erik10

I have a degree in Mathematics and Physics from the Danish University Aarhus, comparable to a masters degree with thesis - majoring in Mathematics. In 1991-92 I was a visting scholar at UCLA, Los Angeles, following graduate courses in Applied Mathematics. Since 1992 I have been a teacher in a high school (gymnasium) in Denmark. Special interests: Applied mathematics, graphics and popularizing Mathematics.

MaplePrimes Activity


These are questions asked by erik10

Dear Maple users

An engineering student asked me how Maple is handling complex numbers in polar form. He told me that his fellow students are using another CAS, whereas he himself prefer Maple. When making calculations with AC currents having different phases the other students were using the easy notation depicted in the first line on the picture below. Obviously here the angle (argument) is measured in degrees. I tried to perform the same calculations in Maple, but found it to require a very heavy notation: the other three lines on the picture. Now my question is: Does it really have to be that messy, or maybe there are some package, which will accomplish the task in a more neat way? I mean it is a rather common operation in the engineering sciences.

NB! Of couse one can argue about the educational value of using the notation of the other CAS! From that viewpoint they will probably not learn anything ...

 

 

Regards,

Erik

 

Dear Maple users

Sometimes I would like to place certain Maple content on my website, for example making it possible for the user to rotate 3d objects (created in Maple) directly on the webpage, in the browser. I did that on one of my own webpages, written in Danish though:

http://www.matematiksider.dk/soapbubbles.html

If you scroll to the Catenoid shape, almost at the bottom of the page, one should be able to click this object to have a Javaapplett started. I made this years ago with the help of the great tools created by Konrad Polthier:

http://www.javaview.de/maple/index.html

It wasn't easy, but I made it work. Things have changed since that time, however. Java is more and more "in bad standing". I was blocked when I tried opening it because of security. Banks is looking for alternatives, also because of security. And the mostly used browser now, Chrome, has stopped supporting it.

Now my question: Is there an alternative? Will HTML5 make it possible to make some kind of "Maple plugin" for Interactive Maple objects to be placed on webpages and interacted with in a Webbrowsers?

Erik

 

Dear Maple users

I am delighted that Maple has builtin commands to plot so many polyhedrons in 3D. Here I am talking about the polyhedraplot command in the plots package. I was however disappointed that the socalled Truncated Icosahedron is not supported (not present in the supported list ...). My first question is:

1. Why isn't it supported?

It seems more relevant than many of the other polyhedrons which are supported. It is a member of the Archimedian Solids (see https://en.wikipedia.org/wiki/Truncated_icosahedron). Besides it is the basic structure for soccer footballs. I found out that a TruncatedIcosahedron command is available in the geom3d package. This command is able to deliver data for the faces and more. With this command I succeded in writing a small program to actually plot this polyhedron in 3D:

-----------------------------------------------------

restart;
with(geom3d):
with(plots):
TruncatedIcosahedron(football,point(C,(0,0,0)),1):

PlotFootball:=proc(tr::float)
    
    local i::integer,
         FootballFace::Vector(datatype=float[8]),
         plotFace::Vector(datatype=float[8]);    
    
    for i from 1 to 32 do
        FootballFace[i]:=faces(football)[i];
        plotFace[i]:=polygonplot3d(Matrix(FootballFace[i]),axes=none,scaling=constrained,transparency=tr);
    end do;
    
    display(seq(plotFace[i],i=1..32)):
    
end proc:

PlotFootball(0.00);

-----------------------------------------------------

Since I am not really experienced in programming in Maple, here is my last question:

2. Can I simplify something in my code above?

 

Best wishes,

Erik

 

Dear Maple users

I am unsure how to handle events and their probabilities in Maple. Let's say I know that an event A has the probability say 0.3 and another event B has probability 0.8. I would like to make the following assignments:

P(A):=0.3:

P(B):=0.8

and maybe defining the conditional probability:

P(A|B):=0.55

but I am not allowed to do so in Maple because if will regarded as a function definition. My purpose is to make simple calculations with those probabilities for example:

P(C):=P(A)*P(B)  etc.

My problem is therefore more of a notational problem than a mathematical one. I hope someone can advice me on a proper setup. I am using 2D math notation, by the way. I could of course name the variables containing the probability using simple names like X1, X2, etc., but then I need constantly to remember what they really mean. The above assignments would be much better, because they are easier to handle mentally.

Regards,Erik

I need to make a lot of similar calculations and wonder if it can be done in a smart way in Maple. Microsoft Excel is perfect for this kind of calculations, because you can downcopy cells. I would like to do everything in Maple, if possible, though. I have a number of points A, B, C, D, E, ... , which all lie on various circles in the plane. For every point radius and angle is given, so actually you can say that every point is delivered with polar coordinates. I want to have their rectangular coordinates. 

Maybe I could deliver their radii in a list and their angles in degrees in another list?

r:=[12,56,29,...., 78]:

v:=[15,45,75,..., 102]: 

......

I need to be able to refer to a certain point thorugh an index. At best it would be A, B, C, ... , but 1, 2, 3, ... will be acceptable. So in the end I need to be able to access say x_C and y_C or x_3 and y_3 (understood as index lowered). I hope someone can help me do the task in a nice a efefctive way.

NB! Maybe you have a solution, which involve transformation from polar to rectangular coordinates. That will be nice, but please also tell me how it can be done from scratch, because I want to be able to know about handling many points at once for other purposes, when the function is not r*cos(v), but an arbitrary function.

Regards,

Erik

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