[Blindmath] Pascal's Triangle in Braille?

Alexa Schriempf ats169 at psu.edu
Fri Aug 1 21:01:12 UTC 2014 

Ah, I see what you mean. Hmm. At that point, I'd move towards using a
Braille label maker to make each number, and stick each label inside a
printed line drawing, on very large paper. The problem is the 3 and 4 digit
numbers that take up more space than the single digit numbers.

Thank you all for the ideas! Have a good weekend,
Alexa


On Fri, Aug 1, 2014 at 1:21 PM, Dave <davidct1209 at gmail.com> wrote:

> Apologies for the more than likely upcoming typo since I'm on my phone.
>
> Suppose that you list the numbers in the following fashion in a tabular
> format.
>
> 1 1 1 ...
> 1 2 3 ...
> 1 3 ...
> 1 ...
>
>
> Are the first three rows of the triangle. If you printed this table out,
> and just rotated the page 45° clockwise, you will have the beginnings of
> pascals triangle. Again, this has the obvious drawback that the numbers
> will be slanted in either print or Braille. You will also have to ensure
> that each box containing the numbers (the cells of the table) are even we
> spaced.
>
> From mobile dictated
>
> On Aug 1, 2014, at 9:48 AM, Alexa Schriempf <ats169 at psu.edu> wrote:
>
> 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
>
>
>


-- 
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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