionally, you can link a general solutions package (as seen here) if individual solutions aren’t necessary for each question. Below is an example of what the Q&A cards can look like from the users point of view.
This creator is a great example of the Maple Learn documents you can create through scripting in Maple. With a single script, you can create an infinite amount of content and quizzes. If you are interested in Maple scripting, here is a link to the Q&A cards script. If this script looks intimidating, feel free to check out this blog post on the basics of Maple scripting!


If you are interested in creating your own Q&A quiz, you can go to this document to get started. If you get stuck at any point creating your card set, check out the instructions included in the document for clarification. We hope you enjoy creating some quizzes with this document!

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

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

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

We hope to see you there!

Maple Learn has so much to offer, but it can be tricky to know where to start! Even for those experienced with Maple Learn, sometimes, we miss an update with new features or fall out of practice with older ones. Luckily, we have the perfect solution for you–and it shows up right when you open your first document.

Introducing our brand-new Walkthrough Tutorial!

The tutorial covers all the main features of Maple Learn: from assigning functions, to using the Plot commands and Context Panel operations, all the way to creating your own visualizations with the Geometry commands. Stuck? Hints are provided throughout, or just click "Next" and the step will be completed automatically. 

If you're just starting out with Maple Learn, try the Beginner tutorial and work up to Advanced. This will introduce you to a holistic view of Maple Learn's capabilities along with some Maple Learn terminology. If you have some experience, starting with the Beginner tutorial is still a great option, but you may wish to begin with the Intermediate and Advanced tutorials. The Intermediate and Advanced sections cover how to use newer features of Maple Learn and you might discover something you haven't seen before!

How do I access the tutorial?

The tutorial will automatically launch when you open a new document. Head to https://learn.maplesoft.com and click "Open new document".

If the tutorial doesn't open automatically, it may have been disabled. You can manually open it by clicking the "Help" button in the top right, then clicking "Walkthrough Tutorial". 

There you have it! I had been using Maple Learn for the past few months and only recently discovered these two incredible features:

Silencing Groups (Intermediate - 6/7)

Live Sessions (Advanced - 6/6)

I found these features thanks to the Walkthrough Tutorial and my experience on Maple Learn hasn't been the same since! The Walkthrough Tutorial is a great introduction for new users, and a quick refresher for experts, but isn't the end of exploring Maple Learn's capabilities. See our How to Use Maple Learn (maplesoft.com) collection and our Getting Started with Maple Learn (youtube.com) video for more. You can also challenge The Treasure of Maple Learn (maplesoft.com) – a collection of documents designed to gamify exploring Maple Learn's features. Check out our blog post on The Case of the Mysterious Treasure - MaplePrimes to learn more about this collection. 

Hope you enjoy our new tutorial and let us know what you think!

This is a reminder that presentation applications for the Maple Conference are due July 17, 2024.

The conference is a a free virtual event and will be held on October 24 and 25, 2024.

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.

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

Kaska Kowalska
Contributed Program Co-Chair

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

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

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

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

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

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

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

Kaska Kowalska
Contributed Program Co-Chair

Hello, in a Maple script intended for Maple Learn I need to use a slider but I don't know how to get its value.

What should I do to get it?

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

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

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

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

To celebrate this day of mathematics, I want to share my favourite equation involving Pi, the Bailey–Borwein–Plouffe (BBP) formula:

This is my favourite for a number of reasons. Firstly, Simon Plouffe and the late Peter Borwein (two of the authors that this formula is named after) are Canadian! While I personally have nothing to do with this formula, the fact that fellow Canadians contributed to such an elegant equation is something that I like to brag about.

Secondly, I find it fascinating how Plouffe first discovered this formula using a computer program. It can often be debated whether mathematics is discovered or invented, but there’s no doubt here since Plouffe found this formula by doing an extensive search with the PSLQ integer relation algorithm (interfaced with Maple). This is an example of how, with ingenuity and creativity, one can effectively use algorithms and programs as powerful tools to obtain mathematical results.

And finally (most importantly), with some clever rearranging, it can be used to compute arbitrary digits of Pi!

Digit 2024 is 8
Digit 31415 is 5
Digit 123456 is 4
Digit 314159 is also 4
Digit 355556 is… F?

That last digit might look strange… and that’s because they’re all in hexadecimal (base-16, where A-F represent 10-15). As it turns out, this type of formula only exists for Pi in bases that are powers of 2. Nevertheless, with the help of a Maple script and an implementation of the BBP formula by Carl Love, you can check out this Learn document to calculate some arbitrary digits of Pi in base-16 and learn a little bit about how it works.

After further developments, this formula led to project PiHex, a combined effort to calculate as many digits of Pi in binary as possible; it turns out that the quadrillionth bit of Pi is zero! This also led to a class of BBP-type formulas that can calculate the digits of other constants like (log2)*(π^2) and (log2)^5.

Part of what makes this formula so interesting is human curiosity: it’s fun to know these random digits. Another part is what makes mathematics so beautiful: you never know what discoveries this might lead to in the future. Now if you’ll excuse me, I have a slice of lemon meringue pie with my name on it 😋

References
BBP Formula (Wikipedia)
A Compendium of BBP-Type Formulas
The BBP Algorithm for Pi

     On International Women’s Day we celebrate the achievements of women around the world. One inspiring story of women in STEM is that of Sophie Germain (1776-1831), a French mathematician and physicist who made groundbreaking strides in elasticity theory and number theory. She learned mathematics from reading books in her father’s library, and while she was not permitted to study at the École Polytechnique, due to prejudice against her gender, she was able to obtain lecture notes and decided to submit work under the name Monsieur LeBlanc. Some prominent mathematicians at the time, including Joseph-Louis Lagrange and Carl Friedrich Gauss, with whom Germain wrote, recognized her intellect and were supportive of her work in mathematics. 

     Sophie Germain is remembered as a brilliant and determined trailblazer in mathematics. She was the first woman to win a prize from the Paris Academy of Sciences for her contributions in elasticity theory and was among the first to make significant contributions toward proving Fermat’s Last Theorem. Among her many accomplishments, one special case of Fermat’s Last Theorem she was able to prove is when the exponent takes the form of what is now known as a Sophie Germain prime: a prime, p, such that 2p+1 is also a prime. The associated prime, 2p+1, is called a safe prime. 

     To mark International Women’s Day, I’ve created a document exploring the Ulam spiral highlighting Sophie Germain primes and safe primes, as an adaptation of Lazar Paroski’s Ulam spiral document. The image below displays part of the Ulam spiral with Sophie Germain primes highlighted in red, safe primes highlighted in blue, primes that are both a Sophie Germain prime and safe prime highlighted in purple, and primes that are neither in grey. 

     The document also contains small explorations of these types of prime numbers. For instance, one interesting property of safe primes is that they must either be 5, 7 or take the form 12k-1 for some k≥1. This can be shown from the fact a safe prime q must equal 2p+1 for some prime, p (a Sophie Germain prime), by definition. Then, since q and p are prime, for q > 7 we can determine through contradiction that q ≡ 3 (mod 4) and q ≡ 5 (mod 6), to conclude q ≡ 11 (mod 12) ≡ -1 (mod 12). And so, q = 12k-1 for some k≥1. The Maple Learn document can be found here along with its Maple script. The document also includes a group where you can test whether some positive integer of your choice, n, is a Sophie Germain prime or a safe prime. Alternatively, given n, a button press will display the next Sophie Germain prime greater than n, using Maple’s NextSafePrime command in the number theory package.  

     In mathematics, there is no shortage of interesting rabbit holes to dive into; many of which are the result of past and present women in mathematics, like Sophie Germain, who have persevered despite their hardships. 

Maple Transactions frequently gets submissions that contain Maple code.  The papers (or videos, or Maple documents, or Jupyter notebooks) that we get are, if the author wants a refereed submission, sent to referees by a fairly usual academic process.  We look for well-written papers on topics of interest to the Maple community.

But we could use some help in reviewing code, for some of the submissions.  Usually the snippets are short, but sometimes the packages involved are more substantial.

If you would be interested in having your name on the list of potential code reviewers, please email me (or Paulina Chin, or Jürgen Gerhard) and we will gratefully add you.  You might not get called on immediately---it depends on what we have in the queue.

Thank you very much, in advance, for sharing your expertise.

Rob

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

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

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

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

Overview of the Fractals Package  

Overview of the Fractals:-LSystem Subpackage 

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

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

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

Happy Lunar New Year! 

Curve sketching is an important skill for all calculus students to learn. In an era where technology is increasingly relied upon to perform mathematical computations and representations, maintaining fundamental skills such as curve sketching is more important than ever.

The new “Curve Sketching” collection is now available on Maple Learn. This collection provides background information on the process of curve sketching and opportunities to put this knowledge into practice. By starting with the “Curve Sketching Guide” and “Relationships Between Derivatives” documents, students are exposed to observational and computational strategies for drawing a function and its 1st and 2nd derivatives.

After looking through these documents, students can begin to practice sketching by observing and interpreting graphical properties with the “Sketch Derivative From Function Graph”, “Sketch Second Derivative From Function Graph”, and “Sketch Function From Derivative Graphs” activities:

Once a student has mastered extracting sketching information by graphical observation, they are ready for the next step: extracting information from a function’s definition. At this point, the student is ready to try sketching from a blank canvas with the “Sketch Curve From Function Definition” activity:

This collection also has activities for students below the calculus level. For example, the “Curve Sketching Quadratics Activity”, can be completed using only factoring strategies:

Whether you are a quadratics rookie or a calculus pro, this collection has an interactive activity to challenge your knowledge. Have fun sketching!

Two solstices occur on Earth every year, around June 21^st and December 21^st, often called the “June Solstice” and the “December Solstice” respectively. These solstices occur when the sun reaches its northernmost or southernmost point relative to the equator. During a solstice, the Northern Hemisphere will either experience the most sunlight of the year or the least sunlight of the year, while the Southern Hemisphere will experience the opposite phenomenon. The hemisphere with the most sunlight experiences a summer solstice, while the other hemisphere experiences a winter solstice.

Canada is located in the Northern Hemisphere and this Thursday, December 21^st, we will be experiencing a winter solstice. As the day with the least sunlight, this will be the shortest day of the year and consequently the longest night of the year.

Here in Canada, the sun will reach its minimum elevation during the winter solstice, and it will reach its maximum elevation during the Southern Hemisphere’s summer solstice on the same day. 

How high in the sky does the sun really get during these solstices? Check out our new Maple Learn document, Winter and Summer Solstice Sun Angles to find out. The answer depends on your latitude; for instance, with a latitude of approximately 43.51°, the document helps us find that the maximum midday elevation of the sun, which occurs during a summer solstice, will be 69.99°.

But how is the latitude of a location determined in the first place? See Maple Learn’s Calculating Latitude document to find out how the star Polaris, the center of the Earth, and the equator are all connected to latitude.

Latitude is one of two geographical coordinates that are paired together to specify a position on Earth, the other being longitude. See our Calculating Longitude document to explore how you can use your local time to approximate your longitude.

Armed with these coordinates, you can describe your position on the planet and find any number of interesting facts, such as your solstice sun angles from earlier, the time for sunrise and sunset, and the position of the Moon.

Happy Winter Solstice!

A new “Sudoku Puzzle” document is now on Maple Learn! Sudoku is one of the world’s most popular puzzle games and it is now ready to play on our online platform. 

This document is a great example of how Maple scripts can be used to create complex and interactive content. Using Maple’s built-in DocumentTools:-Canvas package, anyone can build and share content in Maple Learn. If you are new to scripting, a great place to start is with one of the scripting templates, which are accessible through the Build Interactive Content help page. In fact, I built the Sudoku document script by starting from the “Clickable Plots” template.

A Sudoku puzzle is a special type of Latin Square. The concept of a Latin Square was introduced to the mathematical community by Leonard Euler in his 1782 paper, Recherches sur une nouvelle espèce de Quarrés, which translates to “Research on a new type of square”. A Latin Square is an n by n square array composed of n symbols, each repeated exactly once in every row and column. The Sudoku board is a Latin Square where n=9, the symbols are the digits from 1 to 9,  and there is an additional requirement that each 3 by 3 subgrid contains each digit exactly once. 

Mathematical research into Sudoku puzzles is still ongoing. While the theory about Latin Squares is extensive, the additional parameters and relative novelty of Sudoku means that there are still many open questions about the puzzle. For example, a 2023 paper from Peter Dukes and Kate Nimegeers examines Sudoku boards through the lenses of graph theory and linear algebra.

The modern game of Sudoku was created by a 74-year-old Indiana retiree named Howard Garnes in 1979 and published under the name “Number Place”. The game had gained popularity in Japan by the mid-1980s, where it was named “Sudoku,” an abbreviation of the phrase “Sūji wa dokushin ni kagiru,” which means “the numbers must be single”.

Today, Sudoku is a worldwide phenomenon. This number puzzle helps players practice using their logical reasoning, short-term memory, time management, and decision-making skills, all while having fun. Furthermore, research from the International Journal of Geriatric Psychiatry concluded that doing regular brain exercises, like solving a Sudoku, is correlated with better brain health for adults over 50 years old. Additionally, research published in the BMJ medical journal suggests that playing Sudoku can help your brain build and maintain cognition, meaning that mental decline due to degenerative conditions like Alzheimer’s would begin from a better initial state, and potentially delay severe symptoms. However, playing Sudoku will by no means cure or prevent such conditions.

If you are unfamiliar with the game of Sudoku, need a refresher on the rules, or want to improve your approach, the “Sudoku Rules and Strategies” document is the perfect place to start. This document will teach you essential strategies like Cross Hatching:

And Hidden Pairs:

After reading through this document, you will have all the tools you need to start solving puzzles with the “Sudoku Puzzle” document on Maple Learn. 

Have fun solving!