[Blindmath] Pascal's Triangle in Braille?

Fri Aug 1 16:48:48 UTC 2014

Good idea. Can you say more -- I'm visualizing printing this out on our
embosser. The embosser we have is an old express. As far as I know, I can't
print sideways (ie portrait vs landscape orientation). So I'm not sure how
I would print at 45 degrees?

perhaps I'm missing something?

thanks!

On Fri, Aug 1, 2014 at 12:42 PM, Dave via Blindmath <blindmath at nfbnet.org>
wrote:

> One of the key observations that makes the geometric or visual layout
> important is that the triangle is really an inverted tree.
>
> Any particular note of the tree can be calculated by summing its two
> children
>
>
>
> Here are some other ideas that you might consider.
> If you laid out the numbers in a tabular format, and simply had this
> student rotate the paper 45°, you could get all of the numbers in the
> triangle on one sheet of paper.
>
> To add even more rows, you could just attach additional papers that would
> fold out like a triangle, and continue the numbers that way.
> This has the obvious drawback that the numbers will be slanted, but you
> can go arbitrarily deep in the tree.
>
>
> From mobile
>
> > On Jul 31, 2014, at 12:26 PM, Elise Berkley via Blindmath <
> blindmath at nfbnet.org> wrote:
> >
> > Oh, okay.  I have a better idea.  Thanks everyone.
> >
> > -----Original Message-----
> > From: Blindmath [mailto:blindmath-bounces at nfbnet.org] On Behalf Of
> > Rasmussen, Lloyd via Blindmath
> > Sent: Thursday, July 31, 2014 11:44 AM
> > To: 'Joseph Lee'; 'Blind Math list for those interested in mathematics'
> > Subject: Re: [Blindmath] Pascal's Triangle in Braille?
> >
> > 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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-- 
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