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The development of the calculation of moments using force vectors is clearly observed by taking a point and also a line. Different exercises are solved with the help of Maple syntax. We can also visualize the vector behavior in the different configurations of the position vector. Applications designed exclusively for engineering students. In Spanish.

Moment_of_a_force_using_vectors_updated.mw

Lenin Araujo Castillo

Ambassador of Maple

This is Maple:

These are some primes:

22424170499, 106507053661, 193139816479, 210936428939, 329844591829, 386408307611,
395718860549, 396412723027, 412286285849, 427552056871, 454744396991, 694607189303,
730616292977, 736602622363, 750072072203, 773012980121, 800187484471, 842622684461

This is a Maple prime:


In plain text (so you can check it in Maple!) that number is:

111111111111111111111111111111111111111111111111111111111111111111111111111111
111111111111111111111111111111116000808880608061111111111111111111111111111111
111111111111111111111111111866880886008008088868888011111111111111111111111111
111111111111111111111116838888888801111111188006080011111111111111111111111111
111111111111111111110808080811111111111111111111111118860111111111111111111111
111111111111111110086688511111111111111111111111116688888108881111111111111111
111111111111111868338111111111111111111111111111880806086100808811111111111111
111111111111183880811111111111111111100111111888580808086111008881111111111111
111111111111888081111111111111111111885811188805860686088111118338011111111111
111111111188008111111111111111111111888888538888800806506111111158500111111111
111111111883061111111111111111111116580088863600880868583111111118588811111111
111111118688111111111001111111111116880850888608086855358611111111100381111111
111111160831111111110880111111111118080883885568063880505511111111118088111111
111111588811111111110668811111111180806800386888336868380511108011111006811111
111111111088600008888688861111111108888088058008068608083888386111111108301111
111116088088368860808880860311111885308508868888580808088088681111111118008111
111111388068066883685808808331111808088883060606800883665806811111111116800111
111581108058668300008500368880158086883888883888033038660608111111111111088811
111838110833680088080888568608808808555608388853680880658501111111111111108011
118008111186885080806603868808888008000008838085003008868011111111111111186801
110881111110686850800888888886883863508088688508088886800111111111111111118881
183081111111665080050688886656806600886800600858086008831111111111111111118881
186581111111868888655008680368006880363850808888880088811111111111111111110831
168881111118880838688806888806880885088808085888808086111111111111111111118831
188011111008888800380808588808068083868005888800368806111111111111111111118081
185311111111380883883650808658388860008086088088000868866808811111111111118881
168511111111111180088888686580088855665668308888880588888508880800888111118001
188081111111111111508888083688033588663803303686860808866088856886811111115061
180801111111111111006880868608688080668888380580080880880668850088611111110801
188301111111111110000608808088360888888308685380808868388008006088111111116851
118001111111111188080580686868000800008680805008830088080808868008011111105001
116800111111118888803380800830868365880080868666808680088685660038801111180881
111808111111100888880808808660883885083083688883808008888888386880005011168511
111688811111111188858888088808008608880856000805800838080080886088388801188811
111138031111111111111110006500656686688085088088088850860088888530008888811111
111106001111111111111111110606880688086888880306088008088806568000808508611111
111118000111111111111111111133888000508586680858883868000008801111111111111111
111111860311111111111111111108088888588688088036081111860803011111111863311111
111111188881111111111111111100881111160386085000611111111888811111108833111111
111111118888811111111111111608811111111188680866311111111111811111888861111111
111111111688031111111111118808111111111111188860111111111111111118868811111111
111111111118850811111111115861111111111111111888111111111111111080861111111111
111111111111880881111111108051111111111111111136111111111111188608811111111111
111111111111116830581111008011111111111111111118111111111116880601111111111111
111111111111111183508811088111111111111111111111111111111088880111111111111111
111111111111111111600010301111111111111111111111111111688685811111111111111111
111111111111111111111110811801111111111111111111158808806881111111111111111111
111111111111111111111181110888886886338888850880683580011111111111111111111111
111111111111111111111111111008000856888888600886680111111111111111111111111111
111111111111111111111111111111111111111111111111111111111111111111111111111111

This is a 3900 digit prime number. It took me about 400 seconds of computation to find using Maple.

It turns out be be really easy to do because prime numbers are realy quite common.  If you have a piece of ascii art where all the characters are numerals, you could just call on it and get a prime number that is still ascii art with a couple digits in the corner messed up (for a number this size, I expect fewer than 10 of the least significant digits would be altered).  You may notice, however, that my Maple Prime has beautiful corners!  This is possible because I found the prime in a slightly different way.

To get the ascii art in Maple, I started out by using to import ( )  and process the original image.  First then and to get a nice 78 pixel wide image.  Then to make it a pure 1-bit black or white image.

Then, from the image, I create a new Array of the decimal digits of the ascii art and my prime number.  For each of the black pixels I randomly use one of the digits or and for the white pixels (the background) I use 's.  Now I convert the Array to a large integer and test if it is prime using (it probably isn't) so, I just randomly change one of the black pixels to a different digit (there are 4 other choices) and call again. For the Maple Prime I had to do this about 1000 times before I landed on a prime number. That was surprisingly fast to me! It is a great object lesson in how dense the prime numbers really are.

So that you can join the fun without having to replicate my work, here is a small interactive Maple document that you can use to find prime numbers that draw ascii art of your source images. It has a tool that lets you preview both the pixelated image and the initial ascii art before you launch the search for the prime version.

Prime_from_Picture.mw

Was just pondering this idea and posted this in the post topic for discussion. 

Each Maple finished version of Maple may still have certain bugs that will not be updated for that version, so I am suggesting (I think anyone could implement it) that if there is a workaround, one could wrap it up in something I would call a patch package updateable by us users we could update here on mapleprimes.  It would be good for people who haven't upgraded or can't upgrade due to costs etc...

For example, there was recent issue with pdsolve that was fixed quite quickly in the seperate updateable Physics package.  Things could be done similarily that might work with other workarounds using this patch package idea. 

If anyone thinks this is good or even viable idea then lets implement it.  I envisioned it with just this one rule to follow - the name of the patch package would reflect the version we are patching (ie. with(patch12) or with(patch2016) for Maple 12 and Maple 2016 respectively etc...)  We could make these patch packages available in this post or start another.

As I said, I'm just throwing the idea out there.  Thoughts?

As you can see this app performs the trace of a given path r (t), then locate the position vector in a specific time. It also graphs the velocity vector, acceleration, Tangential and Normal unit vectors, along with the Binormal. Very good app developed entirely in Maple for our engineering students.

Plot_of_Position_Vector_UPDATED.mw

https://youtu.be/OzAwShHHXq8

Lenin Araujo Castillo

Ambassador of Maple

We have just released an update to Maple. Maple 2017.2 includes updated translations for Japanese, Traditional Chinese, Simplified Chinese, Brazilian Portuguese, French, and Spanish. It also contains improvements to the MapleCloud, physics, limits, and PDEs. This update is available through Tools>Check for Updates in Maple, and is also available from our website on the Maple 2017.2 download page.

 Eithne

It appears google doesn't know about the haversine formula.  Huh?  Well at least google can't draw the proper path for it.  I typed in google "distance from Pyongyang to NewYork city"  and got 10,916km.  Ok that's fine but then it drew a map

The map path definitely did not look right.  Pulled out my globe traced a rough path of the one google showed and I got 13 inches (where 1 inch=660miles) -> 8580 miles = 13808 km .. clearly looks like google goofed. 

So we need Maple to show us the proper path.
 

with(DataSets):
with(Builtin):
m := WorldMap();
AddPath(m, [-74.0059, 40.7128], [125.7625, 39.0392]):
Display(m):

Ok so you say that really doesn't look like the shortest path.  Well, lets visualize that on the globe projection

Display(m, projection = Globe, orientation = [-180, 0, 0])

Ah, now it is clear
Pyonyang_to_NewYork.mw

 

As a momentary diversion, I threw together a package that downloads map images into Maple using the Google Static Maps API.

If you have Maple 2017, you can install the package using the MapleCloud Package Manager or by executing PackageTools:-Install("5769608062566400").

This worksheet has several examples, but I thought I'd share a few below .

Here's the Maplesoft office

 

Let's view a roadmap of Waterloo, Ontario.

 

The package features over 80 styles for roadmaps. These are examples of two styles (the second is inspired by the art of Piet Mondrian and the De Stijl movement)

 

You can also find the longitude and latitude of a location (courtesy of Google's Geocoding API). Maple returns a nested list if it finds multiple locations.

 

The geocoding feature can also be used to add points to Maple 2017's built-in world maps.

 

Let me know what you think!

This app is used to study the behavior of water in its different properties besides air. Also included is the study of the fluids in the state of rest ie the pressure generated on a flat surface. Integral developed in Maple for the community of users in space to the civil engineers.

App_for_fluids_in_flat_state_of_rest.mw

Lenin Araujo Castillo

Ambassador of Maple

 

A few days ago I was browsing through some books in my collection, that by Gradshteyn and Ryzhik in particular. What fraction of the intregrals, series and products therein can Maple handle correctly?  Besides special functions these properties are valuable components of symbolic mathematical software.  If the answer to this question is not nearly everything in that printed compilation, this inclusion in Maple is a worthy objective.

We have just released the 3rd edition of the Mathematics Survival Kit – Maple Edition.

The Math Survival Kit helps students get unstuck when they are stuck. Sometimes students are prevented from solving a problem, not because they haven’t understood the new concept, but because they forget how to do one of the steps, like completely the square, or dealing with log properties.  That’s where this interactive e- book comes in. It gives students the opportunity to review exactly the concept or technique they are stuck on, work through an example, practice as much (or as little) as they want using randomly generated, automatically graded questions on that exact topic, and then continue with their homework.

This book covers over 150 topics known to cause students grief, from dividing fractions to integration by parts. This 3rd edition contains 31 additional topics, deepening the coverage of mathematical topics at every level, from pre-high school to university.

See the Mathematics Survival Kit for more information about this updated e-book, including the complete list of topics.

eithne

Do you have Maple content that you want to protect from editing and viewing, while still allowing others to execute the code within and obtain results? In Maple, worksheets can be password protected so the users of your Maple application can benefit from the specialized routines you've created while the details remain hidden.


The password protection feature can be useful for a variety of situations, such as:

  • • Providing a Maple-based solution while protecting the intellectual property embodied in your algorithms
  • • Ensuring the users of your application can not accidentally make changes that break your code

 

To learn more about this feature in Maple, you can download the free Tips & Techniques from the Application Center.

We just posted a submission to the Maple Application Center that I thought people might be interested in. Mathematics for Chemistry isn't a typical application - it's an e-book, written in Maple by J.F. Ogilvie. It covers both standard mathematics topics chemistry students are expected to know,  such as calculus and linear algebra, as well as chemistry-specific topics like chemical equilbrium, quantum chemistry, and nuclear-magnetic-resonance spectra.

There's lots of interesting content on the Application Center, and the range of topics is always fascinating, but it's not every day I see an entire e-book come across my desk(top)!

If you are interested, you can find it on the Application Center, here: Mathematics for Chemistry

eithne

   It’s that time of year again for the University of Waterloo’s Submarine Racing Team – international competitions for their WatSub are set to soon begin. With a new submarine design in place, they’re getting ready to suit up, dive in, and race against university teams from around the world.

 

   The WatSub team has come a long way from its roots in a 2014 engineering project. Growing to over 100 members, students have designed and redesigned their submarine in efforts to shave time off their race numbers while maintaining the required safety and performance standards. Their submarine – “Bolt,” as it’s named – was officially unveiled for the 2017 season on Thursday, June 1st.

 

 

   As the WatSub team says, "Everything is simple, until you go underwater."

 

 

    Designing a working submarine is no easy task, and that’s before you even think about all the details involved. Bolt needs to accommodate a pilot, be transported around the world, and cut through the water with speed, to name a few of the requirements if the WatSub team is to be a serious competitor.

 

    To help squeeze even more performance out of their design, the team has been using Maple to fine tune and optimize some of their most important structural components. At Maplesoft, we’ve been excited to maintain our sponsorship of the WatSub team as they continue to find new ways to push Bolt’s performance even further.

 

 

   The 2017 design unveiling on June 1st. After adding decals and final touches, Bolt will soon be ready to race.

 

   This year, the WatSub team has given their sub a whole new design, machining new body parts, optimizing the weight distribution of their gearbox, and installing a redesigned propeller system. Using Maple, they could go deep into design trade-offs early, and come away knowing the optimal gearbox design for their submarine.

 

   In just over a month, the WatSub team will take Bolt across the pond and compete in the European International Submarine Races (eISR). Many teams competing have been in existence for well over a decade, but the leaps and strides taken by the WatSub team have made them a serious competitor for this year.

  Best of luck to the WatSub team and their submarine, Bolt – we’re all rooting for you!

We have just released an update to Maple.  It includes updates to the Maple Workbook, the video component, the Physics package, and many other small improvements throughout the product. It is available through Tools>Check for Updates in Maple, and is also available from our website on the Maple 2016.2 download page.

eithne

Ian Thompson has written a new book, Understanding Maple.

I've been browsing through the book and am quite pleased with what I've read so far. As a small format paperback of just over 200 pages it packs in a considerable amount of useful information aimed at the new Maple user. It says, "At the time of writing the current version is Maple 2016."

The general scope and approach of the book is explained in its introduction, which can currently be previewed from the book's page on amazon.com. (Click on the image of the book's cover, to "Look inside", and then select "First Pages" in the "Book sections" tab in the left-panel.)

While not intended as a substitute for the Maple manuals (which, together, are naturally larger and more comprehensive) the book describes some of the big landscape of Maple, which I expect to help the new user. But it also explains how Maple is working at a lower level. Here are two phrases that stuck out: "This book takes a command driven, or programmatic, approach to Maple, with the focus on the language rather than the interface", followed closely by, "...the simple building blocks that make up the Maple language can be assembled to solve complex problems in an efficient way."

 

 

 

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