# Pascal's triangle

Paul Barton shared this question 11 years ago

I have developed a dynamic version of pascal's triangle, but would like it to be able to toggle between a version of pascal's triangle that shows numbers and one that shows binomial coefficients. Nearly everything is in place, but I am having trouble making Geogebra display a formatted list of texts that contain Latex. At present i get unformatted binomial coefficients.

Drag the slider entitled NumbersOrCoefficients and you will see the issue I currently have.

To generate the binomial coefficients, I am using the Geogebra Text command inside the Geogebra Sequence command. See properties of L_10.

My aim is to be able to demonstrate the properties of pascal's triangle, first by observing number patterns and then switching to the binomial coefficients. I realise I could just insert the first 10 rows of binomial coefficients individually and set their positions via the properties dialogue box but I was hoping for a more elegant solution using a list.

Any ideas?

Thankyou.

Paul.

https://ggbm.at/542075

1

I'm not sure that's possible at the moment. I'll have a think tonight for a solution, but you may be able to achieve what you want using unicode fonts instead:

superscripts = {"⁰", "¹", "²", "³", "⁴", "⁵", "⁶", "⁷", "⁸", "⁹"}

subscripts = {"₀", "₁", "₂", "₃", "₄", "₅", "₆", "₇", "₈", "₉"}

1

Is this what you wanted?

I used '_' instead of '^'

Tony

https://ggbm.at/542077

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Thanks Tony, but I actually wanted the number preceding the capital C to be a superscript.

Murkle, I read in some Latex or Tex documentation about a command named \binomial{}{} that seemed to format the text in the way i wanted it but when I tried it was unsuccessful. I guess this is the same issue as I am currently having with attempting to use Latex as an argument in the Text command?

Unicode is probably what I need to try. Where do i get a list of the unicode characters? Google it?

Thanks.

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Unicode is probably what I need to try. Where do i get a list of the unicode characters? Google it?

Yes... or just cut and paste from my last post :)

1

HI

Itmay be works

Daniel

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Just curious .... using superscript in combination notation is rarely seen in U.S. schools. Is this a common notation in other countries?

1

Hi,

Just checked a couple of UK textbooks - looks like superscript and subscript, or two subscripts, or nCr are all used! Plus, of course, the column vector form, with curved brackets (braces?)

Kathryn

1

Alternative notations include C(n, k), nCk, nCk, \scriptstyle C^{n}_{k}, \scriptstyle C^{k}_{n},[2] in all of which the C stands for combinations or choices. {Wikipedia, image}

I see the different styles in Wikipedia, is there any historical reason to use one over one of the others?

Tony

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Sorry everyone for my tardiness in replying. I have been on a school camp for the last 3 days.

Regarding the different notations used for binomial coefficients: It is just the notation used in our syllabus document, so all the texts in Australia use it too. I am not sure if there is a historical reason for this.

I was wondering if there was a reserved word for indicating that what follows was a Latex string. I tried it but it doesn't work either.

Paul.

1

{^n}C_r

Just tried this in GG and it works, I have not tried it in your applet however as I prefer the rewrite that I gave you.

Source of Code after the following Google search:

latex math symbols scriptstyle binomial coefficient
it is first entry.

Tony

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Alternative notations include C(n, k), {^n}C_r, _n C_r, \scriptstyle C^{n}_{k}, \scriptstyle C^{k}_{n}.

Although I know you want to use the syntax of your texts, but I have tried to implement it into applet the LaText form {^n}C_r. I have been unable to do so. But this could be a teaching moment by adding the above as a statement on the page.

"Alternative\;notations\;include\;C(n,k),\;{^n}C_r ,\;_n C_r,\;\scriptstyle C^{n}_{k},\;\scriptstyle C^{k}_{n}"

Of course, you must check LaTex.

Tony

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Thanks Tony. I'll give it a try.

Before I read your latest post I used Murkle's superscripts and subscripts lists with some further List commands to develop the formatting I required. This did create extra lines of code but it worked OK. The fonts in these superscript and subscripts lists were inconsistent so the finished product is not perfect but it would suffice. I'll post it later. Haven't got it with me right at this moment. Hopefully your method can reduce this extra code and remove the inconsistency in the fonts.

Thanks again.

Paul.

1

Here is the latest version of pascal's triangle promised in my last post. If you wish to see more rows of the triangle increase the maximum value for the slider NumberOfTriangleEntries. You will be restricted by the number of rows you can see as the numbers become so large that they will overlap and they will disapear below the bottom of the screen. If you really wish to see particular entries of more rows you can use the zoom and move drawing pad tools. However doing this will not allow you to see the entire triangle. In theory you could use this sketch to generate the first 999 rows of pascals triangle. The lists of superscripts and subscripts I generated from Murkle's original lists of 10 numbers will prevent any more rows from being generated although these could be extended further if anyone feels the need. I have not attempted to generate more than about 50 rows as I fear the processing time will slow down significantly. I have included a US and UK version of the coefficients. For completeness, I would like to have included the vector notation of the coefficients but as yet I still cannot work out how to include Latex templates as the text argument (or attribute) in the Geogebra Text command.

i.e. Text[<text>,<position>,<true or false>].

In case anybody wants it I have also included my original attempt at pascals triangle that generates pascals triangle one row at a time. This file does not have the coefficients representation, as it did not suit my requirements.

Enjoy.

Paul Barton.

https://ggbm.at/542149

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:D 8)

Fantastic work...I would like to post on my web site with your permission...

Thanks for all of your hard work.

Tony

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Here's another workaround, not elegant at all, but works.

https://ggbm.at/545301

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Here are some files demonstrating some of the patterns in Pascals triangle. I was trying to demonstrate these to my classes and that was my motivation for creating them inthe first place.

Since I started thinking about creating these files I have since learnt a lot more about working in geogebra and you'll notice that there are a lot less lines in the construction protocol.

Unfortunately, I have not had the opportunity to use these in a class yet so I would appreciate any feedback on their effectivness. Also any improvements or constructive critisms welcome.

THERE ARE MORE FILES IN THE NEXT POST.

Enjoy

Paul.

https://ggbm.at/550411

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TWO MORE IN THE NEXT POST.

https://ggbm.at/550417

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Last two files

https://ggbm.at/550421