Talk:Pingala

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Can anyone provide independent confirmation or an independent reference for any of this? Google only has pages based on Wikipedia; Britannica has nothing at all.--Niels Ø 20:00, Jun 15, 2005 (UTC)

I searched through MathSciNet and found 10 reviews mentioning Pingala including:

• Datta, Bibhutibhusan; Singh, Awadhesh Narayan; Use of permutations and combinations in India. Indian J. Hist. Sci. 27 (1992), no. 3, 231--249.
• Kak, Subhash; Computational aspects of the \=Aryabha\d ta algorithm. Indian J. Hist. Sci. 21 (1986), no. 1, 62--71.

However, I didn't get the papers. -- Jitse Niesen (talk) 14:29, 5 December 2005 (UTC)

• The book Indian Mathematics and Astronomy by Dr. Chandrashekar a proffessor of Mathematics, contains Sanskrit verses from Pingalas writings unfortunatly soft copy of the same is not available.

~rAGU 16:42, 7 December 2005 (UTC)

the article seemed to confuse the 10th century commentary with the actual work. "zero as a dot" certainly refers to the 10th century work, as does Pascal's triangle. I'll try to unearth an edition or a scholarly discussion of the text, but so far the content of the article is entirely anecdotal. dab (ᛏ) 09:10, 8 April 2006 (UTC)

9th century or earlier?

Sorry, the "Varahamihira" in my edit summary was a mistake. I meant Brahmagupta. Most sources say that the first inscription showing the use of positional zero is from the 9th century (Gwalior). However, no historian would ever claim that this means that zero was invented in the 9th century. There are enough other convincing evidences, and most historians believe that by the 6th century, zero as a positional numeral was very much in use. For example, Brahmagupta from the 7th century explains all the arithmetic of zero that we know today (except he messes up 0/0) in his book Brahmasphutasiddhanta. It is also recognized that Al Fazali translated this book into Arabic in the 8th century. It is very likely that Brahmagupta was not the inventor either, but just reported in the text a mathematical artifice that was in contemporary use. deeptrivia (talk) 17:03, 11 April 2006 (UTC)

you are confusing positional and arithmetical zero. We have discussed this at length at the numeral system articles. Brahmagupta in the 6th century certainly knew the arithmetical concept. There is still no evidence of positional zero predating the 9th c., and I am very doubtful that "most historians" believe that positional zero dates to the 6th c.; while it is not inconceivable that positional zero was introduced earlier than the 9th c., say 8th or 7th c., it is patently false to claim that "no historian would ever claim positional zero was invented in the 9th c.", let alone because of the work of Brahmagupta , which is entirely irrelevant to the question. dab (ᛏ) 17:18, 11 April 2006 (UTC)

Basic ideas of Fibonacci number

I do not understand the claim that the commentary includes the "basic ideas" of the Fibonacci numbers. In what sense does it contain the basic ideas, but not a description of the numbers themselves? (You would not reasonably refer to all theory around or applications of the Fibonacci numbers; since that would disqualify Fibonacci himself.)-JoergenB (talk) 21:09, 12 January 2008 (UTC)

Pascal's triangle?

Is the image of Pascal's triangle added in this edit really from a preserved text by Pingala from 200 BC? Otherwise, the text and caption (and image desciption at meta) should clarify where it is from and how it is believed to relate to Pingala. Nø (talk) 07:31, 17 October 2023 (UTC)

I replicated the "description" field of the image at commons. Its source field links to https://archive.org/details/ChhandaSutra-Pingala/page/n203/mode/2up which seems in Hindi language, which I can't read. The text may, or may not, refer to a preserved text by Pingala from 200 BC - I hope somebody else will be able to check this. - Jochen Burghardt (talk) 07:51, 17 October 2023 (UTC)

To: @Nø and @Jochen Burghardt

I apologise for creating ambiguity through the edit. Well, for clarification, the image appears to have been taken from a later version of Pingala's original composition not from a preserved text. I mean, this work was probably written post 1000 CE... It is Sanskrit (not Hindi) in the Devanagari script. The original version might have been passed on orally for some time before it was written down in some other script and transliterated in Devanagari.

The title reads, "Vargā Meruḥ", which means, "The Squares of Meru".

The words on the left of the table read, "Ekākṣarasya Prastāraḥ", "Dvayakṣarasya ...", etc, meaning "The Step of the First Letter", "... of the Second Letter", etc as I interpret it.

The numbers in the boxes are

1

1 1

1 2 1

(etc.)

The numbers to the right of the boxes are the sums of the number in each row, i.e., 2, 4, 8, 16, etc, with the sum of the 0th row being omitted.

I agree it was my fault to not have mentioned that it appears in a version jotted down more than a millennium after the composition of the text.

As per my knowledge, the diagram is based on poetic descriptions from the verses of the text, and so it should be understood that the diagram was not drawn in the 2nd century BCE, but was mentally visualised.

If you consent, I could add the image back with an updated caption, otherwise I shall leave it.

One more thing...

The description at Commons should read:

"Pascal's Triangle as depicted in the Chandas Shastra, composed by the poet Pingala around 200 B.C., but written many centuries later."

I will change it after posting this message.

I also apologise for the unreliably-sourced highly-assertive claim of "binary digits"...

Thanking you,

Yours faithfully,

 Felixdor  (talk) 16:09, 10 April 2024 (UTC)

Be bold :-) Nø (talk) 07:29, 11 April 2024 (UTC)

Thank you :-)

 Felixdor  (talk) 09:44, 11 April 2024 (UTC)

Binary numbers?

Earlier than Pingala's, I Ching also has a representation or an arrangement that can be interpreted as binary numbers. However, I think neither I Ching nor Pingala actually have binary numbers - they do not (I think) actually relate their binary representations to numbers in general, or suggest their use to represent numbers outside of their respective limited contexts. Nø (talk) 07:35, 17 October 2023 (UTC)