Revolution in Mathematics and its aspects on Physicson Physics

Scripted by : Sagar ChowdhuryScripted by : Sagar Chowdhury M.Tech in Science Communication Bits pilani,2016

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.

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.

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

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.

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 pointsB)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.

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.

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.

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

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, , 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

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.

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).