Happy Valentine’s Day! Love is celebrated all around the world on this day, but did you know of some other love celebrations, and some of the mythology around the holiday?

First of all, Cupid. We all know of the image of Cupid and his bow, shooting arrows to make couples fall in love. But where exactly did this come from?

Cupid is a Latin deity, the son of Venus and Mars. With his parents being love and war, it’s no surprise that he ended up with a bow! In one legend, he shoots a golden arrow at Apollo, which makes him fall in love with a nymph. Unfortunately for Apollo, he also shoots a lead arrow at the nymph, making her repulsed by him.

Roses are another popular tradition with Valentine’s Day. Red roses persist as a symbol of Aphrodite, the mother of Cupid, and are a symbol of love. Did you know you can draw them in Maple Learn with our geometry palette? See one rendition below of a stained glass rose. The link to the document is HERE.

Now, there are a few other love traditions around the world. Did you know that not everyone celebrates love only on Valentine’s Day? There are other important days around the world, and some pre-date Valentine’s Day.

For example, in China, the Miao people celebrate the Sister’s Meal Festival, likely our earliest form of a Valentine’s Day tradition in the world. This occurs in March. Young women make dyed rice representing the different seasons, and when the men come by to sing, they give them packages of the rice. Inside the rice are objects, each with different meanings. A pair of red chopsticks means the woman returns the man’s affection, while one red chopstick is a polite refusal. A clove of garlic or a chili pepper means a strong refusal, and pine needles mean that she is waiting for him to woo her.

We’ve created a document to join in on the fun, even if you’re not participating in this Festival this year. Follow the link HERE to work with fraction tiles to pack your own rice packages, and your own responses to declarations of love. 

We hope everyone has a lovely Valentine’s day!

Happy Lunar New Year to everyone here in the MaplePrimes community, as we enter the Year of the Tiger! There are different traditions followed in the many countries around the world where the Lunar New Year is celebrated. In my own Canadian-Chinese family, we usually cook a big meal and share with family members and friends. 

The pandemic has made this year's celebration more muted, but I did cook a large batch of our favourite dumplings and made up several packages to take to friends. That led to the question: how many ways can I arrange 10 dumplings on a plate from the 3 kinds I made? Of course, that called for a Maple Learn document to compute the answer: A Counting Problem: Selecting Dumplings
 

I was also interested in understanding the formula used in this computation, and so I created a second document showing a special case of this problem. By moving the sliders around, you can see how the "Stars and Bars" method for counting the ways one can choose a number of items from distinct bins works: Visualization the Stars and Bars Method.

I hope you enjoy trying out these documents and I wish everyone good health, happiness and prosperity in the coming year!

When I was in middle school, I was really into puzzles.  At one point I attempted the Three Utilities Problem.  This famous problem is deceptively simple: three houses and three “utilities” (heating, water, and electricity) are represented by dots on a flat piece of paper.  The goal is to connect each house to the three utilities without crossing any lines.

Figure 1: A starting setup.

I spent hours drawing lines.  I eventually looked it up online, and the internet told me that the problem was impossible.  I didn’t believe it, and tried for several more hours until I was forced to accept its impossibility.  I still remember this intense stint of puzzling to this day.

Figure 2: Cue twelve-year-old me saying “I’ll get it eventually…”

Looking back, I wonder if this sparked my interest in graph theory.  I know now that the Three Utilities Problem is truly unsolvable.  I know that the graph’s formal name is K_3,3 and I know a full graph theory proof explaining its nonplanarity.  Nevertheless, I still love this puzzle, and I’ve recently recreated it in Maple Learn.

To do this, I created a table of x and y values and plotted all of them using the Point() command.  This allows the points to be fully click-and-drag-able.  Line segments joining two points automatically move with the points as well.  We then have a fully interactive graph directly in the Maple Learn plot window.  I can move the “houses” and “utilities” around all I want to try and solve the unsolvable.  I can also create other graphs to further explore planarity, paths, matchings, or any other aspects of the wide world of graph theory.

If you want to check out the document for yourself, it can be found here. 

The Bohemian Matrix Calendar 2022 is up!  You may find it at https://rcorless.github.io/ (four versions: letter/A4 paper, Sunday/Monday start to the week).

It prints quite well (with proper equipment).  I wish you all the best for 2022.

Since the start of the pandemic, I have been involved in online mathematics tutoring. I tried many different applications to best communicate with my students, and ended up sticking with Maple Learn. Here’s my setup, and why I chose Maple Learn.

My Setup

When I have an online tutoring session, I join a scheduled video call to “see” my students. I then open a blank Maple Learn document, and share my screen. I explain whatever I need to explain, while writing key information on the Maple Learn document. When I don’t want Learn to interpret what I write, I go into text mode; when I do (e.g. when I want to graph a function), I stay in math mode. When the class is over, I send the document’s sharelink to my students by email, so that they can access it. 

Here is an example of a Maple Learn document (pictured below) that I created while teaching trigonometry to a student. Keep in mind that I typed this while on call with the student, so the document is very simple - it only uses the most basic features of Maple Learn.

Why I Chose Maple Learn

My main student wants me to teach him trigonometry ahead of it being taught to him at school. For this, I need to be able to write lots of text and math easily, while on video call with him. 

Microsoft Word is not good enough for this: the equation editor is too clumsy. I also tried drawing tools where you can move your mouse to draw on the screen, but they make it too hard to write text. I even tried pointing a camera at my desk and writing the notes by hand, but my handwriting is terrible, and I could never find the right position for the camera. That’s the main reason why I chose Maple Learn: it lets me write both text and math quickly and simply, unlike many other applications.

There are some other benefits to using Maple Learn. I like that I can organize what I write in a visually appealing manner on the canvas, by moving groups around. I like that I can graph functions within Maple Learn, without having to open a graphing calculator in a separate tab. Finally, I find the sharelink feature convenient for sending the notes to my students after class.

Disclaimer: I discovered Maple Learn while working at Maplesoft during a co-op term.

Dear all,

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

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

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

-r

Hi to all,

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

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

Dear all,

Recently I discovered the noncommuting variables in the Physics package due to Edgardo Cheb-Terrab; doubtless there are many posts here on Maple Primes describing them.  Here is one more, which shows how to use this package to prove the Schur complement formula.

https://maple.cloud/app/6080387763929088/Schur+Complement+Proof+in+Maple

I guess I have a newbie's question: how well-integrated are Maple Primes and the Maple Cloud?  Anyway that seemed the easiest way to share this.

-r

Dear all,

Recently we learned that the idea of "anti-secularity" in perturbation methods was known to Mathieu already by 1868, predating Lindstedt by several years.  The Maple worksheet linked below recapitulates Mathieu's computations:

https://github.com/rcorless/MathieuPerturbationMethod

Nic Fillion and I wrote a more general introduction to perturbation methods using Maple and you can find that paper at 

https://arxiv.org/abs/1609.01321

and the supporting Maple code in a workbook at 

https://github.com/rcorless/Perturbation-Methods-in-Maple

For instance, one of the problems solved is the lengthening pendulum and when we do so taking proper account of anti-secularity (we use renormalization for that one, I seem to remember) we get an error curve that is bounded over time.

Hope that some of you find this useful.

Hi everyone! It's been a remarkably long time since I posted on MaplePrimes -- I should probably briefly reintroduce myself to the community here. My name is Erik Postma. I manage the mathematical software group at Maplesoft: the team that writes most of the Maple-language code in the Maple product, also known as the math library. You can find a longer introduction at this link.

One of my tasks at Maplesoft is the following. When a request for tech support comes in, our tech support team can usually answer the request by themselves. But no single person can know everything, and when specialized knowledge of Maple's mathematical library is needed, they ask my team for help. I screen such requests, answer what I can by myself, and send the even more specialized requests to the experts responsible for the appropriate part of the library.

Yesterday I received a request from a user asking how to unwrap angles occurring in an expression. This is the general idea of taking the fact that , and similarly for the other trig functions; and using it to modify an expression of the form  to make it look "nicer" by adding or subtracting a multiple of  to the angle. For a constant, real value of  you would simply make the result be as close to 0 as possible; this is discussed in e.g. this MaplePrimes question, but the expressions that this user was interested in had arguments for the trig functions that involved variables, too.

In such cases, the easiest solution is usually to write a small piece of custom code that the user can use. You might think that we should just add all these bits and pieces to the Maple product, so that everyone can use them -- but there are several reasons why that's not usually a good idea:

• Such code is often too specialized for general use.
• Sometimes it is reliable enough to use if we can communicate a particular caveat to the user -- "this will not work if condition XYZ occurs" -- but if it's part of the Maple library, an unsuspecting user might try it under condition XYZ and maybe get a wrong answer.
• This type of code code generally doesn't undergo the careful interface design, the testing process, and the documentation effort that we apply to the code that we ship as part of the product; to bring it up to the standards required for shipping it as part of Maple might increase the time spent from, say, 15 minutes, to several days.

That said, I thought this case was interesting enough to post on MaplePrimes, so that the community can take a look - maybe there is something here that can help you with your own code.

So here is the concrete question from the user. They have expressions coming from an inverse Laplace transform, such as:

with(inttrans):
F := -0.3000*(-1 + exp(-s))*s/(0.0500*s^2 + 0.1*s + 125);
f := invlaplace(F, s, t)*u(t);
# result: (.1680672269e-1*exp(1.-1.*t)*Heaviside(t-1.)*(7.141428429*sin(49.98999900*t-
#         49.98999900)-357.*cos(49.98999900*t-49.98999900))+.1680672269e-1*(-7.141428429*sin
#         (49.98999900*t)+357.*cos(49.98999900*t))*exp(-1.*t))*u(t)

I interpreted their request for unwrapping these angles as replacing the expressions of the form  with versions where the constant term was unwrapped. Thinking a bit about how to be safe if unexpected expressions show up, I came up with the following solution:

unwrap_trig_functions := module()
local ModuleApply := proc(expr :: algebraic, $)
  return evalindets(expr, ':-trig', process_trig);
end proc;

local process_trig := proc(expr :: trig, $)
  local terms := convert(op(expr), ':-list', ':-`+`');
  local const, nonconst;
  const, nonconst := selectremove(type, terms, ':-complexcons');
  const := add(const);
  local result := add(nonconst) + (
    if is(const = 0) then
      0;
    else
      const := evalf(const);
      if type(const, ':-float') then
        frem(const, 2.*Pi);
      else
        frem(Re(const), 2.*Pi) + I*Im(const);
      end if;
    end if);
  return op(0, expr)(result);
end proc;
end module;

# To use this, with f defined as above:
f2 := unwrap_trig_functions(f);
# result: (.1680672269e-1*exp(1.-1.*t)*Heaviside(t-1.)*(7.141428429*sin(49.98999900*t+
#         .27548346)-357.*cos(49.98999900*t+.27548346))+.1680672269e-1*(-7.141428429*sin(
#         49.98999900*t)+357.*cos(49.98999900*t))*exp(-1.*t))*u(t)

Exercise for the reader, in case you expect to encounter very large constant terms: replace the calls to frem above with the code that Alec Mihailovs wrote in the question linked above!

HI Maple Primes people and other interested parties,

I was a teacher for more that ten years.  Most of my teaching was at community college level.

Although I am not a biological father, my extended family is important to me.

I graduated from university two times with special diplomas.  The next two years (99 to 01) were hectic for me.  After that I went to see about females, and now I am in the happily married club.

I'm glad I kept my Maple 13 student version software because like my father, I like to make computer code.

0_2_20_tuple_to_share.pdf

Mathematical truth will outlast the stars in the sky.  but government and good behavior will always kick the ass of any expression.

Consider this 

Regards

Matt

C_MRB is defined below. See http://mathworld.wolfram.com/MRBConstant.html.

Starting by using Maple on the Inverse Symbolic Calculator, with over 21 years of research and ideas from users like you, I developed this shortlist of formulas for the MRB constant.

• C_MRB=  

That is proven below by an internet scholar going by the moniker "Dark Malthorp:"

•  denoting the kth derivative of the Dirichlet eta function of k and 0 respectively was first discovered in 2012 by Richard Crandall of Apple Computer.

The left half is proven below by Gottfried Helms and it is proven more rigorously considering the conditionally convergent sum, below that. Then the right half is a Taylor expansion of η(s) around s = 0.

At https://math.stackexchange.com/questions/1673886/is-there-a-more-rigorous-way-to-show-these-two-sums-are-exactly-equal,

it has been noted that "even though one has cause to be a little bit wary around formal rearrangements of conditionally convergent sums (see the Riemann series theorem), it's not very difficult to validate the formal manipulation of Helms. The idea is to cordon off a big chunk of the infinite double summation (all the terms from the second column on) that we know is absolutely convergent, which we are then free to rearrange with impunity. (Most relevantly for our purposes here, see pages 80-85 of this document, culminating with the Fubini theorem which is essentially the manipulation Helms is using.)"

I am a high school Teacher in Denmark, who have been using Maple since version 12, more than 12 years ago. I suggested it for my school back then and our math faculty finally decided to purchase a school license. We are still there. We have watched Maple improve in a lot of areas (function definitions, context panels, graphically etc., etc ). Often small changes makes a big difference! We have been deligted. We we are mostly interested in improvements in GUI and lower level math, and in animations and quizzes. I have also been enrolled as a beta tester for several years yet. 

One of the areas, which is particually important is print and export to pdf, because Danish students have to turn in their papers/solutions at exams in pdf format! I guess the Scandinavian countries are ahead in this department. They may quite possible be behind in other areas however, but this is how it is. 

Now my point: Maplesoft is lacking terrible behind when regarding screen look in comparison with print/export to pdf. 

I am very frustrated, because I have been pinpointing this problem in several versions of Maple, both on Mapleprimes and in the beta groups. Some time you have corrected it, but it has always been bouncing back again and again! I have come to the opinion that you are not taking it seriously? Why?

Students may loose grades because of missing documentations (marking on graphs etc.). 

I will be reporting yet another instance of this same problem. When will it stop?

Erik

 

I make a maple worksheet for generating Pythagorean Triples Ternary Tree :

Around 10,000 records in the matrix currently !

You can set your desire size or export the Matrix as text ...

But yet ! I wish to understand from you better techniques If you have some suggestion ?

the mapleprimes Don't load my worksheet for preview so i put a screenshot !

Pythagoras_ternary.mw

Pythagoras_ternary_data.mw

Pythagoras_ternary_maple.mw