This presentation is about the most famous mathematical equation that changed our World drastically and which has influenced the world most.

1. Avadhesh Kumar Shukla
Scientific Officer
DAE/Govt. of India
Email: avadheshshukla.amd@gov.in

2. What is an equation?
An expression that tells that two things are equal.
L
H
S
R
H
S
The form of the World that we
perceives today…

3. 2 2 2
a b c Pythagoras, 530 BC
What does it tell us?
 Link between the lengths of the sides on a right angled triangle, linking geometry and algebra
What did it lead to?
Distances between places without actually having to measure them, current theories of space, time, and
gravity…
Basis of Trigonometry

4. log log logxy x y 
John Napeir, 1610
What does it tell us?
 Big to small numbers
What did it lead to?
“Shortening the proceedings”
 Exponential, Radioactive decay, and rates of growth, Earthquakes(Scales), (a predecessor to the calculator!)

5. 0
( ) ( )
lim
h
df f t h f t
dt h
 

Rate of
change of
quantity
With
respect to
some
quantity
Change
Newton, 1688
What does it tell us?
 It tells us how to find the way in which function changes at any given moment in time, such as the speed of a car
What did it lead to?
 Formulae for the volume & area of solids, laws of motion
 Base of Calculus
 Almost all the math in physics roams around calculus…

6. 1 2
2
m m
F G
d

What does it tell us?
 It allows us to work out the gravitational force between two objects
What did it lead to?
“The system of the world”
 How gravity works
 Explanation to planetary motion; Earth and outside,
 Basis for the laws of motion
 the building of satellites
Newton, 1687

7. 1 i 
What does it tell us?
 That the square of the number i is -1, even though this is impossible!
What did it lead to?
“First term of Quantum Mechanics”
 Creation of imaginary and complex numbers, which are used to explain waves, heat, electricity, and magnetism
 Fourier series and Fourier Transform
Rafael Bombelli, 1572

8. 1 H
E 0 E
c t

    

1 E
H 0 H
c t

   

Electric
Field
Magnetic Field
Divergence = 0
Curl
Speed of
light
What does it tell us?
 That electricity and magnetism are linked
What did it lead to?
“Waves in ether”
 Unification of two great forces.
 It predicted the existence/generation of electromagnetic waves other than light,
leading to radio, radar, and wireless computing
J. C. Maxwell, 1865

9. 2
E mc
What does it tell us?
“One thing is absolute”
 Matter contains energy equal to its mass multiplied by the speed of light squared (a tiny
amount of matter contains lots of energy!)
What did it lead to?

Einstein, 1905

10. Thank you!