Number and Quantity
Currently in our society we don’t worry about where the numbers come from, we
don’t care about where this concept of numbers and mathematics began. We know
that we can do operations with them, how we can figure out how much change we
should get at the grocery store or how long it will take us to go to school. In this class
we learned where numbers come from. How everything started. The first number
system was the Tally system, and it is tens of thousands of years old. It is thought that
woman created the system to keep truck of their menstrual cycles. It was a very basic
system where numbers go up and down by tallies, however it was impossible to make
very big numbers with this system.
The Egyptians and Babylonians are responsible for coming up with better number
systems. The Egyptians used symbols for their numbers. They developed a base 10
number system with a different symbol for every tenth power. They could perform
operations like addition, subtraction, multiplication and division. Our number system
is also a base 10 system, this is why the Egyptians have influenced us a lot. On the
other hand, the Babylonians used a base 60 number system with only two different
symbols to represent their numbers. In this system unlike the Egyptian, the position
where the symbol is placed matters. These three systems have been crucial for the
development of our current mathematics.
Algebra
The word “Algebra” is derived from an Arabic word al-jabr. The development of our
modern idea of Algebra was made by Muhammed Ibn-Musa al-Khwarizmi., who also
brought Hindu-Arabic mathematics to Europe He wrote a book called “ The book of
calculation by completion and Balancing” focused on linear and quadratic equations
using words, not symbols or mathematic notation. However we can see some type of
algebra on the Babylonians due to their use of positional number system. They were
able to solve some equations such as quadratics or cubes. The Babylonians didn’t have
an specific notation for completing or expressing this operations, so they would use
words instead. In order to properly divide numbers, they created a table of
reciprocals.
Another civilizations where Algebra can be seen is the Greeks. Although most of their
mathematics are based on geometry, there was one mathematician, Diophantus, who
focused on algebra. He wrote a book called “Arithmetica” based on the work from the
Babylonians. He worked with equations with more than one variable, giving more
than one solution to the system.
The greatest development of Algebra took place on the 16th century with a French
mathematician called Viete. He gave a proper notation for Algebraic equations,
introducing the terms of constants and variables, which allow us to write equations
with multiple unknowns. Another mathematicians, Girolamo Cardano gave s solutions
for cubics and quadratics, as well as the concept of imaginary numbers. Algebra is one
of the most important branches of mathematics and the way we know it now,
wouldn’t had been possible without these civilizations or mathematicians.
Geometry
Everyone knows that the Greek civilization was the founder of Geometry. This
mathematical field is one of the most fundamental in human history. It is used in a lot
of different fields to know the shapes of molecules or built different structures.
Although the Greeks were the most influential on this field the Egyptians and
Babylonians also contributed to the development of Geometry, focusing on being
practical rather than beuty. The Egyptians found the areas of triangles, rectangles and
approximation for the area of the circle. The Babylonians also calculated the equation
for the circle using 3 as pi.
In Greece they focused more on the beauty of art and sculpture. Thales of Miletus, a
Greek mathematician and philosopher proved vertical angles as well as the Pons
Asinorum. This last basically is the proof that the base angles of an isosceles triangle
are congruent. He based most of his studies in Egyptian geometry looking at the
pyramids. Pythagoras is another mathematician from this period. We all know about
the Pythagoras theorem, but he also came up with some other interesting facts such as
the addition of the interior angles of a triangle is 180 degrees and the golden ratio
derivation.
However the “father of Geometry” is considered to be Euclid of Alexandria. He wrote a
series of books called “the elements” which are the most influential books in
mathematics. He introduced definitions and the five postulates of Euclidean geometry,
being the fifth controversial since it was never proved. All of non-Euclidean geometry
has appeared by neglecting this last postulate, since in non-Euclidean geometry lines
can’t be parallel.
Some other Greek contributors to Geometry were Archimedes, who gave a better
