MATHS IN ART AND CULTURE

Transcription

1 MATHS IN ART AND CULTURE ABSTRACT: Mathematics and Art have a historical relationship. Maths can indeed be defined as the general science of pattern and structure whereas Art involves patterns and structures, so Art and Maths relate to each other in many natural ways. Purpose of this presentation is to infer relation of Maths with Art and Culture, to emphasise on the deep affinity of both the streams, to show their interdependence and strong bonding. Structure of presentation is as below: Use of Mathematics Concepts 1) In my school( rangoli competition, jewellery designs etc.) 2) In Nature & Art. 3)Contribution of Ancient Indian Scholars in progress of Maths.

2 As rightly said by great mathematician G.H.HARDY that A mathematician like a painter or poet is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas. When we observe our natural surroundings, we admire the patterns made in bee hives or in petals of a sunflower or in nest of "baaya. We appreciate it as being a "work of art. So our surroundings have mathematical concept like PATTERNS & SYMMETRY embedded in natural ways, that we see and admire, hence knowingly or unknowingly we do learn & reproduce them. Maths & art share a wonderful creative aspect Though Art is more subjective and less precise, but the criteria for judging the merit of art work is not uniform. While there are laws of form and composition, these are not generally expressed in a systematic way as compared to the highly structured proofs in mathematics, but the fundamental creativity is central to both disciplines.

3 INTEGRATION OF MATHS IN ART IN V.V.D.A.V 1)Maths in color rangoli at V.V.D.A.V. If mathematical concepts are blended with the traditional ways and culture, who is not going to like, relish, adore and live this amazing subject. One step towards it was taken by us at V.V. D.A.V. to promote the beauty and serenity of Maths through interschool Rangoli competition. Class X students of more than 25 schools enjoyed making their own Rangoli patterns and colouring them to form a symmetrical design using various mathematical concepts like parallel lines, geometry, properties of circles, mathematical symbols etc.

4 The image cannot be displayed. Your computer may not have enough memory to open the image, or the image may have been corrupted. Restart your computer, and then open the file again. If the red x still appears, you may have to delete the image and then insert it again. The image cannot be displayed. Your computer may not have enough memory to open the image, or the image may have been corrupted. Restart your computer, and then open the file again. If the red x still appears, you may have to delete the image and then insert it again. Maths in cultura l heritage Maths in impact of urbanization Maths in colourf ul patterns Mathematical patterns in Shapes of LifE.

5 Acknowledging creativity and felicitations 2)Intra school activities a)maths magazine b)maths & creativity jewellery design at V.V.D.A.V.

6 INTEGATION OF MATHS IN ART IN THE WORLD: 1)HYPERCUBE Salvador Dalí, the master of surrealism, had a keen interest in natural science and mathematics. He was fascinated by hypercube, and it is featured in the painting Crucifixion (Corpus Hypercubus). Here Christ is crucified on figure of unfolded hypercube. 2)Style of Klaus-Peter Kubik 3)Architectural Blossoming of the Lotus temple: The beautiful concept of the lotus, as conceived by the architect, had to be converted into definable geometrical shapes such as spheres, cylinders and cones.

7 4)GOLDEN RATIO: The concept of golden ratio has been found in: a)monalisa painting made by Leonardo da vinci b)egyptian Pyramid c)parthenon d)fibonocci series e)body parts a)leonardo da Vinci ( ) Renowned primarily as a painter, Leonardo incorporated many mathematical concepts into his artwork despite never having received any formal mathematical training. Golden rectangles superimposed on the MonaLisa A Golden Rectangle whose base extends from her right wrist to her left elbow and reaches the top of her very head can be constructed. Golden triangles In the MonaLisa

8 b)golden Ratio in great pyramids The ancient Egyptians and Greeks knew about the golden ratio, regarded as an aesthetically pleasing ratio, and incorporated it into the design of monuments The Great Pyramid. Evidence of mathematical influences in art is present in the Great Pyramids, built by Egyptian Pharaoh Khufu and completed in 2560BC Golden Ratio & Kepler Triangle in Great Pyramids. c)golden Ratio in PARTHENON The front elevation of Parthenon was designed based on the overall dimensions of the Golden Ratio and it was then sub divided into smaller segments, still pertaining to the proportional dimensions of the golden ratio d)fibonacci Series Even before the Renaissance, the medieval mathematician Fibonacci uncovered a sequence of numbers that follows this very same ratio. The Fibonacci spiral, as an example, is visible in everything from the arrangements of flower petals to

9 the strands of our DNA. 21 angstroms. A DNA strand is exactly 34 by e)golden RATIO IN HUMAN BODY The Golden Ratio is found throughout our body. If we use our fingernail length as a unit of measure, the bone in the tip of our finger should be about 2 fingernails, followed by the mid portion at 3 fingernails, followed by the base at about 5 fingernails. The final bone goes all the way to about the middle of our palm, whichh is a length of about 8 fingernails. 3)The contribution mathematics: of India in the development of 1. Number system 2. Indus civilisation 3. Vedic mathem atics 4. Brahmi numerals 5. Religion 6. Aryabatta 7. Bhaskara 1 & II 8. Kerelan mathematician 9. Ramanujan

10 Maths in Indian culture a)beautiful number system invented by the Indians on which much of mathematical development has rested. b)indus civilisation which began around 2500 BC and survived until 1700 BC or later. The people were literate and used a written script containing around 500 characters. We do know that the Harappans had adopted a uniform system of weights and measures. An analysis of the weights discovered suggests that they belong to two series both being decimal in nature with each decimal number multiplied and divided by two, giving for the main series ratios of 0.05, 0.1, 0.2, 0.5, 1, 2, 5, 10, 20, 50, 100, 200, and 500. Several scales for the measurement of length were also discovered during excavations. One was a decimal scale based on a unit of measurement of 1.32 inches (3.35 centimetres) which has been called the "Indus inch". Of course ten units is then 13.2 inches which is quite believable as the measure of a "foot. c)vedic Maths

11 Geometry has been described in the Vedic mythology text the Shatapatha Brahmanaa and the Taittiriya Samhita. d)brahmi numerals Before the end of the period of the Sulbasutras, around the middle of the third century BC, the Brahmi numerals had begun to appear. Heree is one style of the Brahmi numerals; e)contribution of religion in mathematics Religion too played a major role in astronomical investigations in India for accurate calendars had to be prepared to allow religious observances to occur at the correct times. f)aryabhata

12 By about 500 AD the classical era of Indian mathematics began with the work of Aryabhata.. His ideas of astronomy were truly remarkable. He replaced the two demons Rahu, the Dhruva Rahu which causes the phases of the Moon and the Parva Rahu which causes an eclipse by covering the Moon or Sun or their light, with a modern theory of eclipses. He introduced trigonometry in order to make his astronomical calculations, based on the Greek epicycle theory, and he solved with integer solutions indeterminate equations which arose in astronomical theories. f)bhaskara I (AD AD 680) was a 7 th century Indian mathematician, who was apparently the first to write numbers in the Hindu-Arabic decimal system with a circle for the zero. g)brahmagupta is probably the earliest astronomer to have employed the theory of quadratic equations and the method of successive approximations to solving problems in spherical astronomy. h)a contemporary of Brahmagupta who headed the research centre at Ujjain was Bhaskara I who led the Asmaka school.

13 i)the main mathematicians of the tenth century in India were Aryabhata II and Vijayanandi, both adding to the understanding of sine tables and trigonometry to support their astronomical calculations. j)in the eleventh century Sripati and Brahmadeva were major figures but perhaps the most outstanding of all was Bhaskara II in the twelfth century. He worked on algebra, number systems, and astronomy. Bhaskara II may be considered the high point of Indian culture. Bhaskara is said to have been the head of an astronomical observatory at Ujjain. k)the most remarkable contribution after this period, however, was by Madhava Madhava of Sangamagrama (c ) who invented Taylor series and rigorous mathematical analysis in some inspired contributions. Some of the remarkable discoveries of the Kerala Mathematicians are a formula for the ecliptic; the Newton-Gauss interpolation formula etc.

14 The image cannot be displayed. Your computer may not have enough memory to open the image, or the image may have been corrupted. Restart your computer, and then open the file again. If the red x still appears, you may have to delete the image and then insert it again. l)srinivasa Ramanujam Now, as of this century who in the world does not know Ramanujam- the young, brilliant and par excellence and brilliance Indian mathematician and his unparallel contributions. Hyper-geometric series, Elliptic functions, Prime numbers, Bernoulli`s numbers, Divergent series, Continued fractions etc. No wonder then, that the greatest mathematicians across the world have rightfully recognized India s huge contribution. Albert Einstein once said, We owe a lot to the Indians, who taught us how to count, without which no worthwhile scientific discovery could have been made. That is the beauty, the pride of being an Indian. THANK YOU. SONIA MALIK V.V.D.A.V. PUBLIC SCHOOL VIKASPURI NEW DELHI

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