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