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.

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.

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.

Ma

Ma

Ma

M

The image cannot be displayed. Your computer may not ha

aths in c

aths in i

aths in c

Mathemaave 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

cultura

mpact

colourf

atical pagain.

l herita

of urba

ul patte

patterns

The image cannot be displayed. Your computer may not

ge

anizatio

erns

s in Sha

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

on

apes of

t it again.

f LifE.

Acknowledging creativity and felicitations

2)Intra school activities a)maths magazine

b)maths & creativity – jewellery design at V.V.D.A.V.

 

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.

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 (1452–1519)

  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

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

the21

e)GThewethefingfingfingaboabo

3)Themath 1. N2. I3. V4. B5. R6. A7. B8. K9. R

e strand angstro

GOLDENe Gold

e use oue bone gernailgernailgernailout theout 8 fi

e contrihematic

Numberndus ciVedic mBrahmi ReligionAryabatBhaskaKerelanRamanu

ds of ouoms.

N RATIOen Ratur fingein the ts, follos, follos. The

e middlengerna

ibution cs:

r systemivilisatio

mathem numern tta ra 1 &

n matheujan

ur DNA.

O IN HUtio is foernail letip of owed bywed byfinal be of ouails.

of India

m on atics als

II ematicia

A DNA

MAN Bound thength a

our fingy the my the bone go

ur palm

a in th

an

A strand

ODY hroughoas a uner sho

mid portase at

oes all t, which

e devel

d is exa

out ournit of muld be tion at about the wah is a le

lopmen

ctly 34

r body. measure

about 3 5 y to ength o

nt of

by

If e, 2

of

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

GeotextSam

d)B

BefaroBrasty e)CRelinvbe at t

f)Ar

ometryt the Shmhita.

Brahmi

fore theound thahmi nule of th

Contribuligion toestigat preparthe cor

ryabhat

y has behatapa

numera

e end oe middumeralse Brah

ution ofoo playeions in ed to arect tim

ta

een destha Bra

als

of the pele of ths had bmi num

f religioed a m India follow rel

mes.

scribed ahmana

eriod ofhe third begun tomerals;

on in maajor rolor acculigious

in the a and t

f the Su centuro appea

athemae in ast

urate caobserv

Vedic mhe Taitt

ulbasutry BC, thar. Here

atics tronom

alendarances t

mytholotiriya

tras, he e is one

mical s had tto occu

ogy

e

to ur

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 600 - AD 680) was a 7th 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.

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. 1340-1425) 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.

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

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.