[Blindmath] Pascal's Triangle in Braille?

Thu Jul 31 18:44:05 UTC 2014

If I remember the triangle correctly, it looks somewhat like this (ignore centering in this version, it's not quite correct):
                   1
                1  2  1
             1  3  3  1
          1  4  6  4  1
         1  5 10 10 5 1

... etc.
I think it's easier to set this up on a brailler or a braille editor than to try to get a braille translator/formatter to do the right thing.
My advice would include:  reproduce only the second half of each row (perhaps including the number before the center line to show that it is repeated).
Assign the widest columns to the longest number you are going to be able to accommodate, and allow the width of your columns to get narrower as you approach the right end of a line.
Omit number signs, with the possible exception of the first 2 or 3 rows.
Consider producing longer rows on facing pages.
I don't know how many rows you could get this way, but think it would approach 13.  It could certainly illustrate the pattern of the numbers.

Lloyd Rasmussen, Senior Staff Engineer
National Library Service for the Blind and Physically Handicapped
Library of Congress   202-707-0535
http://www.loc.gov/nls
The preceding opinions are my own, and do not necessarily reflect those of the Library of Congress, NLS.

-----Original Message-----
From: Blindmath [mailto:blindmath-bounces at nfbnet.org] On Behalf Of Joseph Lee via Blindmath
Sent: Thursday, July 31, 2014 7:45 AM
To: 'Elise Berkley'; 'Blind Math list for those interested in mathematics'; 'Alexa Schriempf'
Subject: Re: [Blindmath] Pascal's Triangle in Braille?

Hi,
Pascal's Triangle describes a pattern for locating factorials, permutations and combinations. It is arranged like a pyramid, with the first entry being 1. Each level of the triangle describes the following: each row represents each number (1, 2, ... n), and each column describes the permutations. For example, if someone says, "what is 5 choose 3," then the person would look at the fourth column of row six (the top row is zero).
I think the simplest way to represent Pascal's Triangle in braille is not to use the visual layout; rather, start from the leftmost margin, with each line being a row from the triangle, with columns separated by a space.
Cheers,
Joseph

-----Original Message-----
From: Blindmath [mailto:blindmath-bounces at nfbnet.org] On Behalf Of Elise Berkley via Blindmath
Sent: Thursday, July 31, 2014 4:16 AM
To: 'Alexa Schriempf'; 'Blind Math list for those interested in mathematics'
Subject: Re: [Blindmath] Pascal's Triangle in Braille?

Okay.  I am claiming ignorance here.  I am not familiar with Pascal's triangle and I cannot get a visual of it.  Can someone help me a little bit here?  Or, if someone has a simple example in braille, I can pay for a copy in the mail?  This is interesting.  Elise

-----Original Message-----
From: Blindmath [mailto:blindmath-bounces at nfbnet.org] On Behalf Of Alexa Schriempf via Blindmath
Sent: Tuesday, July 29, 2014 7:15 PM
To: blindmath at nfbnet.org
Subject: [Blindmath] Pascal's Triangle in Braille?

Dear Listers:

Today I made a Braille version of Pascal's triangle for a student. Needless to say, because I could not adjust the font size of the Braille, and because our paper is 11 inches wide, I had some issues with recreating it with Duxbury and our embosser.

Pascal's Triangle is a very specific pattern of numbers, and the orientation of the numbers is carefully placed in a honeycomb pattern. To make 4 digit numbers fit in the honeycomb slot of the same size that holds a 1 digit number, typical images of Pascal's triangle simply use a smaller font size.
This does not work when using Braille of course.

I tried to put this in a table, but the table cells need to be staggered.
In the end, I I simply printed out each row and cut the rows into strips, taped the strips together where needed, and then glued the whole thing to cardboard.

However, while this will work for understanding some of the basics, it won't help where it's necessary to see how the numbers align physically on the paper because the inability to change the size and spacing of Braille dots means that I can't fit a four digit number to fit underneath a 2 digit number.

Surely, this learning object must already exist in Braille someplace?
Please advise.

Thank you so much!
Alexa
--
Alexa Schriempf, Access Tech Consultant
Office for Disability Services
Teaching and Learning with Technology: Accessibility Group Adaptive Technology Services, University Libraries Penn State https://sites.psu.edu/aschriempf/ http://equity.psu.edu/ods http://tlt.its.psu.edu/ http://www.libraries.psu.edu/psul/adaptivetechnologies.html
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