As the sun eclipses the stars by his brilliancy, so the man of knowledge will eclipse the fame of others if he proposes algebraic problems, and still more if he solves them.
-Brahmagupta
Ancient Indians gave utmost importance to mathematics due to the belief that it codes nature's laws. The Vedanga Jyotisha, a text of astronomy that is at least 3200 years ago, declares that mathematics is at the head of all knowledge.
The earliest evidence of this mathematics is found in the 2nd millennium-BCE text Shatapatha Brahmana and in the later Sulbasutras prescribing techniques for the construction of fire altars. Using simple tools of ropes and stakes, the altar builders created complex geometric forms, and they solved problems such as that of transforming one plane figure into a different one of equal area. They were aware of the Pythagoras theorem, knew values for the ratio of the circumference of a circle to its diameter (i.e., π), and values for the ratio of the diagonal of a square to its side.
Much of our knowledge of classical Indian mathematics is supplied by astronomical texts and other texts dealing with music, permutations, and business applications.
Brahmagupta (born 598 CE) speaks of the distinction between pati-ganita (arithmetic) and bija-ganita (algebra).
The Vedic view sees reality as a play, and consistent with that mathematics was introduced to the student in an engaging manner through stories.
Bhaskara II (12th century CE) wrote a charming book called the Lilavati for his daughter, which contains many interesting poems that pose mathematical problems. Here is one poem from Lilavati:
A fifth part of a swarm of bees came to rest on the flower of Kadamba, a third on the flower of Silinda. Three times the difference between these two numbers flew over a flower of Krutaja, and one bee alone remained in the air, attracted by the perfume of a jasmine in bloom. Tell me, beautiful girl, how many bees were in the swarm?
The problems of Lilavati are for recreation and mental stimulation. Chandrahas Halai's My Mathematical Musings carries the old Indian tradition of recreational mathematics forward. I trust that it will not only bring pleasure but also inspire the reader to plunge into doing useful mathematical problems.
Prof. Subhash Kak is Regents Professor Emeritus at Oklahoma State University in Stillwater and Distinguished Academic Scholar at Chapman University in Orange, California.
He is the author of thirty books that include Mind and Self, The Wishing Tree, and The Circle of Memory. He is a member of the Indian Prime Minister's Science, Technology and Innovation Advisory Council (PM-STIAC).
"I am pretty bad at Mathematics."
"I am afraid of Maths."
"I hate Mathematics."
"Maths is abstract and boring."
"What is the use of all these Maths we are forced to learn?"
"How do we apply Mathematics?"
The These are the responses or shall I say reactions of most of the people whenever I am introduced to them as a Mathematician or as an author of books on Mathematics.
Please note Mathematics on the contrary is the most fascinating, practical and significant of all the subjects. always say that Mathematics is the most refined way of thinking.
This book showcases the beauty of mathematics to the reader. This book is a compilation of my articles / papers on mathematics, especially recreational mathematics, which shows the reader that they can have fun with maths while learning it, applying it or while solving challenging problems. There is something in this book for everyone.
I have collected these gems of mathematics from number of sources on mathematical curiosities, puzzles, challenging problems and recreational mathematics right from my teenage.
In my school days I used to read a science magazine for teenagers called "Scifun". In one of its issues, published in 1986, I came across an interesting problem. I tweaked and raised the levels of challenge of that problem. That is presented as the chapter 13, "How Many Measures of Oil?".
In the year 1989, my brother Sanjeev had challenged me with a puzzle, which forms the chapter 16, "Red or Blue?".
The Handshake problem given in chapter 5, "Handshakes" was posed to me as a challenge by Dr. Prasanna Dabholkar in the year 1992.
I received a number puzzle in the year 2015 as a WhatsApp forward. This is now chapter 1, "Finding a Needle in a Haystack".
The puzzle of Chapter 15, "When is the Bus?" was forwarded to me by Sanjeev during the lockdown days of April 2020.
The problem "What's the Area?" from Chapter 18, was forwarded to me by Mr. Suresh Jani in the year 2022.
The problems of chapter 2, "Mathematics of Single Elimination Tournaments" and chapter 19, "Mathematics in Motion: Von Neumann and the Fly Dilemma" were posed to me by my Guru and mentor late prof. Bhalachandra A. Naik.
This book was written to ignite the minds of the reader and develop a liking for mathematics in them. Solving the problems given in this book can improve your problem-solving skills.
I hope you have as much fun while solving these problems as I had writing about them.
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