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
body.
of
Srilanka
had
many
Mathematical
figures
all
over
its
The mother owl and the
baby
Mathematically!
owl
were
similar
figures
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.
+ 2
Curved surface area = 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
patterns.
rangoli
forms
are
based
on
Mathematical
shapes
and
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
kada 4
kada 4
kada 4
kada 4
bangles
bangles
bangles
bangles
bangles
4bangles
8
12
16
20
bangles
bangles
bangles
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
pictures.
the
number
of
petals
in
the
given
Picture 1
2
3
4
1
2 (1+1) 3(2+1)
5
6
7
5(3+2)
8(5+3)
13(8+5)
no
No
of 1
petals
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
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?
upside
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
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
Mathematical
Find Mathematics in dance forms.
Activity 9
Find
nature.
Mathematical
symmetry
in
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.
FROM
JYOTI PANDEY PGT MATHEMATICS KVJNU
ADDRESS FOR CORRESPONDENCE
FLAT NO 6062/6
SECTOR –D, POCKET -6
VASANT KUNJ
NEW DELHI 110070
PH NO 9911700808.