Teaching simple programming and Monte Carlo methods with Geogebra CAS

Ilpo Numminen shared this question 5 months ago
Answered

Hi!


I want to incorporate more programming to my math lessons & I wanna do this with Geogebra.


So lets say that I want to simulate this simple problem:

Roll two D20 dice. What is the probability that the geometric mean of these two dice rolls is a integer?

If possible, I want to do the following commands in CAS-view.


Geogebras Algebra has this variable: numberofsuccess:= 0

And now in to CAS-view

LINE 1. // a:=RandomBetween(1 ,20)

LINE 2. // b:=RandomBetween(1 ,20)

LINE 3. // sqrt(a*b) - floor( sqrt(a*b) )

LINE 4. // if( $3==0, numberofsuccess:=numberofsuccess +1 )

LINE 5. // command that repeats LINES 1-4 2500 times ??

LINE 6. // after this I can just do the division: numberofsuccess/2500 ... ... ...

OK the ROW 4 does not work because Geogebra "does not understand" c:=c+1 ... so first of all how do I do ROW 4? Can I utilise lists or spreadsheet in doing this?

Thanks already for your help.

Best Answer
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You make a list

MC:=Sequence(Zip(sqrt(A*B)−floor(sqrt(A*B)),A,{Random(1,20)},B,{Random(1,20)}),i,1,n)

CountIf(x ≟ 0,MC)

Or you want to write it to 1 line...

Do you want to test IsInteger() or mod(a,floor(a))=0

You should avoid to test difference =0

Comments (5)

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1

You make a list

MC:=Sequence(Zip(sqrt(A*B)−floor(sqrt(A*B)),A,{Random(1,20)},B,{Random(1,20)}),i,1,n)

CountIf(x ≟ 0,MC)

Or you want to write it to 1 line...

Do you want to test IsInteger() or mod(a,floor(a))=0

You should avoid to test difference =0

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1

Thank you! Works like a charm.


Can you elaborate a little bit why modulo is better than difference?

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1

As Michael told IsInteger() is not working in CAS you can use it in AlgebraView.


I dont know wether the calculation of difference with floor is exact (for sure not in AlgebraView) what will mean the difference not equals exact 0 (e.g. better to test abs(difference)<10^-15 ). Mod is a CAS function that hopefully works exact.

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2

all your commands work in algebra view. why we must to use CAS

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1

If you make long lists CAS is slow. Use Algerra View with long sequences.

M

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