# Did the Indian Mathematician Aryabhata discover that the earth was round and calculate diameter of earth

Aryabhata was a genius mathematician, no doubt. But there is also the books about astronomy supposedly written by him. It is believed by Indians that he stated that earth was round. He belonged to 476 AD.

1. The earth is round from all sides

2. He had also accurately calculated the diameter of the Earth.
(Aryabhatattiyam, Chapter 1 — sloka five)

• en.wikipedia.org/wiki/Eratosthenes determined the circumference of the Earth 700 years earlier from measurements and mathematics... – user2276 Feb 21 '18 at 6:04
• Is certainly is possible at least since the Greek geographer Eratosthenes calculated the size of the Earth and the tilt of its rotational actions at around 200 BCE. Aryabhata made many more contributions to astronomy, quite more sophisticated ones, if the Wikipedia page is to be believed. – MichaelK Feb 21 '18 at 6:05
• I don't see what the notable claim here must be. Is there any doubt whatsoever that classical if not ancient astronomers determined far more complicated details than the earth's roundness and its approximate circumference and diameter? – Nij Feb 21 '18 at 6:40
• Frankly, a 12-year-old kid who lives near the ocean and can get close to ships could come up with a reasonable approximation of the circumference of the earth, using instruments constructed with sticks and nails. The two prerequisites of this are knowing the formulae for a circle and having the courage to believe that maybe other people are wrong. – Daniel R Hicks Feb 21 '18 at 13:19
• @HorusKol Strictly speaking that doesn't help answer this question though - OP doesn't ask if he was first. – arboviral Feb 21 '18 at 13:27

# What the text says

There is an English translation of The Aryabhatiya with notes is available online.

Regarding the spherical Earth, the text says (page 64 of the book)

The sphere of he Earth, being quite round, situated in the center of space, in the middle of the circle of asterisms, surrounded by the orbits of the planets, consists of water, earth, fire, and air.

Regarding the second claim, the text says (page 15 of the book)

A yojana consists of 8000 times a nr. The diameter of the Earth is 1050 yojanas.

A nr is the height of man. Assuming the men of Aryabhata's time were a bit shorter than at the present time, let us suppose this to be 1.6 meters. This gives one yojana as as 12800 meters. 1050 yojanas is then 13440 km. The actual diameter of the Earth is 12742 km.

# How accurate is this translation?

The translation I am using is a scholarly work published in 1930 by Walter E. Clark, a Professor of Sanskrit at University of Chicago. This translation was not made from original manuscripts, but from earlier published translations which were cross referenced with abstracts of Aryabhata's work by later Indian authors. The original manuscripts are listed in the preface of in the link; the later Indian commentators include Varahamihira's siddhantas, the Suryasiddhanta, Lalla's Sisyadhivrddhida, and Bramagupta's Brahmasphutasiddhanta and Khandakhadyaka.

For the first claim of a spherical Earth, Lalla's work summarizes this claim, attributing it to Aryabhata. It is also included by two other ancient writers.

For the second claim of the diameter of the Earth, both Brahmagupta and Lalla include the same calculation.

I searched for original manuscripts of The Aryabhatiya, but wasn't able to find anything. I don't read Sanskrit anyways, so I doubt finding an original manuscript would do me much good. However, since both claims are published in a scholarly work, and backed up by other ancient sources, both claims appear to be true.

• Because the question asks if he 'discovered' that the Earth is round, I think mention has to be made of Eratosthenes similar calculation, made 600 years earlier. While it is possible that Aryabhata did not know about Eratosthenes work, 'discover' is usually used only for the first person to find something out. – DJClayworth Feb 21 '18 at 23:34
• @DJClayworth The word 'discover' does not appear in the OP's linked claim. That site simply claims that ancient Indian science knew of it before Galileo and Copernicus in the 1500s. Perhaps the title to the question should be edited? – kingledion Feb 21 '18 at 23:42
• The description of the spherical earth in the middle of space is very similar to the models built by ancient Greek philosophers such as Aristotle. I would be surprised if there was no influence. – ugoren Feb 22 '18 at 7:49
• @kingledion Is there any mention of how he actually came to these conclusions? – Dudey Feb 26 '18 at 8:51
• @Dudey No. The text that survives reads like a powerpoint presentation. Clark and others suspect that it is just a summary of a longer original work, which just lists the conclusions, point by point, perhaps as some sort of teaching text. – kingledion Feb 26 '18 at 12:49

The roundness of the Earth was well-known in Greek Antiquity. For example, Aristotle gives three different arguments, circa 350 BCE. Besides the three in that article, he is apparently also responsible for the observation that ships disappear from the hull first. This suggests to me that any civilization capable of ocean navigation will come to the same conclusion.

On a charitable interpretation of measurements, Erastosthenes' calculation mentioned in the other answers is remarkably precise, but using a ship of known height enables anyone to make an order-of-magnitude estimate with elementary trigonometry.

• This is not relevant to the question as what is being asked is whether or not Aryabhata discovered Earth shape and calculated its diameter, not if others did it before him. – Samuel Churlaud Feb 22 '18 at 2:32
• Discover implies something unknown. That's like asking if my 8th grade geography book discovered the same data. It's in it, but it isn't a discovery. – Andrew Lazarus Feb 22 '18 at 15:59
• To be more specific, I don't find it credible that by the 5th Century, a civilization that bordered a large body of water and had ships could believe the earth was flat. Hence, any statement from such a time and place that the earth is round is a mere recapitulation of existing knowledge. – Andrew Lazarus Feb 22 '18 at 18:31
• Discovery doesn't have to be something unknown to all of humanity, there can be independent discoveries. One can also use it for something one didn't know, (example : "I discovered this shop around the corner"). In this context I don't see how Aristotle knowledge is relevant to Aryabhata except if he read it. Furthermore, observing the curvature of the sea doesn't prove the Earth is round, only that it is curved. Saying the Earth is round was certainly not "a mere recapitulation of existing knowledge" 15 centuries ago. en.wikipedia.org/wiki/Flat_Earth#South_Asia – Samuel Churlaud Feb 23 '18 at 19:08