You are currently browsing the tag archive for the ‘geometry’ tag.

This is a story from long time ago. You’ll have to go back to a sunny day in the middle of 12th century, to the grand old city of Ujjain in central India. It was to be a memorable day in Leelavati’s life. A day that was expected only once in a girl’s life time – the day when she would be the bride. The day when the groom would tie the golden bridal necklace around her neck. The time had been carefully chosen. You know, the bride’s father was none other than Bhaskara Acharya – Or “the learned teacher Bhaskara”, who was considered as one of the very best mathematician, astronomer and astrologer during those times.

Bhaskara was immensely happy when his daughter Leelavati was born. As was customary in those times, he prepared a chart of planetary positions at the time of his daughter’s birth. When he saw what those positions predicted, he really had to start worrying because the positions indicated the girl would never get married. But how could he not marry off his daughter? Marrying off ones daughter was considered as one of the most critical duties of a family man. Giving the hand of a daughter to a suitable groom was a guaranteed way for a good place in the heavens after death.

But Bhaskara did not leave this worry affect his bringing up of the little child Leelavati. Life went on as usual and Leelavati grew to become a young beautiful and intelligent girl. Bhaskara did leave no effort in educating her with the arts and sciences he was proficient at.  There qas no paucity of material to be taught. Leelavati was especially fond of mathematics, and Bhaskara would often compose terse verses with mathematical problems and ask her to solve.

When it was the appropriate age for Leelavati to get married, her father dug into his books again to see if there was a way to get her married, in spite of the shortcoming in her planetary charts. Finally, after careful evaluation, he found an auspicious time, when all the planets would be at the right locations conducive of a long, happy married life. But time was of the essence, and he had to make sure that the wedding ceremonies began exactly at the prescribed time.

Bhaskara went off to search for a suitable match for his girl. He found a groom to his daughter’s and his liking. All arrangements were made. The wedding hall was decorated with flower garlands. The water clock was also brought to the wedding hall to make sure that the ceremonies began at the right time. The water clock consisted of a big pot of water, in which a metallic bowl of accurate size, shape and weight that had a small hole of accurate dimensions at the bottom would float. Water would constantly come up into the floating bowl filling it up with water, and ultimately sinking it down, which acted as an accurate time marker.

Young Leelavati, still curious at heart, wanted to take a peek into the new water clock that was brought into the wedding hall. When no one was looking, she went near the water clock and peeped inside, and as luck would have it, one of the pearls from her nose ring fell into the floating bowl and covered the hole at the bottom. Unluckily, Leelavati did not take note.

Everyone was waiting for the arrival of the groom’s family, so that the wedding ceremonies might start at the appointed hour. Bhaskara went and checked the clock and was satisfied to see that the appointed hour had not come, because the bowl was still floating. After a while, he checked it again, again to see the bowl at the same position. Now he was sure something had gone terribly wrong. He looked carefully, and saw the pearl that came in between his daughter and her marital bliss, by getting stuck in the hole in the bowl and thus making the auspicious hour pass. The planets had indeed foretold the truth. The groom’s family did not make it to the wedding venue after all.

Bhaskara became sad for a while, but he was a learned man. He went to his daughter Leelavati, and said: “Oh my dear girl, don’t worry. I wanted to get you married so that you could have a family of your own, have good children who would carry the family’s name. But the planets proposed something else. I don’t consider this a defeat. I will make your name immortal”.

He then went on to write a book, which comprised of all those problems that he was giving his daughter, which she was very fond of solving. It had 278 verses, dealing with different fields in mathematics like arithmetic, geometry and algebra. And he called this book after his little girl “Leelavati”, and making his girl immortal as he promised.

Here is one verse from Leelavati (on calculations involving fractions) translated by your truly:


ಬೇಟದಾಟದಲಿರೆ ಇನಿಯ ಇನಿಯೆ, ಮುತ್ತಿನ ಸರವವಳದು ಹರಿಯೆ
ಮೂರಲ್ಲೊಂದು ಉರುಳಿದವು ನೆಲಕೆ; ಐದರಲೊಂದು ಹಾಸಿಗೆ ಕೆಳಗೆ;
ಅವಳು ಹುಡುಕಿದಳು ಆರಲ್ಲೊಂದು; ಇನಿಯ ಹೆಕ್ಕಿಹನು ಹತ್ತರಲೊಂದು
ದಾರದಲೀಗ ಉಳಿದರೆ ಆರು, ಸರದಲಿ ಮೊದಲೆಷ್ಟು ಮುತ್ತಿದ್ದಾವು ಹೇಳು!

ಸಂಸ್ಕೃತ ಮೂಲ: 56th verse of Leelavati

ಹಾರಸ್ತಾರಸ್ತರುಣ್ಯಾ ನಿಧುವನ ಕಲಹೇ ಮೌಕ್ತಿಕಾನಾಂ ವಿಶೀರ್ಣೇ
ಭೂನೌ ಯಾತಾತ್ರಿಭಾಗಃ ಶಯನತಲಗತಃ ಪಂಚಮಾಂಶೋಂಸ್ಯ ದೃಷ್ಟಃ |
ಪ್ರಾಪ್ತಃ ಷಷ್ಟಾಃ ಸುಕೇಶ್ಯಾ ಗಣಕ ದಶಮಕಃ ಸಂಗ್ರಹೀತಃ ಪ್ರಿಯೇಣ
ದೃಷ್ಟಂ ಷಟ್ಕಂಚ ಸೂತ್ರೇ ಕಥಯ ಕತಿಪಯೈಃ ಮೌಕ್ತಿಕೈರೇಷ ಹಾರಃ ||


p.s: The skeleton of this narration is based on Indian folklore – but the details are my imagination.
p.p.s: This post came from the script of speech I gave at my Toastmaster’s club (And won the best speaker of the day too!)
p.p.p.s: Solving the puzzle of pearls is left as an exercise to my readers 🙂


  • 720,760

My book “Hamsanada” for iPad, iPhone or iPod

A Collection of  Samskrta Subhashitas, translated to Kannada

My Book, on Google Play!

My Book Hamsanada, on Google Play

My Book Hamsanada, on Google Play

Enter your email address to follow this blog and receive notifications of new posts by email.

Join 5,032 other followers

ಅವಧಿಯಲ್ಲಿ ಹೀಗಂದರು:

"ಅಲ್ಲಿದೆ ನಮ್ಮ ಮನೆ…ಇಲ್ಲಿ ಬಂದೆ ಸುಮ್ಮನೆ… ಎಂಬ ಘೋಷ ವಾಕ್ಯದೊಂದಿಗೆ ಬ್ಲಾಗ್ ಮಂಡಲದಲ್ಲಿ ಕಾಣಿಸಿಕೊಂಡವರು ನೀಲಾಂಜನ. ಅಲ್ಲಿದೆ ನಮ್ಮ ಮನೆ ಕನ್ನಡದ ಪರಿಮಳವನ್ನು ಇಂಗ್ಲಿಷ್ ನಲ್ಲಿ ಹರಡುತ್ತಾ ಇದೆ. ಕನ್ನಡದ ವಚನಗಳು, ಸಂಸ್ಕೃತ ಸುಭಾಷಿತಗಳು ಜೊತೆಯಲ್ಲೇ ಸಂಗೀತ ಹೀಗೆ ಹಲವು ಲೋಕವನ್ನು ಈ ಬ್ಲಾಗ್ ಪರಿಚಯಿಸಿದೆ." ಅವಧಿ, ಮೇ ೧೫, ೨೦೦೮

ಇತ್ತೀಚಿನ ಟಿಪ್ಪಣಿಗಳು

Manjugouda police pa… ರಲ್ಲಿ Ugra Narasimha of Vijayan…
neelanjana ರಲ್ಲಿ Samasya Poornam – Part…
neelanjana ರಲ್ಲಿ Samasya Poornam – Part…
charukesha ರಲ್ಲಿ Where in the World is Mount…
ನೇಸರ್ ರಲ್ಲಿ Samasya Poornam – Part…
ಜುಲೈ 2020
ಸೋಮ ಮಂಗಳ ಬುಧ ಗುರು ‍ಶು ಶನಿ ಭಾನು

ಬಗೆ ಬಗೆ ಬರಹ