Bhaskara II and His Timeless Contributions to Math and Astronomy

Bhaskara II was a great astronomer and mathematician of medieval India. The number II is added to his name to differentiate him from the earlier mathematician with the same name, Bhaskara. Bhaskara II’s monumental contributions in mathematics and astronomy spread far and wide, influencing scholars across cultures. His greamt stature led him to be called Bhaskaracharya, meaning “Bhaskara the Teacher.”

Early Life and Background of Bhaskara II

Bhaskara II was born in 1114 in India in Bijapur, Karnataka. He belonged to a Deshastha Rigvedi Brahmin family, a scholarly community known for their contributions to mathematics and astronomy. His father, Mahesvara, was an astrologer who taught him about stars and mathematics from a young age. As a young man, Bhaskara moved to the city of Ujjain, which was the leading mathematical centre of ancient India at that time.

In Ujjain, Bhaskara II became the head of an astronomical observatory and followed in the footsteps of great scholars like Brahmagupta, Shridhara, Mahavira and Padmanabha before him. It was in Ujjain that Bhaskara II carried out his most important work, studying both numbers and the night sky. Later, Bhaskara II is believed to have lived in the Sahyadri region, near Patnadevi in Maharashtra. Bhaskara II had a son named Loksamudra, who continued his father's scholarly tradition.

Scholarly Contributions of Bhaskara II

Bhaskara II carried out an enormous amount of work in mathematics. In total, Bhaskara II wrote at least six important works. He wrote his mathematical findings in Sanskrit verse, which was the style of most Indian scholars of the time. The verses made the rules easy to remember for students who learned by listening and reciting. He often included puzzles, riddles, and real-life examples. Some of Bhaskaracharya’s achievements are enumerated below.  

(a)   Lilavati

Bhaskara II wrote several books that explained mathematics in new and clearer ways. His most famous book is Lilavati, which means “The Beautiful”. Lilavati is a book on basic mathematics with 13 chapters and is written in the form of poetry with puzzles and problems. It covers many topics, such as arithmetic (related to numbers), geometry (related to shapes), and practical mathematics like money and measurement units.

According to a legend, Bhaskara named this book after his daughter, Lilavati, to console her after an unfortunate event. It is said that he had calculated an auspicious moment for her wedding using a water clock. However, a pearl from Lilavati’s dress dropped into the clock’s cup and blocked the water, causing the lucky hour to pass. The wedding was missed, and Bhaskara wrote the book to cheer up his heartbroken daughter. Although it is not known if this story is true, the Lilavati book became very famous.

(b)   Bijaganita

Another major book Bhaskara II wrote is Bijaganita, which means “Seed Counting” or algebra, a field of mathematics. In Bijaganita, Bhaskara explored more advanced mathematics such as equations and algebraic calculations. He built upon the work of earlier mathematicians like Brahmagupta and solved difficult problems that earlier scholars could not.

Like we use x and y in algebra today, Bhaskara II used words and abbreviations to represent unknowns. He could solve equations with more than one answer or even endless answers. There are some special and somewhat tricky maths problems with big numbers, called Pell’s Equations, that Bhaskara solved. If you are already familiar with algebra, here is an example: x² = 1 + 61y². Bhaskara solved these equations hundreds of years before European mathematicians!

(c)   Other Mathematical Accomplishments

From Decimals and Negative Numbers to Infinity! 

Bhaskara II used a decimal number system just like we do today—using digits 0 to 9 to write all kinds of numbers—both whole numbers and numbers with parts (fractions or decimals). Negative numbers are numbers less than zero that show things like temperatures below zero. Bhaskara II knew how to add, subtract, and multiply negative numbers and even explained that a negative times a negative equals a positive. 

Bhaskara thought about infinity—something that never ends, whether you go forward or backward. He said that if you divide a number by zero, you get something without limit, which was an idea ahead of his time.

Estimating Pi

The circumference of any circle, when divided by the diameter, always gives a special number, which remains the same for all sizes of circles. This number is denoted by the Greek letter π (pi). But knowing the exact value of π i is very difficult. Bhaskara worked out an approximate value of π. He used a 384-sided shape inside a circle and got π ≈ 3.141666, which is really close to the actual value!

(d)   Bhaskara as an Astronomer

Besides being a master of numbers, Bhaskara II was also a brilliant astronomer. Astronomy is the science of observing the sun, moon, planets, and stars. At Ujjain’s observatory, Bhaskara studied the movements of celestial bodies very carefully. In 1150, he completed his great treatise on mathematical astronomy, the Siddhanta Shiromani, which means “Crown of Treatises”. Aside from Lilavati and Bijaganita, the Siddhanta Shiromani is the third major work of Bhaskara II.

Bhaskara also created a simplified version of his astronomy book called Karana Kutuhala. This simpler book allowed other people to calculate planetary positions and eclipses in an easier way. He was also well-versed in astrology, which at the time was closely related to astronomy.

Ganitadhyaya, the third section of Siddhanta Shiromani, focuses on mathematical astronomy, such as positions of planets and eclipses. Influenced by Aryabhata and Brahmagupta, Bhaskara also thought that the Earth rotates on its axis. He made precise calculations of astronomical quantities, including an accurate estimate of the sidereal year, which is the time it takes for the Earth to orbit the Sun once, relative to the fixed stars. 

(e)   Bhaskara’s Wheel and Yashti-Yantra

Bhaskara II described a perpetual motion machine called Bhaskara’s Wheel around 1150 CE. It was a wheel with curved spokes filled with mercury, designed to keep spinning on its own without stopping. But today we know, from science and the laws of energy, that such a machine cannot work forever without losing energy. So, his wheel was an early idea or experiment in understanding motion. He also used a tool called the Yashti-yantra, which helped him measure angles in the sky. This tool, like a stick with markings, helped him study stars and planets.

Legacy and Recognition

Bhaskara II died around 1185 CE. During his life, he was respected as one of the greatest mathematicians of medieval India. Just a few decades after his death, a school was established in 1207 by Loksamudra's son, dedicated to preserving and teaching his works, that passed on his knowledge to future generations.

His books were studied for centuries in India. In the 16th century, parts of Lilavati were translated into Persian. Later, some of his works were translated into Arabic and English, making his ideas known beyond India. In the 19th century, British scholars translated his books, spreading his fame in the West.

Modern historians recognise Bhaskara II as a pioneer who developed ideas centuries ahead of Europe. His thoughts on zero, infinity, equations, and planetary motion were far ahead of his time. To honour him, the Indian Space Research Organisation (ISRO) named a satellite after him: Bhaskara-II in 1981. Today, colleges and science institutes in India bear his name, such as the Bhaskaracharya College of Applied Sciences in Delhi and Bhaskaracharya Pratishthana in Pune. Bhaskaracharya’s life continues to inspire students interested in mathematics and science.  

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