Ancient Advances in Mathematics


Ancient knowledge of the sciences was often wrong and wholly
unsatisfactory by modern standards. However not all of the knowledge of the
more learned peoples of the past was false. In fact without people like Euclid
or Plato we may not have been as advanced in this age as we are. Mathematics is
an adventure in ideas. Within the history of mathematics, one finds the ideas
and lives of some of the most brilliant people in the history of mankind\'s\'
populace upon Earth.
First man created a number system of base 10. Certainly, it is not just
coincidence that man just so happens to have ten fingers or ten toes, for when
our primitive ancestors first discovered the need to count they definitely would
have used their fingers to help them along just like a child today. When
primitive man learned to count up to ten he somehow differentiated himself from
other animals. As an object of a higher thinking, man invented ten number-
sounds. The needs and possessions of primitive man were not many. When the
need to count over ten aroused, he simply combined the number-sounds related
with his fingers. So, if he wished to define one more than ten, he simply said
one-ten. Thus our word eleven is simply a modern form of the Teutonic ein-lifon.
Since those first sounds were created, man has only added five new basic
number-sounds to the ten primary ones. They are “hundred,” “thousand,” “
million,” “billion” (a thousand millions in America, a million millions in
England), “trillion” (a million millions in America, a million-million millions
in England). Because primitive man invented the same number of number-sounds as
he had fingers, our number system is a decimal one, or a scale based on ten,
consisting of limitless repetitions of the first ten number sounds.
Undoubtedly, if nature had given man thirteen fingers instead of ten,
our number system would be much changed. For instance, with a base thirteen
number system we would call fifteen, two-thirteen\'s. While some intelligent and
well-schooled scholars might argue whether or not base ten is the most adequate
number system, base ten is the irreversible favorite among all the nations.
Of course, primitive man most certainly did not realize the concept of
the number system he had just created. Man simply used the number-sounds
loosely as adjectives. So an amount of ten fish was ten fish, whereas ten is an
adjective describing the noun fish.
Soon the need to keep tally on one\'s counting raised. The simple
solution was to make a vertical mark. Thus, on many caves we see a number of
marks that the resident used to keep track of his possessions such a fish or
knives. This way of record keeping is still taught today in our schools under
the name of tally marks.
The earliest continuous record of mathematical activity is from the
second millennium BC When one of the few wonders of the world were created
mathematics was necessary. Even the earliest Egyptian pyramid proved that the
makers had a fundamental knowledge of geometry and surveying skills. The
approximate time period was 2900 BC
The first proof of mathematical activity in written form came about one
thousand years later. The best known sources of ancient Egyptian mathematics in
written format are the Rhind Papyrus and the Moscow Papyrus. The sources
provide undeniable proof that the later Egyptians had intermediate knowledge of
the following mathematical problems: applications to surveying, salary
distribution, calculation of area of simple geometric figures\' surfaces and
volumes, simple solutions for first and second degree equations.
Egyptians used a base ten number system most likely because of biologic
reasons (ten fingers as explained above). They used the Natural Numbers
(1,2,3,4,5,6, etc.) also known as the counting numbers. The word digit, which
is Latin for finger, is also another name for numbers which explains the
influence of fingers upon numbers once again.
The Egyptians produced a more complex system then the tally system for
recording amounts. Hieroglyphs stood for groups of tens, hundreds, and
thousands. The higher powers of ten made it much easier for the Egyptians to
calculate into numbers as large as one million. Our number system which is both
decimal and positional (52 is not the same value as 25) differed from the
Egyptian which was additive, but not positional.
The Egyptians also knew more of pi then its mere existence. They found
pi to equal C/D or 4(8/9)ª whereas a equals 2. The method for ancient peoples
arriving at this numerical equation was fairly easy. They simply counted how
many times a string that fit the circumference of the circle fitted