# Questions tagged [ancient-india]

For questions about events occurring in India and the immediate areas around it between 2500 B.C. and 1500 A.D.

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### Did ancient/medieval non-European cultures have a concept of energy? If so, what are the similarities and differences to the modern concept?

For example, do we find something related to the modern energy concept in Ancient China, Ancient India, or the Islamic Golden Age? Among "similarities and differences", conservation is obviously ...
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### Why did India miss the Great Revolution in Maths and Science?

UPDATE: I've updated the title of the question from Why did India lag behind in discovering Maths and Science? to ...
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### Why do South Asians often use "lakhs" and "crores" instead of "millions"? What is the historical origin of this system?

I noticed that South Asians often write 10,00,000 instead of 1,000,000. My questions are: What is the origin of this special numbering system? Was there a more practical reason for having a special ...
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### Did Indian astronomers realize the sphericity of the earth independently of the Greeks?

Reading Wikipedia's articles on the flat earth, spherical earth, and history of geodesy makes it clear that virtually every society recognizing the spheroidal shape of the earth today owes the ...
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### When Indian mathematicians learn of Euclid's Elements?

Transfer of mathematical knowledge from India to Europe (such as a positional number system with zero) allowed Europeans to develop arithmetic. But was there also a reverse direction (probably via ...
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### History of summing integers with natural powers

In my 10th class school material, it is given that Aryabhatta discovered the following formulas: $\sum n=\dfrac{n(n+1)}{2}$ $\sum n^2=\dfrac{n(n+1)(2n+1)}{6}$ $\sum n^3=\dfrac{n^2(n+1)^2}{4}$ Is ...
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### First use of zero as a number

The first know use of $0$ as it's own number was in India, but what was the equation in which it was used? Also, what was the tablet/scroll/whatever about?
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### Do we have any in depth material on Baudhayana?

I know he wasn't strictly a mathematician, but as I understand, Baudhayana recorded information on (what we know as) the Pythagorean Theorem and other geometrical properties like $\sqrt{2}$, in the ...
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### Is it true that Aryabhata explicitly understood or stated the irrationality of $\pi$?

It is well known that Aryabhata, the prominent Indian mathematician and astronomer of the 5th century CE, made significant contributions to mathematics, including approximations of $\pi$ (pi). In his ...
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### Yuktibhāṣā, 16th century, first modern proof of $\frac{\pi}4=\int_0^1 \frac{dt}{1+t^2}=\sum_{n\ge 0} \frac{(-1)^n}{2n+1}$

It is an Indian (Kerala) text, it would be the first modern proof (based on earlier knowledge) of $$\frac{\pi}4=\int_0^1 \frac{dt}{1+t^2}=\sum_{n\ge 0} \frac{(-1)^n}{2n+1}$$ The integral would be a ...
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### Is it possible to narrow down possible dates for the following eclipse pattern?

I am searching for an year which satisfies the following criteria. Dates are in Gregorian calendar. Criteria Year range 3800 BC to 500 BC Solar Eclipse of any kind between October 14 and October 22 ...
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### Did the Maclaurin series for sine and cosine unsettle Indian mathematicians?

As many of you may know, sometime around the 14/15th centuries an Indian mathematician by the name of Madhava of Sangamagrama derived the Maclaurin series for sine and cosine for the first time in ...
1 vote
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### What is the Expected Durability/Digitization Efforts of Pre-Hellenistic works that are made from Materials like Papyrus, Bamboo, Bark, Stone, e.t.c?

Currently, I am reading "Foundations and Fundamental Concepts of Mathematics Third Edition" by Howard Eves, and I have came across this paragraph: In our study of early mathematics we are ...
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1 vote
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### When was the first time the number 0 came to mean a multiple of ten? [closed]

The earliest number notation I can find is the sexagesimal digit notation of cuneiform. From my understanding of that, in order to make numbers bigger than 60, you would just add the smaller numbers ...
1 vote
125 views

### What would be some earlier comments on "1+2+3+4=10"?

"1+2+3+4=10" is an arithmetical triviality that is popular as an example of Pythagoreanism. There seems to be no mention of it in ancient Greek texts prior to Speusippus (e.g. ca. 350BCE; ...
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### Did Baudhayan publish Pythagoras theorem before Pythagoras?

In NCERT textbook for class X mathematics, it is given that Baudhayan gave the relation between the hypotenuse square and sum of squares of the other sides of a right angled triangle. Is it true? ...
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178 views

### What is the intuition behind Brahmagupta’s rule for multiplying negative numbers?

The rule says: The product (or quotient) of two debts is a fortune What I’m struggling with is what exactly is the product of two debts? What accounting need forces one to multiply debts? How do ...
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### How the ancient iron Pillar of Delhi was created?

Afaik, even in the middle ages was it impossible to melt iron. Thus, alloys had to be also impossible. Next to that, the ancient Indians surely didn't knew nickel, which is alloyed into the today's ...
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### Group theory in non-European/subaltern cultures?

I'm doing undergraduate research on the history of abstract algebra (specifically permutation groups) and the notion of symmetric groups in indigenous artwork has come up several times. Is anyone ...
As in what were the main factors, personalities, policies, etc involved in its decline during the $16^{th}$ century to the present day?