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

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

Dear Maple users

I have a question which is maybe easily solved, but I cannot seem to find the solution myself. A vector X of coefficients has been computed earlier in the Maple document and I want these coefficients placed in front of some written symbols in order to make Maple display the final result in a nice way. I made an attempt with the Vector command as shown in the image, but I cannot make the indices start at -2. In addition I want some written math placed in front of the expression. In fact I want it displayed like shown on the image marked with a red rectangle. I did write this manually, but want Maple to do it automatically when given the coefficients vector calculated earlier. I hope someone can help me here!

(It is about finite difference methods, by the way)

 

Regards,

Erik 

Dear Maple users

My question is probably simple, but I can't seem to figure out how to do it in a smart way way without using procedures: My task is to create a cumulative list from a list. Ex: From [3,-2,5,1,10,7] I want to create the list [3,1,6,7,17,24]. Every entrance in the new list is the sum of the previous ones including the actual entrance. The Statistics package contain a command named CumulativeSum, but unfortunately a list is not returned ... I hope someone can help doing it is a simple way.

Regards,

Erik

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