Revolution of mathematics and its effect on physics

1. Revolution in Mathematics and its
aspects on Physicson Physics
Scripted by : Sagar ChowdhuryScripted by : Sagar Chowdhury
M.Tech in Science Communication
Bits pilani,2016

2. Introduction
Mathematics is the study of numbers, quantity, space, structure, and change.
Mathematics is used throughout the world as an essential tool in many fields,
including natural science, engineering, medicine, and the social sciences.
Between 600 and 300 BC the Ancient Greeks began a systematic study of
mathematics .
Mathematics has since been greatly extended, and there has been always a
fruitful interaction between mathematics and Physics,
Through different inventions of mathematicians, physics has enriched and
modern technology has developed.

3. Fibonacci
Leonardo of Pisa or commonly known Fibonacci felt doing
arithmetic is more difficult in roman inscription than doing it in
hindu Arabian system, so he wrote a famous book BOOK OF
CALCULATION on number system
 9 8 7 6 5 4 3 2 1were developed by ancient Indian
civilization, With these nine figures,
The sign 0 which is called zephirum by Arabs
 Any number can be written, as will be demonstrated with the
help of those ten numbers.

4. Viète and Algebra
 François Viète understood the
value of symbols. He used
letters as symbols for
quantities, both known and
unknown.
 It was known as Algebra.
 It uses some fundamental rules
on those known and unknown
equations to rearrange and
solve equations.
 It was a powerful tool to solve
scientific and engineering
problems, it opened the door to
a scientific and mathematical
revolution
François Viète

5. Napier’s Logarithms
 In 1614 John Napier
developed the concept of
logarithms as an aid to
calculation.
John Napier
 Logarithm(log) is a power of 10. If a number is written as 10X ,
Then it is log X
For Example 100 could be written as 102
therefore the log of 100 is 2
 It does not always use the power of 10, another common number used instead
of 10, called as Base e = 2.7. It is called a natural log.

6. Kepler and the Planetary motion
Johannes Kepler
Kepler attempted to describe
planetary orbits used a model of
regular polyhedra (Platonic
solids).
Keplers Law of Planetary motion
A)Law of Ellipses
The path of the planets about the sun are elliptical in
shape, with the sun at one of the focal points
B)Law of Equal Areas
An imaginary line drawn from the center of the sun to
the center of the planet will sweep out equal areas in
equal intervals of time.
C)Law of Harmonies
The ratio of the squares of the periods of any two
planets is equal to the ratio of the cubes of their
average distances from the sun.

7. Newton’s Contribution to Mathematics
Isaac Newton
Newton wrote Principia Mathematica
(1687) on the study of Euclid’s
Elements.
Newton developed the main ideas of
calculus . This research was closely
connected to his studies in physics.
Many years later he published his
results to establish priority for himself
as inventor the calculus.

8. Role in Physics
 He explained inertia for both body at rest an in motion.
 He also explained the relationship between forces, mass and acceleration
 He unified astronomy and classical mechanics with his Universal law of
Gravitational
 He gave the concept of mass and concept of momentum.
 He made the distinction between absolute and relative space , motion and
time.

9. Leibniz’s Calculus
 Leibniz and Newton both
independently developed the
calculus during the same time
period.
 Although Newton was considered
the inventor calculas Leibniz called
the father of modern calculus.
Gottfied Leibniz

10. Leonhard Euler
 After Newton and Leibniz, Leonhard Euler was the
most popular mathematics writer of all time.
 Euler was also great teacher of mathematics. It was
observed that all calculus textbooks since 1748 are
copies of either Euler or extensively copies of copies
Euler.
 Euler’s writing standardized modern mathematics
notation with symbols such as:
f(x), e, π, i and ∑ .
 His most important discoveries in calculus is graph
theory.
 Graph can be considered as an equation showing an
array of X and Y value which are calculated from
EQUATION
Leonhard Euler

11. Boolean Algebra
 Boolean algebra was introduced by George Boole in his first
book The Mathematical Analysis of Logic (1847),
 It is based on common binary value.
 It is common to interpret the digital value 0 as false and the
digital value 1 as true
 Three common Boolean operators are AND, OR, and NOT
 Later on Boolean algebra was applied to computing by John
Vincent Atanasoff.
 It is the base of modern Digital Electronics.

12. Conclusion
 Mathematics and Physics have always been closely interwoven, in the sense
of a “two-ways process”.
 Mathematical methods are used in Physics. That is, Mathematics is not only
the “language "of Physics (i.e. the tool for expressing, handling and
developing logically physical concepts and theories), but also, it often
determines to a large extent the content and meaning of physical concepts.
 Any distinction between Mathematics and Physics, seen as general attitudes
towards the description and understanding of an (empirical, or mental) object,
 It imply that the history of Mathematics independent of the history of Physics
is necessarily incomplete (and vice versa).