Integration of Mathematics with Art and Culture.

It is said that

“The moving power of Mathematical invention is not reasoning but imagination.”

A Demorgan.

Imagination is the moving power of Mathematics as well as Art. Mathematics lies in the core of Art in fact it is the thinking ability Art forms. The peacock dancers use Pythagoras theorem to fall at the snake along the hypotenuse. The lake painting uses the laws of symmetry. The dance forms like “Azeemoshan shehenshah” from “JODHA AKBAR” uses many formations of mathematics such as circle, loci and concurrency theorem. The Rangolis of south India, the makeup of bride with bindis are based on the principle of equitable distribution of dots. It is like stick two bindis (points) towards the edge of the eye brows and insert n arithmetic means along the length of the curve drawn on the forehead. The most basic shape of heart which all of us know since childhood is also a mathematical equation of cardiod. That is

X = a(2cost-cos2t)

Y = a(2sint-sin2t)

The “TIE AND DYE” work from Rajasthan is based on the principle of symmetry. The musical pillars of Hampi are based on the calculations of music notes. The mathematical calculations of planetary positions emerged as JYOTISH SHASTRA. NUMEROLOGY is also based on Mathematics.

If Mathematics is taught along with its integration with Art and culture one can get rid of the monotonic nature of Mathematics class.

This paper tries to identify the essence and the presence of Mathematics in Art and culture. It also endeavours to integrate the secondary school Mathematics curriculum with Art and culture. This project was started to help few students who were very good in Art but faced humiliated when they scored less in Mathematics. All I would discuss in this paper is an attempt to kindle the Mathematical flame in a student who is an excellent Artist and kindle the artistic flame in a student who is excellent in Mathematics

Mathematics is an omnipresent discipline. All forms of life, discipline

and culture do show the essence of mathematics. The sense of Mathematics is

very important and human beings are blessed with that sense. While I have

already mentioned that Mathematics is an omnipresent discipline, so all human

beings who contest to be an expert in certain discipline must have some concept

of Mathematics, at least at subtle level if not at magnanimous level. Sometimes

the flame of Mathematics is so subtle or hidden in the individual that he himself

does not know that it is present. As a teacher, our job is to discover that flame

of Mathematics inside the child and kindle it to the maximum possible level.

The foundation stone of this paper was laid in my mind in one of the

parent teacher meeting. Actually, few students who were excellent in art were

not doing well in Mathematics. As a teacher, I was immensely moved by their

work in art and as an individual I am ardent fan of that creative talent. The

parents were not happy as their children could not do well in Mathematics. In

fact, they were aggressive and frustrated over this issue. That was the day; I

realized that “Mathematics is the queen of all Sciences”.

“Why my ward is not doing well in Mathematics?” was the question. I

knew the answer but I had a strong conviction that my answer will not be

acceptable to them. I knew that nothing succeeds like success. Hence for my

answer to be acceptable to the parents and for the reader of this article, I reserve

my comments for the time being. Let me discuss my method which is

integrating Mathematics with art to make students achieve better in

Mathematics. Art file of students was explored to find Mathematics in it.

Tortoise of Srilanka had many Mathematical figures all over its

body. The mother owl and the

baby owl were similar figures

Mathematically!

Christmas tree has the principle of

symmetry.

Honey Comb has hexagon tightly packed the photographs are similar figures.

The Peacock has cardioids and oval shapes in its feathers. The body line of

peacock was a concave

curve! Ants are

seen moving in a straight line. Mixing of colours (the colour wheel) teaches the

concept of permutation and combination. Three basic primary colours RED,

YELLOW AND BLUE taken to at a time made three new colours ORANGE,

GREEN AND VIOLET so 3C2 = 3. These colours are known as secondary

colours.

One student participated in the “best out of waste competition”. He took

many bangles and glued them one over another to make a cylindrical pen stand!

We identify that the width of bangles is 1mm.

So Curved surface area of the cylinder = perimeter of bangle 1 +

perimeter of bangle 2 + ………………………….+ perimeter of bangle n

(approximately).

All the bangles were of same size and hence of same radius, in fact their shapes

represented congruent circle.

Curved surface area = 2 + 2 + ………………………………n

times.

= 2 (n)

= 2 h

(If there are ten bangles height is 10mm, if there are n bangles height is n (mm))

So a beautiful pen stand gave us the concept of cylinder and circle.

“What would we have not paid to see the moonrise if the nature improvidently

had not made it a free entertainment”.

We explored the beautiful geographical locations and found “Maths” as

the prime cause of these mysterious images. For example, the oceans that never

meet each other is due to the fact that their densities are

different.

These two bodies of water were merging in the middle of The Gulf of Alaska and there was a foam developing only at their

junction. It is a result of the melting glaciers being composed of fresh water and the ocean has a higher percentage of salt

causing the two bodies of water to have different densities and therefore makes it more difficult to mix.

The Mathematical number of amount of salt per unit volume in the two oceans

results in this beautiful art form of geographical location.

Math and Art come to us as colorful symbols too and symbols tell us

many facts. For example, whether a particular food is vegetarian or non-

vegetarian can be found by a combination of mathematical shapes and artistic

colours.

White rectangle with green field circle tells us that the food content is

vegetarian and white rectangle with red and brown field circle tells that the food

content is non-vegetarian or it contains egg

.

Let us now discover mathematics in the modern culture. The most

addicting networking website FACEBOOK is safe when you use the right

permutations and combinations of the security password. The hacker has to be

a good mathematician to decode the password. You must have seen that the

website indicates the password strengths as strong, medium and weak. What is

the reason? The answer lies in mathematics.

If your choose the 8-digit password with alphabets only, then there are

26P8 ways of this kind but with numbers and alphabets it becomes 36P8

And if you add symbols too then it becomes around 40P4 ways or more.

It is now evident that which one is easy to decode. Let us come to

another important day of the contemporary culture i.e. Valentines ‘Day! and

“heart” that is related to Valentine’s day is known as cardiod

mathematically.

The rangoli forms are based on Mathematical shapes and

patterns.

After discussing these facts with the students, I took up some concepts like

“ARITHMETIC PROGRESSIONS”, “Symmetry” etc from various grade of

NCERT textbooks. The concepts were divided into various activities which are

integration of Mathematics and Art. The details are as follows:-

(1) Discovering Arithmetic Progressions

Activity 1: Discovering Arithmetic Progressions in arranging Bangle

sets.

Materials Required

Bangles of different colours, shapes and similar size.

Method A woman wants to wear off white saree with red border.

Arrange bangle set for her.

Complete the table

kada 4

bangles

kada 4

bangles

kada 4

bangles

kada 4

bangles

kada 4

bangles

4bangles 8

bangles

12

bangles

16

bangles

20

bangles

K=1 4 K=2 8 K=3 12 K=4 16 K=5 20

1) Write the Arithmetic progression obtained.

2) Let the number of bangles be 4K. What will be the number of bangles if

K=6?

3) For human beings what values of K and 4K is practically possible?

4) What is the first term ‘a’ and the common difference‘d’in the given

progression?

5) Is a=d? Can there be another sequence where a=d.

Activity 2

Discovering Arithmetic Progression in arranging diwali bulbs.

Case 1 a=d.

Materials required. Flowers,

wires.

Method

Suppose you want to make a series of glittering diwali bulbs.

Complete the following table.

No of bulbs Length of wire

B1 6 units

B2 12 units

B3 18 units

B4 24 units

1) Write the sequence obtained.

2) Find the value of ‘a’ and ‘d’.

Is a=d? Find out some other Arithmetic progressions where a=d.(here this

progression appears to be the table of 6!).

Activity 3

Discovering Arithmetic Progression in arranging diwali bulbs.

Case 1 a is not equal to d.

Materials required. Flowers

,wires.

Method

Suppose you want to make a series of glittering diwali bulbs. But the first part

has to be longer for power connection.

Complete the following table.

No of bulbs Length of wire

B1 20 units

B2 26 units

B3 32units

B4 38 units

1) Write the sequence obtained.

2) Find the value of ‘a’ and ‘d’.

3) Is a=d? Find out some other Arithmetic progressions where a is not equal

to d.(here this progression appears to be the auto fare chart!)

Activity 4

Finding Fibonacci sequence in nature

Write the number of petals in the given

pictures.

Picture

no

1 2 3 4 5 6 7

No of

petals

1 1 2 (1+1) 3(2+1) 5(3+2) 8(5+3) 13(8+5)

1)Write the sequence obtained for the number of petals.

2) What did you observe in the sequence?

3) What is this sequence known as?

Activity 5

Find out how was the logo of apple designed using Fibonacci

sequence?

Activity 6

Find the sum of first n natural numbers.

Method

Look at the following bunch of grapes

The number of grapes in the bunch is

1+2+3+4+5+6+7+8. The sum of first 8 natural numbers.

Lets put two bunches of maximum 4 grapes upside

down.

Now there are n+1 grapes in n rows

So

1) How many grapes are there 1 row?(4+1)(n+1)

2) How many rows are there? (4)

3) What is the total number of grapes in two bunches?

4) What is the total number of grapes in a bunch?

5) What is the sum of first 4 natural numbers?

6) What is the sum of first n natural numbers?

Drawing using Mathematics

Activity 6

.

Draw the logo of icloud using Mathematical

concepts.

1) What is Golden ratio?

2) Find out some applications of golden Ratio?

Activity 7

Divide a circle into 3 parts using curves.

Activity 8

Find Mathematics in dance forms.

Activity 9

Find Mathematical symmetry in

nature.

Activity 10

Find Mathematical proverbs in various cultures/languages.

Towards the end of the paper, it is very important to reveal the answer that I had promised. The question was very common which any parent would ask the Mathematics teacher “Why my child is not doing well in Mathematics?” or “Why my child is not interested in Mathematics?” or “Why my child is afraid off Mathematics?”. The answer to all these questions is very simple. “The child is not doing well in Mathematics or the child is not interested in Mathematics or the child is afraid off Mathematics because the child has not felt the joy of Mathematics instead the child has always faced and felt the pressure of Mathematics. Now how the child will feel the joy of Mathematics. This paper is an effort to make the child feel the joy of Mathematics. “Is there an alternative way?” the answer is “YES”. As I have already said we must explore the flame in the child. If a child has natural flame of Mathematics, use the flame to kindle the flame of art hidden in Mathematics. If a child has natural flame of art, use the flame to kindle the flame of Mathematics hidden in art. As a teacher its our privilege to do so. And only a human teacher can do it not any robot teacher. That is why; human teacher can never be replaced. Humane touch is very much essential in teaching, hence teaching is not just Science it is also an Art. Hence teaching Mathematics is not just Science it is also an Art.

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