10 Mathematical
Equations That
Changed the Face of
the World
2
E = Mc
This is probably the most famous equation in the world. It was
discovered byAlbert Einstein in 1915
One of Einstein's great insights was to realize that matter and energy
are really different forms of the same thing. Matter can be turned into
energy, and energy into matter. In this equation E stands for energy, M
stands for matter, c stands for the speed of light.
So what does this all mean? Because the speed of light is so big
(300,000 kilometres per second) it means that everything – from big
things like tables and chairs to very small things like atoms have a
massive amount of energy inside them. This is the basis of nuclear
power and nuclear bombs – if you can split the atoms you can release
enormous amounts of energy.
2
2
a +b =c
2
This is called Pythagoras theorem – it was discovered by the
mathematician Pythagoras in around 500 BC. The formula links
the lengths on a triangle. c is the length of the hypotenuse, a and
b are the lengths of the other two sides.
It is the basis of a lot of construction and architecture – as it
allows people to work out the height of objects or the length of
slopes.
1-1 = 0
This looks pretty simple – but the concept of using a number to express
“nothing” actually took some time to come about. Many early
mathematicians used forms of writing numbers (like Roman numerals)
which did not contain any zeroes. As a result simple calculations like
addition and multiplication were much more difficult.
The concept of zero as a number and not merely a symbol for
separation is attributed to India from about the 9th century AD.
2
A = πr
This formula can be used to find the area of a circle. π = 3.14 (2 dp).
This formula is essential for all sorts of geometry and design, and π is possibly
the most important number in the world. π appears in a huge number of
mathematical formula that describe the universe around us.
The first theoretical calculation of a value of pi was that of Archimedes of
Syracuse who lived about 2200 years ago. He was one of the most brilliant
mathematicians of the ancient world. He worked out an approximation for π
and then demonstrated how this number could be used to work out the area
of circles.
F = ma
This is one of Sir Isaac Newton’s most famous equations. They were
published by Newton in England in 1687. It means that the force of an object
is equal to its mass multiplied by its acceleration. Newton’s laws have formed
the basis of how we understand the world around us. Without Newton there
would be no engineering, no space travel, and nophysics! Newton placed
maths at the heart of science.
iπ
1+ e = 0
This is possibly the most remarkable equation ever discovered – indeed
it has been voted the most beautiful equation in mathematics. Called
Euler’s Identity after the Swiss mathematician who discovered it, it
manages to link 5 of the fundamental constants in mathematics into
one formula:
 The number 0 – the additive identity
 The number 1 – the multiplicative identity
 The number π – which is fundamental in trigonometry and
geometry
 The number e – which is fundamental to scientific analysis
 The number i – which is the imaginary unit of complex number (i2 =
-1 )
This is the quadratic equation which gives solutions to the equation:
ax2 + bx + c = 0
It was first published in this form by Ren Descartes in 1637 – who has been described
as the father of modern mathematics and philosophy. Why is it so useful? Well, it
allows you to solve any equation with a squared term in it. This means that algebra
can be used to model numerous real life situations – from population growth to
company break even points.
iѳ
e = cosѳ + isinѳ
Euler's formula, has been described as, "one of the most
remarkable, almost astounding, formulas in all of mathematics."
It is named after Leonhard Euler, and shows the relationship
between the trigonometric functions, the exponential function
and imaginary numbers . It is closely linked to Euler’s Identity.
SOHCAHTOA
The basic trigonometry formulae allow you to find angles or sides
in a right angled triangle. By the 16th Century, when ships
navigated round the world using hand drawn maps, trigonometry
was one of the most important areas of mathematics. It allowed
sailors, map-makers and architects to accurately calculate angles
and distances – heralding a new era of accuracy.
This is possibly the most important formula in the universe. If
you have two objects of mass m 1 and m 2 at a distance d, then
these two objects will attract each other with a force F given in
this formula. G is the gravitational constant.
This formula determines the destiny of our Universe - i.e.
whether it will expand forever or whether it will ultimately
collapse in a Big Crunch.