Indian Mathematicians came up with many concepts of math while performing their daily duties. From the discovery of zero to advanced arithmetic calculations, daily life activities helped them come up with these various concepts.
Many of us hate the subject due to its complexity and are glad that it ends with high school. But does it really? Math is present in every thing we do. Before we learn of the number of ways math accompanies us throughout the day, we shall learn of the contributions of Indian mathematicians.
Baudhāyana in his book Baudhāyana Sulbasutra, one of the oldest books in advanced mathematics, has written in a shloka about the Pythagorean theorem.
“dīrghasyākṣaṇayā rajjuH pārśvamānī, tiryaDaM mānī,
cha yatpṛthagbhUte kurutastadubhayāṅ karoti.”
The shloka translates- A rope stretched along the length of the diagonal produces an area which the vertical and horizontal sides make together. American mathematician David Mumford stated in one of his lectures about how Vedic priests in 800BCE used the Pythagoras theorem to arrange the fire altars. Aryabhata invented the digit zero and this was distinct in his place-value system as place holders for the powers of ten. An ancient text known as the Bakshali Manuscript had the first indications of the usage of zero in it. This was a manual on merchants and it showed dots to indicate void or nothingness. It was thought that ancient Indians calculated using stones and when they removed a stone from its place, the round mark it left on the sand, which represented the movement from something to nothing, was probably the shape they took for the number zero. The earliest recording of Zero was found on a temple wall inscription in a fort in Gwalior. A cultural reason could be that Indians believe that the world was born out of nothing and nothingness is the goal of humanity. This belief system could also be a reason why zero was born.
Following Aryabhata, came Brahmaguptā who gave the principles of calculations with zero. Brahmaguptā employed the concept of fortune and debt to explain positive and negative numbers. A fortune subtracted from zero is a debt and a debt subtracted from zero is a fortune. When a cloth vendor ordered for three pieces of cloth but bought four, they called it a debt and from there negative numbers came into existence. Brahmaguptā used these negative numbers and drew up quadratic equations, as he realised that when an equation was solved, it can have two results- positive and negative. The moment of pride is when a French mathematician Firma tried to solve a quadratic equation in 1657, more than a thousand years later, that Brahmaguptā had already come up with a solution. He, however was stuck with a particular calculation which was 1 divided by 0. Not to worry when the country was filled with great mathematicians. In the twelfth century AD, Bhāskarā solved the calculations and introduced infinity to the world.
Jantar Mantar showcases trigonometric functions, time and astronomy
Indian mathematicians wrote the basics of trigonometry and used the sine functions to survey the land. The Jantar Mantar in New Delhi and in Jaipur erected structures to study trigonometric functions, time and astronomy. They calculated the distance between the Sun and the Earth with a simple brick structure on a half-moon day, without having to leave the Earth. An astronomer and mathematician from Kerala measured the sine functions of various angles and was a pioneer in infinity series, calculus and trigonometry. He worked with the addition of infinite number of fractions to come up with an exact formula for Pi. He opened the Kerala school of the Astronomy and Mathematics. Many mathematics students across the globe thought that the formula for Pi was given by a German mathematician Leibniz and it probably is taught this way in schools even to this date (probably in Indian as well). However, the fact is that it was given by Madhava in the 15th century. To this day, engineers use this formula and the value of pi in measurements related to curves and semi circles.
Vedic mathematics originated in the Vedic age around 1500 BCE to 500 BCE. Our sages were definitely the master of all trade. They were excellent mathematicians and wrote the Ganita Sutras. This work was however ignored as it did not contain any mathematical calculations in it. But little did anyone know the wealth of mathematical knowledge in it. British mathematicians became interested in Vedic maths and even gave lectures in the UK.
Surely there is much more that can be written on the history and heritage of math history in India. Mathematics does not end with high school. It might not be one’s major in university, but it is a part and parcel of one’s life.
Speaking to CSP, Dr Ramasubramanian, (Professor at the Indian Institute of Technology, Bombay), highlighted the importance of studying mathematics. He started of by quoting a verse from the text Gaṇita-Sāra-Sangraha written in the 9th century by Mahaviracarya:
लौकिके वैदिके वापि तथा सामायिकेऽपि य: |
व्यापारस्तत्र सर्वत्र संख्यानमुपयुज्यते ||
छन्दोऽलङ्कारकाव्येषु तर्कव्याकरणादिषु |
कलागुणेषु सर्वेषु प्रस्तुतं गणितं परम् ||
“These verses”, Prof Ramasubramanian says, “brilliantly brings out the ubiquity of mathematics in every sphere of life, be it connected to mundane matters or spiritual pursuits or religious practices as indicated by the use of the word transaction (Vyāpāra). Even if one were to appreciate Chandas (meter), Kavya (literature), Vyākarana (grammar) or Tarka, mathematics is essential. Proceeding further, Mahāvīrācārya declares that you can hardly find anything in the world that is devoid of mathematics. In the same vein, Sripathi, an Indian astronomer, in his treatise on mathematics states that the sole purpose of mathematics was to facilitate the transactions of the world.”
Many do not realise how math exists in everything we do. Before I wrote this piece, I was one among those many. Being good at math is not only an attribute of a researcher or a lecturer. Math is a universal language and it is omnipresent. From the time we wake up in the morning looking at the time to the time we are back in bed, we can observe its existence in our life.
We wake up looking at the clock by our bedside and calculate the time we have to do our morning chores. At night, we set an alarm and calculate the hours of sleep . Measuring the amount of toothpaste on the brush, the amount of water we consume to take a shower involves math and at the same time we are being aware of conservation. The proportion of milk and coffee powder, the amount of coffee or tea we consume, the number of cups and plates used during the day, the amount of vegetables and rice on the plate, the number of glasses of water we drink in a day, all of it teaches us ratio and proportion. The intricate yet beautiful rangoli designs in front of every household involves the knowledge of geometrical shapes and symmetry. The key that goes into the lock involves math.
We use the Global Positioning System (GPS) while travelling to a new destination. When one travels, math takes a ride along. Math is involved in determining our position using the satellite information received by the GPS receiver. Paying at toll booths and calculating the distance travelled and yet to travel are all numbers. The amount of fuel required or burnt to travel a specific distance is math. We tend to calculate the number of clothes and accessories to be packed when we travel.
The fitness band is a common sight nowadays. The fitness band that most wear on their wrists count the number of steps taken. Each have a certain goal to achieve, maybe 5k or 10k. Most people count the number of calories that are to be consumed in a day to attain a particular weight. The weighing scale used at the end of the month to measure the weight lost or gained is numbers.
Grocery shopping requires a broad range of math knowledge from multiplication to estimation and percentages. The vegetable vendors scream out the vegetables they are selling along with the rate per kilogram. Shopping for new clothes includes buying the right fit and hence measurements need to exact. If one doesn’t get the exact fit, those clothes will require alterations.
Banking services involves a series of calculations - withdrawing or depositing cash, taking a loan, calculating the interest and the EMI to be paid. The accounts department of every company or even the residents of a household are involved in transferring the salary to the employee’s accounts; an increment or a bonus too. A foreigner in India or an Indian in a foreign country will make sure to keep an eye out at the currency exchange rates and manage his expenses thereafter. According to experts, those who are poor in basic math skills, are the ones who spend money based on their emotions and find it hard to manage their expenses and end up in debts. Working with children on concepts of compound interest and showing them how real-life math can be applied to financial situations and budgeting will help them to save and spend every penny wisely.
Cooking is a science and like every science experiment it requires measurements to be followed, whether it is making rice for two or twenty people. The amount of masala and salt to be added requires a certain measure to not allow any ingredient be overpowered. Bakers have measuring tins and spoons to measure the exact amount of ingredients to bake a cake. Cooking with children is an excellent way to teach them fractions, decimals, geometry, time and many other concepts.
In medicine, an advanced way mathematics is applied is in a CAT scan. A CAT scan gives a three-dimensional image of the area under inspection. A lithotripter, an instrument that is used to remove gallstones and kidney stones uses the properties of an ellipse. A surgeon has to make the right incisions of a particular length and calculate the number of stitches required. He also needs to prescribe the right dosage of medicines. Diabetes patients measure their blood glucose levels daily and measure the intake of sugar. The tests taken at a hospital usually present the results in a range of numbers, like for example, haemoglobin counts below 8 can be detrimental to one’s health. In medical research, it is essential to calculate the suitable concentration of the drug to be used in further studies on the drug especially during clinical trials.
Music, be it vocal or instrumental, is made of a set of notes played or sung in a particular pattern. Notes can be arranged in different patterns but the number of notes are finite. In math, the result of addition, subtraction, multiplication is finite despite the number of ways it is calculated. This way of connecting math and music is a great way to teach a student. The talas or metre in Indian classical music is intrinsically connected to numbers. Indian classical dance is all about timing and count. It is based on math algorithms. The rhythm involved is again math. Geometrical shapes are involved in math. A study showed how geometry is linked to Bharatanatyam. The line ‘Tha Dhi Thaka Thakadi Thajum’ depicts various geometrical shapes from triangle, right angle, line segment, diagonal, half-circle, circle, diamond, obtuse and acute angles. Most people would think literature is very far off from math. But take a look at poetry, the meter with particular rhythms involves math.
A construction workers life depends on math. He has to be precise with each measurement, angles, the numbers of bricks to be laid and the amount of cement or concrete to be used. As children most of us would have played ‘Lagori’ and how important it is to align each stone one on top of another without letting it tumble down. Or even Jenga, where one needs to pull out a slab and keeping it on top of the structure, making sure the structure doesn’t topple. A game of carrom requires the striker to be at a perfect angle to get the pawn into the socket. Traditional games like Pallanguzhi and Paramapadam are excellent and fun ways to approach mathematical concepts like simple arithmetic, fractions, integers, and probability.
Makeup and hair dressing are also math. It is important to make precise partitions and take exact sections of hair to make sure the hair cut is symmetrical. Contouring the face is all about measurement so that the face looks absolutely symmetrical.
Jewellers use math extensively; they use the concept of measure twice, cut once as they cannot afford to waste material due to the cost. They also use Pi to measure the length of the metal required to make bracelets, rings and the bezel required to set the stones.
Math can be considered our shadow. It is always present in every aspect of our life and does not end with high school. Learning math can be fun when it can be taught with real life situations. It also makes it easier for children to learn math when they practice at home. Math teaches us management, helps to conserve the Earth’s resources, and improves creativity. Who said math cannot be fun? Play with rangoli, or with sea shells, or take a tour to the kitchen and bake and cut a cake, and observe how simple to advanced math can be easily understood.
1. Iyengar Mukunda Kalpana; Bharatanatyam and Mathematics- Teaching Geometry through dance; Journal of Studio and Fine art; Vol. 5(2), pp. 6-17, October 2015
2. M Mahadevan; Mathematics in Daily Life; Association of Mathematics Teachers of India.
3. Christian Yates; Five ways ancient India changed the world – with Math; University of Bath
4. Vijay Dahiya; Why Study Mathematics? Applications of Mathematics in Our Daily Life; IJISET - International Journal of Innovative Science, Engineering & Technology, Vol. 1 Issue 10, December 2014