Maths – The Language of the Universe
The Ishango Bone :
This artefact was discovered in the small African fishing village of Ishango, on the border of
Zaire and Uganda by the Belgian geologist Jean de Heinzelin. The Ishango Bone now lies at
the Museum of Natural Sciences in Brussels, and has been dated to around 20,000 BC. It is
thought to be the oldest mathematical artefact ever discovered.
4000 BC –Middle East
The Sumerians lived in the area between the Tigris and the Euphrates rivers. This was the
time when maths was really needed. Because the Sumerian people were now living in cities,
things had to become organised. Taxes had to be paid, food had to be divided out among the
people and wages had to be paid to labourers. Around this time, the Sumerians gave the
number one its independence. They stopped scratching him on a bone and „set him free‟ by
representing him as a wedge shaped token.
The Ancient Egyptians – 3000 BC
The Sumerians had made the number one part of a complex counting system. The Ancient
Egyptians were to stretch his talents even further. They invented the Ruler and gave the
number one a length. The length of the ruler was the length of a man‟s arm from his
elbow to his fingertips plus the palm of his hand. This was called a cubit. These official
rulers were so important to the Egyptians that they were closely guarded them in their
temples. From them, copies were made so that in any building project from temples to the
pyramids, everyone knew what was meant by a length of one.
Egyptians loved big things, and came up with the first really big numbers. And the way
they wrote them down tells a lot about the hierarchy of Egyptian society.
1 is represented by a plain line
10 is represented by a rope
100 is represented by a coil of rope
1,000 is a drawing of a lotus plant, symbol of pleasure
10,000 is represented by a commanding finger
100,000 by a frog
1,000,000 is the figure of a slave begging for mercy
This was the first ever million, a number that the Sumerians had never even dreamt of, a number that only
the pharaohs would need.
Pythagoras
Pythagoras was Greek, born around 569 BC on the island of Samos. He was one of the
most influential and yet most mysterious figures in mathematics. He was responsible for
the first golden age of maths.
According to Pythagoras, perfection depended on the number‟s divisors, numbers that divide
evenly in to the original one.The divisors of 12 are 1, 2, 3, 4 and 6. 12 is an excessive
number because 1 + 2 + 3 + 4 + 6 equals 16. 10 is defective as its divisors, 1, 2, 5 add up to
only 8. The most significant numbers are the so called perfect numbers. These are numbers
whose divisors add up to the number itself. 6 is a perfect number, because it‟s divisors, 1, 2,
3 add up to 6. The next perfect number is 28, because 1 + 2 + 4 + 7 + 14 = 28. As counting
numbers get bigger it gets harder to find perfect numbers. The next four perfect numbers are
496: 8,128; 33,550,336 and 8,589,869,056.
Perhaps Pythagoras‟ most famous discovery involved right angled triangles. His famous
theory, that in any right angled triangle that the square on the hypotenuse is the sum of the
squares of the other two sides.
Archimedes
Archimedes was another great Greek mathematician.
He followed on from
Pythagoras and took maths even further. He took on the idea that numbers don‟t have to
represent physical things, like the length of a side of a triangle. They could be abstract
things or concepts and could be used to figure out things that were really of no use to
anyone, like how many grains of sand it would take to fill the universe. When the romans
invaded, Archimedes was in the middle of some work and looked at the Roman soldier and
said „I beg you not to disturb this!‟ The Roman was not interested in what Archimedes was
doing and cut off his head.
Roman Maths
The golden age of maths was to end when the Romans came to power in 212 BC, or
thereabouts. The Romans weren’t interested in theoretical maths, as Archimedes and
Pythagoras were. The Romans were only interested in power. They just wanted to use
maths for practical purposes, to record dates, to count the soldiers in their armies. They
devised a number system called Roman Numerals. 1 = I, 2 = II, 5 = V, 10 = X , 50 = L,
C = 100, D = 500, M = 1000.
Indian Mathematics
Though the Roman Empire eventually fell, it’s number system carried on. And with it,
European maths stood still. However, just a little later in history, around 500 AD, Indian
mathematics was flourishing, mostly due to it’s number system.
The Indians were not concerned with military organisation. They were philosophers,
astronomers and scientists and they wanted to know what made up the world and the
universe. Like the Egyptian Pharaohs, they liked big numbers, and were the first civilisation
to come up with the idea of infinity. However unlike the Egyptians, they came up with a
number system that made it easy to write these very large numbers down. Indian
mathematicians worked out the first beginnings of our modern number system. By 100 AD,
people in India were writing the numbers as in the picture below. While the numbers 1, 2 and
3 are pretty clear, nobody knows where the other symbols came from. It may be that they
were taken from letters of an Indian alphabet.
But 1500 years ago Indian Mathematicians came up with the greatest idea that anyone has
ever had in maths, and with it revolutionised the way we do maths and what maths could do.
They came up with the number zero. This was possibly India’s biggest ever contribution to
the world – the idea of zero, or nothing, being a number and it put Indian mathematics and
science centuries ahead of the rest of the world. Combine zero with the other nine numbers
and any number, as big or small as you like becomes easy to write down. Our word "zero"
comes from the Sanskrit word meaning "nothing.
Fermat’s Last Theorem
X³ + +Y³ = Z³ ( as opposed to Pythagoras’ Theorem X²+ +Y²= Z² )
Fibonacci, Fibonacci Numbers and The Golden Ratio
Leonardo of Pisa, nicknamed Fibonacci, is a mathematician who having travelled all over
North Africa he noticed the differences in the number systems used in the Arab World
and in Europe. He eventually introduced the Indian number system to Europe in a book
called Liber Abaci, which made solving mathematical problems much easier.
Numbers not only influence people's personalities, they also have connection with the way
the world is constructed. The Fibonacci numbers are the nature's numbering system. They
appear everywhere in Nature, from the leaf arrangement in plants, to the pattern of the leaves
of a flower, animals, the pinecones or the scales of a pineapple. The Fibonacci numbers are
therefore applicable to the growth of every living thing, including a single cell, a grain of
wheat, a hive of bees, and even all of mankind.
Fibonacci Numbers are 1, 2, 3, 5, 8, 13, 23, …
Golden Ratio = 1.618
Measure the length, l, of head. Now measure the width, w, of head. Find the ratio of
length to width by dividing l by w.