Since time immemorial farmers relied on astrologers and astronomers to tell them when to plant to take advantage of the monsoons. Depending on their culture, astronomers and astrologers were rewarded when their predictions were successful and punished when wrong, sometimes rather severely.

Patrons of Arts

Ancient Rome, India and France are examples where rulers, many benevolent, patronized philosophers, thinkers and artists living in their kingdom, and paid them handsomely to think, paint, predict and write.


Alexander the Great tried in vain to learn geometry from Euclid. Louis XIV had De Moivre, Lagrange, Laplace and many other luminaries in his court. King George III tried to learn mathematics from Leibniz. Jayachamachandra Wodiyar in Mysore, and King Verma in Travancore and Cochin patronized Asthana Vidwans (royal scholars) and mathematicians; Tippu Sultan who fought Jayachamarajendra’s grandfather, Krishnarajendra III (who allied with the British when they were getting their foot inside the rich Indian door) read Euclid at night. So did Lincoln: Abe studied Euclid by lantern light at night which explains, in part, his precise syntax and persuasive arguments to sway even his opponents.

Calculations of Motion

In determining and predicting eclipses, it is important to determine the true instantaneous motion of the planets or stars at any given moment. Tat-Kalika-Gati, or instantaneous calculation of motion, was probably first mentioned and used by Aryabhatta II, Brahmagupta II and Manjula around 1100 CE Bhaskara (1114 to 1185 CE) figured out formulas involving differentials, using the Chakravala method, which is defined as a cyclic method used to solve indeterminate quadratic equations. This knowledge is still a useful tool in today’s calculus theory.

Ghazni destroyed all the parchments of Brahmagupta when he gutted the town where Brahmagupta lived. Only recently, archeologists carefully unearthed parchment fragments of Brahmagupta’s writings which are now housed in the Oxford University Library.

It would have been a great loss for mankind, but for India’s rich oral tradition of memorizing and chanting to help remember information handed down through generations.

Can you imagine Jakanachari, the chief architect of Belur temples in Karnataka communicating the intricacies of design sculpted in stone (full of axi-symmetric tall columns—axi-symmetry is what you get from a potter’s wheel; rotation of the wheel helps the potter design symmetric pots) without using blue prints, emails, SMS, laser beams or even pencil and paper.

Plotting Planets

Historians may disagree on the origin of methods to predict eclipses. But related fields of arithmetic, geometry, metallurgy, and calculus were known to Indians at least 600 years before Europeans started even thinking about them.


A lunar eclipse occurs when Earth prevents Sun’s rays from reaching the Moon. Solar eclipse, on the other hand, happens when Moon prevents some parts of the Earth from getting total view of the Sun. Total eclipses occur when the three objects are in the same exact plane. If the objects do not line up exactly partial eclipses result.

Indians plotted the planet locations in a clever way. They used two stones of different heights whose top ends defined a direction pointing toward a planet, the angle determined by the distance between the stones.

They divided the planets into two types—interior, Mercury and Venus; and exterior, Jupiter, Saturn, Mars. Uranus and Neptune are recent discoveries. Poor Pluto; it is in and out and out right now. Only sometime in 2025 will it come very near Earth as Pluto takes 265 years to go around the Sun once in a bizarre way.

In a town in North Kerala, near the Karnataka border, stones seemingly planted randomly, actually turned out to be pairs of stones plotting the planet locations as seen from Earth. A Kerala astronomer, Parameswara, in the 15th century methodically recorded eclipses and planet locations for 55 years. The details of his observations are in his work Siddhantadipika.

The calculations involved multiplying the distance of the Sun from the Earth by the diameter of the Earth and then dividing the product by the difference between the diameters of the Sun and the Earth. The result is the length of the shadow of the Earth (i.e, the distance of the vertex).

It is true every culture, in every part of the world, had very intelligent people who devised clever ways of making daily lives useful. Bolivians, before the Spanish arrived, knew and built sound elliptic cones, long before Euclid gave the world the concept of ellipses.

I gratefully acknowledge all the eminent scholars for their presentations at the IIT, Gandhinagar conference, who inspired me to write this article.

Krishnamachar Sreenivasan teaches a freshman course at IIT, Ropar, in the Dept. of History and Social Science, that includes material in this article.

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