[OS X TeX] Thu 22 June: TeX Hour: Access and a Fibonacci wedding cake: 6:30 to 7:30pm BST

[Murray Eisenberg]

For some purposes it's more natural to arrage Pascal's triangle like this, where the successive "rows" of the conventional Pascal's triangle become the successive columns of the matrix:

1	1	1	1	1
0	1	2	3	4
0	0	1	3	6
0	0	1	3	4
0	0	0	1	1

Kenneth Iverson, a Turing Awardee, long advocated for that form of presentation. The form is the result of the following two commands in the J programming language (and similar to the situation with Iverson's original APL language):

	d =. i. 5			NB. result there is the list 0 1 2 3 4

	d !/ d			NB. result will be the table above.

Explanation: "/" is the "Table" adverb, which can modify verbs such as + (to produce an addition table) or * (to give a multiplication table) or, as here, the "out of" verb ! which gives the number of combinations.


> On Jun 21, 2023, at 1:49 PM, Jonathan Fine <jfine2358 at gmail.com> wrote:
> 
> Hi
> 
> This is an informal personal talk about the influence of accessibility on a math research problem, and vice versa. The problem is to define something like Pascal's triangle, but with the rows summing to the Fibonacci numbers. Such I call a Fibonacci wedding cake, as it is an elaborate tower made out of multiple tiers.
> 
> TeX Hour: Thursday 22 June, 6:30 to 7:30pm BST
> URL: https://texhour.github.io/2023/06/22/access-fib-wed-cake/ <https://texhour.github.io/2023/06/15/talmo-access-math/>
> Zoom URL: https://us02web.zoom.us/j/78551255396?pwd=cHdJN0pTTXRlRCtSd1lCTHpuWmNIUT09
> 
> Here's something that surprised me. Pascal's triangle can be presented in several ways. For a sighted person the usual way (using Markdown) is:
> 
> ||||| 1 |
> |||| 1 || 1 |
> ||| 1 || 2 || 1 |
> || 1 || 3 || 3 || 1 |
> | 1 || 4 || 6 || 3 || 1 |
> 
> The surprise was the thought that for a blind person (again in Markdown) this left-aligned form might be much better.
> 
> | 1 |
> | 1 | 1 |
> | 1 | 2 | 1 |
> | 1 | 3 | 3 | 1 |
> | 1 | 4 | 6 | 4 | 1 |
> 
> I'd very much welcome any feedback on access to number triangles. Although the Fibonacci wedding cake is connected to some advanced topics, no special knowledge of pure math is required for this talk. Just an interest in learning about and discovering patterns.
> 
> with best regards
> 
> Jonathan
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---
Murray Eisenberg		murrayeisenberg at gmail.com
Mobile (413)-427-5334
503 King Farm Blvd #101		
Rockville, MD 20850-6667	



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