Talk:Pascal's triangle

message: Hello, Iprogram with a much shorter, and, I hope, more comprehensible program. The goal here is to help people understand Pascal's triangle. I don't think the gyrations needed to get the numbers to line up were aiding that understanding. I also don't think the standard Java cruft (class name, imports, try/catch) was helping either. Anyway I'm sure that the floodgates are open now, and we're going to have 200 versions of this program in different languages... which is OK by me, as long as everybody is striving towards comprehension of Pascal's triangle. I claim the existing program is an improvement over the previous one. I don't claim it's the best possible. Happy editing, Wile E. Heresiarch 05:57, 8 Jun 2004 (UTC)
replies: text: As I mentioned on Wikipedia: Wikicode/Specification, I really don't mind you reverting to the Python code; in fact, I probably shouldn't have converted it in the first place, since it's against my policy of leaving real-language code alone. Sorry about that. Derrick Coetzee 17:57, 10 Oct 2004 (UTC)

text: So algorithms (though tied to a specific language) are not encyclopedia worthy? Cburnett 08:36, 6 Mar 2005 (UTC)
replies: text: I agree with Wile that the code does not add any information on Pascal's triangle. The algorithm, based on Pascal's identity is already explained in English in the lead section, and it is straightforward to translate it in a specific programming language. -- Jitse Niesen 15:23, 6 Mar 2005 (UTC)
replies: text:  I've cut the section with the computer code. As I said in the edit summary, "source code doesn't shed any light on Pascal's triangle, and it's a language war magnet". For what it's worth, Wile E. Heresiarch 15:14, 7 Mar 2005 (UTC)
thread_title: Code

message: A recent edit added, with citation: "As the proportion of black numbers tends to zero with increasing n, a corollary is that the proportion of odd binomial coefficients tends to zero as n tends to infinity." In trying to clean this up, I realized that I didn't know what "proportion" meant exactly.
Let O(n) be the number of odd binomial coefficients in row n, and let E(n) be the number of even ones.
It is not true that \lim_{n \to \infty} O(n) / (O(n) + E(n)) = 0, because all coefficients in row n are odd when n = 2^k - 1.
So is the claim instead that 
:\lim_{n \to \infty} \frac{\sum_{i = 1}^n O(i)}{\sum_{i = 1}^n O(i) + E(i)} = 0?
Mgnbar (talk) 12:06, 12 September 2023 (UTC)
thread_title:  Proportion of odd coefficients 

message: We probably should mention the Jia Xian triangle here as well. The Page Jia_Xian#Biography says about this relationship:
> Jia Xian described the Pascal's triangle (Jia Xian triangle) around the middle of the 11th century, about six centuries before Pascal. Jia used it as a tool for extracting square and cubic roots 
This appears to be a kinda important historical fact and probably should be included here as well. Agowa (talk) 01:22, 10 March 2024 (UTC)
replies: text: Jia Xian is already mentioned in the history section of this article.  According to what is written there, his name is not usually attached to it, even in China; do you have any sources that support the contrary view? (The only source in Jia Xian#Biography is not available online as far as I can see, so I am not able to immediately check what is written there.) --JBL (talk) 23:27, 10 March 2024 (UTC)
thread_title:  Mention Jia Xian triangle?