### history_of_mathematics Molly Hanson - AQUINAS

```The History of
Mathematics
By: Molly
Hanson
Noted Mathematicians
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Archimedes
Euclid
Sir Isaac Newton
Pythagoras
Blaise Pascal
Aryabhatta
Ramanujam
Archimedes
He is often considered to be the
greatest mathematician of
ancient times.
He performed geometric proofs
using Euclid’s geometric formulism.
He excelled at computing
volumes and areas using the
method of exhaustion.
Archimedes discovered how to calculate the volume of a sphere. It is twothirds the volume of the smallest cylinder that can contain it. He was so
proud of this discovery that he requested that a figure of a sphere and a
cylinder be engraved in his tombstone.
Euclid
The “Father of Geometry”
• He wrote thirteen books
called “Euclid’s Elements”.
They covered the subjects
of:
• Plane Geometry
• Number Theory
• Eudoxe’s theory of
irrational numbers
• Solid Geometry
• Properties of five regular
polyhedrons
Sir Isaac Newton
-He created the basis
for elementary and
integral calculus.
-He also came up with
the idea that the
integration of a
function is the opposite
procedure of its
differentiation.
*Sir Isaac Newton
developed simple
methods for:
-finding areas
-lengths of curves
-maxima and minima
He is credited with the development of a potent
problem solving and analysis tool in pure
mathematics and physics.
Pythagoras
• He observed mathematics, music
and astronomy and concluded
that “all things were numbers”.
• He is credited with the
Pythagorean Theorem.
• He came up with the idea that
vibrating strings make
harmonious tones if the ratios of
the length of the strings are
whole numbers.
• His followers, Pythagoreans,
discovered that the diagonal of a
square was not an integral
multiple of its side. This
discovery led to proof of the
existence of irrational numbers.
*Later in his
life, he became
involved in
gambling and
found a sudden
interest in
probability.
Blaise Pascal
1623-1662
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He is best known for his triangle,
which is rightly called Pascal’s
Triangle. Pascal’s Triangle is a
triangular expression of binomial
coefficients.
* When studying the mathematics of fluid at
rest, or hydrostatics, his work led to the
invention of the syringe and the hydraulic
press.
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In 1645 he invented the first
calculating machine which had
the ability to calculate
computations.
Aryabhatta 476-550 A.D.
• He found the
approximate value of Pi
• He also discovered that
Pi is irrational
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He was ahead of his time.
He mentions the formula to
calculate the value of a triangle,
which wasn’t discovered until
much later.
He was also already aware that
the earth spins on an axis.
He could explain the planets
movements.
Ramanujam
Ramanujam was one of India’s
greatest mathematicians.
-He did work with Elliptic
Functions, continued fractions, and
infinite series.
-He taught himself how to do
mathematics using a book called;
Synopsis of elementary results in
pure mathematics.
Mathematics and the World
What areas of the world made contributions and what were they?
Mesopotamia
The earliest math.
• The Sumerians, the oldest of
the Mesopotamian
civilizations, developed a
complex system of
metrology. There is also
evidence of them writing
multiplication tables using
geometry and division.
• Clay tablets found from this
civilization also include
equations and the calculation
of regular reciprocal pairs.
Egypt
• Rhind Papyrus
• It is an instruction
manual used by students
in arithmetic and
geometry.
• Moscow Papyrus
• This contains story
problems used to make
mathematics
entertaining
Greek and Hellenistic
• Development of deductive
reasoning rather than
inductive.
• Use of logic to derive
conclusions, and the use of
mathematics to prove these
conclusions.
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Greece gave us many great
mathematicians
Pythagoras
Thales
Eudoxus
Aristotle
Archimedes
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The mathematician Thales of
Greece is credited as the first to
use geometry to calculate the
height of the pyramids and the
distance of ships from the shore.
China
• The use of “Rod Numerals”
allowed for the use of very
large numbers on the Chinese
abacus.
The Nine Chapters on
Mathematical Art is a writing
from the Han Dynasty that
consists of 246 word
problems dealing with
employment of geometry,
figure height spans and
dimension ratios for Chinese
pagoda towers,, engineering,
surveying, and includes
material on right triangles and
values of Pi
India
The Sulba Sutras
• These religious books give
simple rules for building
altars of various shapes
• It also gives methods for
constructing a circle with
approximately the same
area of a given square,
which can bring us close to
finding the value of Pi
The Surya Siddhanta
• This writing gives us sin,
cosine and inverse sin.
The Decimal Place System first
appears in the Aryabhatiya
Islamic World
• The Islamic world
came up with new
methods for solving
equations.
• The Islamic world also
gives us the first
known proof.
• The tangent function
was developed my
the Muslims.
• Khwarizmi is called
“The Father of
Algebra”
• He was the first to
teach Algebra in
elementary form
• He also developed
the idea of
cancellation of like
terms on opposite
sides of the
equation.
```