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 replies submitted by erik10

Thanks Thomas Richard and tomleslie

My file path doesn't contain special International characters (just English). It is strange, because I can open the file in all of the other versions 2019, 2018, 2017, but not 2020. I really hope it has to do with an issue in version 2020 and can be resolved in Maple 2020.1. Else it will be a definite problem, for me and for my students (if they experince the same problem). I just wonder why it works in the recent versions and not in 2020?



Big thanks to both of you.

Carl Love: I didn't know about using the sprintf command in connection with the textplot commnd. Works perfectly! 

Kitonum: Very illustrative! The animation will clearly show how the points are created one by one, using the golden angle. It also gave me the idea to add an animated gif to my webpage. 

My original idea was to somehow paint the solidcircles with different colors in order to more clearly illustrate the spirals going in one direction and the other spirals going in the opposite direction. I guess this is not easy in one figure, because every solidcircle needs both colors then. Another way could be to first create a figure showing the spirals going in positive direction by applying one color to every second spiral and another color for the spirals going in negative direction. Similar for a second figure displaying the spirals going in negative direction. From the numbering I can now identify the points on the indidual spirals. Not surprisingly the difference in numbering is 34 and 55 (Fibonacci Numbers!) for points on either kind of spiral. I will look into that. 

I wish you a happy New Year!

@mmcdara Thanks to both of you. I think the ColumnGraph is the appropriate command here, because I am not going to produce a Histogram by having something counted. I have the height of the columns already. Your file was however valuable afterall, mmcdara! I have tried writing the appropriate command for my easy purpose (see attached file).  I am however surprised that it cannot be done in a more easy default way - if that is the case. I have to fiddle with an offset option. I was expecting Maple to be able to easily produce a default plot with columns just by having the letters on the x-axis and the frequencies - and producing equally spaced columns with the letters in the middle. Or maybe I have overlooked something?

The help page for ColumnGraph wasn't to much help. In contrast to what is usually seen in the help pages, it started out with some very difficult scene, and it was hard for me to deduce anything at all for my easy situation - which again then doesn't seem to be that easy afterall. 


@tomleslie Yes it works that way, but still is using the properties of the normal distribution, i. e. the mean can be put "outside" which makes it possible to accomplish the job by just creating one single sample. Maybe I have confused the situation by connecting my more general question to this specific problem, which can be solved more easily. I think I will close my question here and get back if I later stumble upon a situation where this shortcut is not possible. 


Thanks to both of you, Carl Love and Acer. Very valuable information indeed.


@Daniel Skoog Thanks for the information, Daniel. 

@Kitonum Thanks a lot, Kitonum. I appreciate it!



@Carl Love Indeed very compact. Just what I was looking for. Thanks a lot!


@acer For the sake of completeness in this specific situation it would however be appropriate to have all possible values of X listed. Obviously the difference only show up for small sample sizes, where a frequency might turn out to be 0. 

@acer Thanks to both of you. It is also apparent that when choosing big samples, your code is qite a lot faster!


@acer In addition to your fine histograms, I wanted to calculate the actual sample frequencies. With your list M of possible values for the Random Variable X I did it this way:

Isn't there an even more simple way of doing it? I mean I was surprised not to be able to find a command in the Statistics package which could give the frequencies of a list of numbers right away. Maybe I overlooked something?


@mmcdara Very illustrative indeed!!

@acer Big thanks to you and mmcdara for a splendid work! It has certainly helped my investigations in the department of Random Variables. I guess it isn't possible to easily calculate the probability distributions of Random Variables built on other Random Variables in general. The possibilities are simply too complex. In the case of finite Sample Space you have however shown a way to search or go through all possible outcomes and that way get to the probability distribution. I think I am empty for more questions at the moment :)

@acer Your way of making an animation was indeed ingenious. So now my questions regarding samples are settled. 

I am still working on building intuition in relation to how Maple handles Random Variables. Beside being able to calculate Mean and Variance, I am interested in calculating probablities (including cumulative ones - CDF). In the present example with the player against the banker I cannot make it work. I receive a FAIL. I guess it happens because it is necessary to "invert the problem" internally and that Maple isn't capable of doing so - directly at least. In the following let X equal the profit in one play, viewed from the Players viewpoint. Manually one need to ask: What are the possible combinations of dice, which will yield the value 3 for X? The answer is (2,5), (3,6), (5,2) and (6,3). Each with probability 1/36, so the correct answer is 4/36. But Maple can't do it directly. Is there a smart non-ad hoc way to make problems like this work? (one which doesn't require the user to know the answer beforehand). I tried the technique with the old Random Variable Y = Dice1+Dice2, and it works! But here Maple doesn't need to do "back-tracking" in order to compute the probabilities ...



Best regards,



@acer That was impressing! I will have to look into that one tomorrow. Thanks a lot!


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