4. How mathematics is used in art ?
Mathematics and art are related in a variety
of ways. Mathematics has itself been
described as an art motivated by beauty.
Mathematics can be discerned in arts such
as music, dance, painting, architecture, sculpt
ure, and textiles. This article focuses,
however, on mathematics in the visual arts.
5. Mathematics and art have a long historical
relationship. Artists have used
mathematics since the 4th century BC
when the Greek sculptor Polykleitos wrote
his Canon, prescribing proportions based
on the ratio 1:√2 for the ideal male nude.
Persistent popular claims have been made
for the use of the golden ratio in ancient
art and architecture, without reliable
evidence.
6. Maths in Business
Mathematics is an important part of
managing business. Business and
mathematics go hand in hand this is
because business deals with money and
money encompasses everything in itself.
There is a need for everyone to manage
money as some point or the other to take
7. It helps you know the financial formulas,
fractions; measurements involved in
interest calculation, hire rates, salary
calculation, tax calculation etc. which help
complete business tasks efficiently.
Business mathematics also includes
statistics and provides solution to
business problems.
9. Cooking with Maths
Math is in every kitchen, on every
recipe card, and at each holiday
gathering. The mathematics of
cooking often goes unnoticed, but
in reality, there is a large quantity
of math skills involved in cooking
and baking.
10. Maths and Music
A child who learns music develops physical –
mental skills necessary for the enhancement of the
spatial regions of the brain. Arriving at the correct
part of the rhythm and the necessary ups and
downs of the scale exercises this part of the brain
which subsequently becomes “trained” to handle
complex math problems. In general, children tend
to retain information better when it’s associated
with music and dance rather than just verbal
12. Pythagoras, (born c. 570 BCE,
Samos, Ionia [Greece]—died c. 500–
490 BCE, Metapontum, Lucanium [Italy]), Greek
philosopher, mathematician, and founder of the
Pythagorean brotherhood that, although religious in
nature, formulated principles that influenced the
thought of Plato and Aristotle and contributed to the
development of mathematics and Western
rational philosophy. (For a fuller treatment
of Pythagoras and Pythagorean
thought, see Pythagoreanism).
13. Pythagorean theorem, the well-known geometric theorem that the sum
of the squares on the legs of a right triangle is equal to the square on the
hypotenuse (the side opposite the right angle)—or, in familiar algebraic
notation, a2 + b2 = c2. Although the theorem has long been associated with
Greek mathematician-philosopher Pythagoras (c. 570–500/490 BCE), it is
actually far older. Four Babylonian tablets from circa 1900–
1600 BCE indicate some knowledge of the theorem, with a very accurate
calculation of the square root of 2 (the length of the hypotenuse of a right
triangle with the length of both legs equal to 1) and lists of
special integers known as Pythagorean triples that satisfy it (e.g., 3, 4, and 5;
32 + 42 = 52, 9 + 16 = 25). The theorem is mentioned in the
Baudhayana Sulba-sutra of India, which was written between 800 and
400 BCE. Nevertheless, the theorem came to be credited to Pythagoras. It is
also proposition number 47 from Book I of Euclid’s Elements.
14.
15. Srinivasa Ramanujan, (born
December 22, 1887, Erode, India—died
April 26, 1920, Kumbakonam), Indian
mathematician whose contributions to
the theory of numbers include
pioneering discoveries of the properties
of the partition function.
16. Contribution of S. Ramanujan in Mathematics.
Ramanujan number: 1729 is a famous ramanujan
number. It is the smaller number which can be
expressed as the sum of two cubes in two different
ways- 1729 = 13 + 123 = 93 + 103
Partition of whole numbers: Partition of whole
numbers is another similar problem that captured
ramanujan attention. Subsequently ramanujan
developed a formula for the partition of any number,
which can be made to yield the required result by a
series of successive approximation. Example
3=3+0=1+2=1+1+1;
18. Rational Numbers:
A number which can be expressed as a/b ,where ‘a’ and ‘b’ both are
integers and ‘b’ is not equal to zero, is called rational numbers .
Properties :
1. The sum of two or more rational numbers is always a rational.
2. The difference of two rational numbers is always a rational number. If
a and b are any two rational numbers, then each of a-b and b-a is also a
rational number
3. The product of two or more rational numbers is always a rational
numbers.
4. The division of a rational number by a non-zero rational number is
always a rational number.
20. Square:
If a number is multiplied by itself , the product obtained is
called the square of that number.
For example, the square of 2 is 22 = 2 × 2 = 4. Let us
find the squares up to 50, i.e. from 1 to 50. The square
(the shape) has all its sides equal.
21. Square roots:
The square root of a given number x is the number whose square is x.
Properties of square numbers:
1st property:
The ending digit (i.e. the digit at unit’s place) of the square of a number
is 0 , 1 , 4 , 5 , 6 or 9.
2nd property:
A number having 2 , 3 , 4 , or 8 at its unit place is never a perfect square .
22. 3rd property:
If a number has 1 or 9 at its units place then squar6e of this number always 1
at its unit place .
4th property:
If the digit at the unit place of a number then the square of this number
always has 1 at its units place
5th property:
If a number ends with n zeros ;its square ends with 2n zeros .
6th property:
A perfect square number leaves remainder 0 or 1 on dividing it by 3.
7th property:
For any natural number n, (n+1)2 – n2 = (n+1)+n
24. Cubes :
In arithmetic and algebra, the cube of a number n is its third
power, that is, the result of multiplying three instances of n
together.
The cube of a number or any
other mathematical expression is denoted by a superscript 3, for
example 23 = 8 or (x + 1)3.
Cube roots:
The cube root of a number is a special value that, when
used in a multiplication three times, gives that number.
Example: 3 × 3 × 3 = 27, so the cube root of 27 is 3.
See: Square Root.
25. Properties of cube numbers
The following are the cubes of numbers from 11 to 20.
From the above table we observe the following properties of cubes :
Property 1 :
For numbers with their unit’s digit as 1, their cubes also will have the
unit’s digit as 1.
26. Property 2 :
The cubes of the numbers with 1, 4, 5, 6, 9 and 0 as unit digits will have the same
unit digits.
Property 3 :
The cube of numbers ending in unit digit 2 will have a unit digit 8 and the cube of
the numbers ending in unit digit 8 will have a unit digit 2.
Property 4 :
The cube of the numbers with unit digits as 3 will have a unit digit 7 and the cube of
numbers with unit digit 7 will have a unit digit 3.
Property 5 :
The cubes of even numbers are all even; and the cubes of odd numbers are all odd.
Property 6 :
The sum of the cubes of first n natural numbers is equal to the square of their
sum.
