Arsha Astronomy! ☀️🪐⭐⛈️

Arsha Astronomy

The word 'Jyotish' is often misunderstood as an exclusive fortune-telling branch. But in its true sense, fortune-telling forms a small part of this ancient branch of knowledge. Jyotish in Vedic context formed an important part of Vedic Literature and is considered as one of the six Vedangas (limb of Vedas) thus was attributed as the 'Eyes' of Vedas. It was imperative to understand these six Vedangas to delve deeper into Vedas. Out of the many sub- components included in Jyotish, Astronomy ( Siddhant) formed one of the most significant one.

The influence of celestial entities on various dimensions of human life was known to Vedic people since time immemorial. Movements of Sun, Moon, Stars and other entities played a very important role in the Vedic tradition. Even a superficial study of Vedic Literature points at knowledge of Solar year, Lunar year, constellations, eclipses etc existing in that era.

The Nidan sutra and Latyayan Srautasutra text of Samaveda have clear references to Solar and Lunar years of 360 days and 324/351 days respectively depending on the method of calculation. Due to the difference in the number of days in the Solar and Lunar calenders, an additional month was considered every 3rd year to bring uniformity in both the calendars and prevent widening of gap between both the calenders.This arrangement today is called as the Purushottam month or the Adhik month. As a result, we usually observe that Indian festivals usually fall around the same time in the modern Gregorian calender.

Aitreya Brahman and Kaushtiki Brahaman have clear indication of knowledge of winter and summer solstice and it was used extensively to decide timings of longer sacrifices. The year was divided into two halves of 6 months each; longer sacrifices (Mahavrata) were performed in winter-half while Vishuvat was observed in summer-half. Vedanga Jyotish also records the location of these solstices to be middle of Ashlesha constellation and Dhanistha constellation respectively, which coincides with the time period of that era.

Vedanga Jyotish had also calculated the duration of the day in both the solstices. The shortest day in winter-half is of 12 muhurats and in summer-solstice the longest day is of 18 muhurats ( Muhurat is a unit of Vedic time measurement which is equivalent to 48 minutes approximately).

Astronomy has always been an integral part of Indic tradition. It was not only highly instrumental in professions like agriculture and animal-husbandry but it also played a major role in determining the influence of these celestial bodies on one's day to day activities.


Dr. Karan Mittal
MBBS, MA(PSYCHOLOGY) , MA (SANSKRIT) 

The unknown History of Hypotenuse

The unknown History of Hypotenuse

"Sum of squares of two sides of a right-angled triangle is equal to square of its Hypotenuse ".... A theorem which we have learnt all throughout our school days, popularly known as the 'Pythagoras theorem' .
But, was there any reference to this great inseparable theorem of Geometry in ancient India?

The Shulba Sutras of Vedic Literature are the texts of Ancient Indian Geometry. Out of the many available Shulba sutras composed by different Rishis, Baudhayan Shulba sutra (c.800 BCE) has one of the earliest references to this theorem in context of Geometric applications.This was about 300 years before the date of historical Pythagoras of Samos.The verse in the text is as follows:

दीर्घचतुरस्रस्याक्ष्णया रज्जुः पार्श्वमानी तिर्यग् मानी च यत् पृथग् भूते कुरूतस्तदुभयं करोति ॥

A rope stretched along the length of the diagonal produces an area which the vertical and horizontal sides make together.
In other words: a2=b2+c2

Later in the course of time, Apastambha Rishi and Katyayan Rishi also give reference to these rules in their Shulba sutra texts and elaborate them further.

Although by the Sutra (Aphorism) nature of Shulba texts, its difficult to expect any elaboration of these rules in the texts. But, its certain that the composers of Shulba sutras definitely knew about this theorem.
An unique feature about the composers of various Shulba sutras was that all of them were Rishis and have various Ritual texts (Shraut sutras, Grihya sutras) attributed to them apart from these Geometric texts. Another unique feature being, these mathematical findings were made to arrive at accurate dimensions for creating Yagya Vedis for Fire sacrifices ( Such a high standard for perfection even in Religious rituals!!!). Since these fire rituals were necessary for all householders, it would be safe to assume that people in Vedic era knew the application of this theorem in construction of Yagya Vedis atleast.


There are definitely evidences of knowledge of Pythagorean triplets in Babylonian and Egyptian civilizations. Even the historicity of Pythagoras himself is debated in academic circles.
In Indic context,  with the passage of time, many Sutra texts of Ancient Indian literature have disappeared and many still remain untouched as manuscripts in various museums and libraries. There is still a huge amount of literature which needs to be studied and deciphered.

We as a civilization need to acknowledge our contributions to the journey of scientific achievements of mankind and strive to continue this legacy further!

Life of perfect irrational π

Bharat Musings

Life of perfect irrational π

Geometry lessons are always incomplete without the use of the unique number 'π'. As complicated as its multiplication is, so is its tradition of coming to the value of 3.1416.....

The earliest reference to this value is found in civilizations of Egyptians, Babylonians, Chinese and many more. But where is the contribution of India in this tradition? Have we read about the contribution of Indic scholars in this life of Pi or do we assume it to be completely a discovery of west? 

Indian Vedic literature's component 'Shulba Sutras' (c.800 BCE)  are ancient texts of Indian Geometry. Written for construction of altars for Yagya with precise measurements, these texts contain the earliest material of Indian Geometry. Each of the 4 Vedas have multiple Shulba Sutras under their domain attributed to various Rishis like Apastambha, Baudhayan, Manava and many more. 

The earliest approximation to the value of π in the Indic context comes in Shulba Sutras. Manava Shulba Sutras (c.750 BCE) has mention of approximate value of π to 3.125. In the Baudhayana Sulbasutra (c. 800 BCE) , various approximate values given are 676/225, 900/289 etc. In different Sulbasutras, the values 2.99, 3.00, 3.004, 3.029, 3.047, 3.088, 3.1141, 3.16049 and 3.2022 can all be found. There are various values of π given in Mahabharat, Shatpath Brahaman as well. 

Aryabhatta ( c. 400 CE) in his text Aryabhatiya gives the the accurate value of upto 4 decimal places and also mentions it to be an approximation ( recognising the never ending decimal places). The verse in Aryabhatiya is as follows :

चतुराधिकं शतमष्टगुणं द्वाषष्टिस्तथा सहस्त्राणाम्।

अयुतद्वयस्य विष्कम्भस्य आसन्नौ वृत्तपरिणाहः॥

Add 4 to 100, multiply by 8 and add to 62,000. This is approximately the circumference of a circle whose diameter is 20,000.

(100 + 4) x 8 + 62,000 = 62,832

62832÷20000= 3.1416 = π

Later in 14th century, Indian Mathematician, Madhav gave the correct value of π upto 11 decimal places. This was about 300 years before Gregory and Lebnitz proposed the series to arrive at the value of π. Therefore many historians now call this series of numbers as Madhav-Gregory-Lebnitz series. 

Bharat always had a rich tradition of Rishis who have contemplated on Philosophy and Science both together. The expert town planning of Indus Valley civilization points to existence of advanced mathematics in some form as well. It's essential that one recognises this rich scientific Indian heritage and takes pride in being one. 

Dr.Karan Mittal 

MBBS, MA (Clinical Psychology), MA (Sanskrit).