## 721 Reputation

15 years, 178 days

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.

## MapleWWW...

I didn't know about MapleWWW. It is definitely something I will check out soon. Thanks!

Erik

## Maple T.A....

Forgot to comment on Maple T.A. We have had presentations for this tool at a Lecture. The idea looks very promising, but my impression is that it still lacks some 'ease of use' to get widespread. It is still a bit too complicated for ordinary teachers to produce quizzes of a medium complexity. Hopefully it will be improved in v11. Also I think it requires a 'package' or library of already produced quizzes, for people to start on ...

When those obstacles are overcome, I think it will be very valuable for tests, but not the least for students to test themselves on a daily basis.

Erik

## @acer  Thanks for reminding me that...

Thanks for reminding me that MapleCloud has gone viral, making it possible to sent another person an URL to find it. That is really a great step.

According to using MapleCloud, I have done so since it started up about five years or so ago :) In my classes, we have sent material to one another. Besides I have been using the Opaque option to use it to turn in test solutions.

Erik

## Great site!...

Brillant Carl! I found an expression for the exact radius of the Icosahedron. After rearranging (after my own liking) I use the following code, displaying the football with and without the wireframe.

_________________________________________

restart;
with(geom3d), with(plots):

PlotFootball := proc(L::list)

local FootballFaces;

uses geom3d, plottools, plots;

TruncatedIcosahedron(football, point(C, 0, 0, 0), 1);
FootballFaces := seq(polygon(faces(football)[i], color = `if`(nops(faces(football)[i])=5,L[1],L[2]), linestyle=solid, tickness=3), i = 1 .. 32);
display(FootballFaces, axes = none);

end proc:

plot1:=PlotFootball([red,yellow]); #plot football only and assign to name

R:=1/109*(15*sqrt(5)-12)*sqrt(25+4*sqrt(5)):
plot2:=draw(icosahedron(Icosa,C,R),style=wireframe,thickness=4):

display(plot1,plot2); #plot football with wireframe of Icosahedron

_________________________________________

I also tried displaying a sphere around the football, but somehow Maple didn't like using the geom3d package along with the plottools package. Using them together gave an error message. Anyway I don't really know if it is useful, because it will be hard to see if all vertices is lying on this sphere ...

NB! Impressing how I always receive a bunch of very usefull answers on Mapleprimes. Great website!

Erik

## Can an Icosahedron wireframe be added?...

@erik10

I got an idea for an additional challenge. Obviously the Truncated Icosahedron can be thought of as as an Icosahedron being truncated with a knife making the red faces. It could be very illustrative to have the original Icosahedron added to the plot as a wireframe. Is this possible? The vertices of the Icosahedron will lie on a sphere with radius a bit larger than 1, so it needs to be calculated at first ...

Erik

Beautiful!!

Erik

## @Kitonum  Thanks a lot. A Beachball...

Thanks a lot. A Beachball :)

Erik

## Thanks!...

@acer

Great! That will indeed be appreciated!

Erik

## Many different tools to do the same thin...

Wow! Thanks to all of you. I didn't know about the draw command. I guess Maple simply has many tools to accomplish the same thing. But also sometimes Maple is so big it is hard to know about every smart command to do the job ... It requires more overview pages, but maybe Maple already have that?

NB! Still puzzled though, that this polyhedron is not supported by the polyhedraplot command. The support list contain a long list with more or less obscure polyhedra, but maybe there is a reason ...

Erik

## @Carl Love  Great! I will test it. ...

Great! I will test it.

Erik

## Defining symbols...

Thanks Carl. I appreciate it. No it is not too simple! It can be used for automation purposes.

Now, I notice in the Help pages, that it is possible to manually make set operations using union, intersect, minus and subset. One can even use the ordinary symbols like ∩ as operators, which is great. It would be nice with a complement operator as well. The reason why it is not implementet is probably that it need knowledge about the Sample Space U. I usually use a 'c' written as a superscript to refer to the complement of an event.

Defining the complement of a set using a superscript obviously fails, because putting 'c' as a power to a set is meaningless. Also it fails using a Not operator below. Using a literal index works, and it is acceptable. Maybe I should emphasize that I want the notation to be as close as possible to ordinary math notation, for the sake of my students. I don't want them to bother too much with complex syntax. My question is now: Is it possible to make a definition in some way, so that whenever I write X with a literal index (and the set X and U defined beforehand), Maple will understand that I mean the compelement of X? If this is possible I will not have define the complement for every set or event I use ...

Erik

## Handling sets...

Since the manual thing above worked so well, I have an additional question: Sometimes I would be interested in having Maple handling sets for me and calculating probabilities. Let's say I am throwing two dice, a green and a red one.

Given two events, H and G. I would be interested in having Maple calculate the union and intersection of H and G as well as their probabilities P(H∩G) as well as P(HUG). How is this done conveniently? What about the complement of a set?

Erik

## lists...

Thanks Carl! And I see I am allowed to use set operators as well!

Erik

## @Carl Love Thanks Carl. I didn't mean it...

@Carl Love Thanks Carl. I didn't mean it exactly that way, but I can use your ideas for other purposes. I m actually quite satisfied with how I have got now.

Erik

## Thanks...

@Kitonum Thank you! Nice zip-function to combine the two lists into one and then manipulate this using a map command. I guess this is the most straightforward way to do it without having to use procedures, right? I did rewrite it a bit for my own situation to make it s bit more readable, though:

restart;
with(Gym);
R := [163, 163, 163, 107, 107, 107, 51];
V := [15, 45, 75, 15, 45, 75, 45];
W := zip((x, y) -> [x, y], R, V);
X := map(t -> t[1]*Cos(t[2]), W);
Y := map(t -> t[1]*Sin(t[2]), W);

NB! That way I can easily access X and Y. I have used a custom package to deal with cosine and sine when angles given in degrees.

Regards,

Erik

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