Title: Water lily (also called Lotus) Coil of rope. Heel bone
1The History of Mathematics
http//www.math.wichita.edu/richardson/timeline.h
tml
http//wwwgroups.dcs.stand.ac.uk/history/Indexe
s/HistoryTopics.html
http//wwwgroups.dcs.stand.ac.uk/history/BiogIn
dex.html
2Completing a SquareSolving a Quadratic Equation
alKhwarizmi Iraq (ca. 780850)
x2 10 x 39
x2 10 x 425/4 3925
(x5)2 64
x 5 8
x 3
3The Bridges of KonigsbergTopology
Leonhard Euler Switzerland 1707  1783
 In Konigsberg, Germany, a river ran through the
city such that in its centre was an island, and
after passing the island, the river broke into
two parts. Seven bridges were built so that the
people of the city could get from one part to
another.  The people wondered whether or not one could walk
around the city in a way that would involve
crossing each bridge exactly once
4The city
5Infinite Prime Numbers
Euclid Greece 325 265BC
 Theorem There are infinitely many prime numbers.
 ProofSuppose the opposite, that is, that there
are a finite number of prime numbers. Call them
p1, p2, p3, p4,....,pn. Now consider the number  (p1p2p3...pn)1
 Every prime number, when divided into this
number, leaves a remainder of one. So this number
has no prime factors (remember, by assumption,
its not prime itself).  This is a contradiction. Thus there must, in
fact, be infinitely many primes.
6The Search for Pi
7The Search for Pi
 François Viète (15401603)
 France  determined that
 John Wallis (16161703)
 English  showed that
 While Euler (17071783)
 Switzerland derived his famous formula
 Today Pi is known to more than 10 billion decimal
places.
8Ancient Babylonia
Laura T
The Sumerians had developed an abstract form of
writing based on cuneiform (i.e. wedgeshaped)
symbols. Their symbols were written on wet clay
tablets which were baked in the hot sun and many
thousands of these tablets have survived to this
day. It was the use of a stylus on a clay medium
that led to the use of cuneiform symbols since
curved lines could not be drawn. The later
Babylonians adopted the same style of cuneiform
writing on clay tablets. The Babylonians had an
advanced number system, in some ways more
advanced than our present systems. It was a
positional system with a base of 60 rather than
the system with base 10 in widespread use today.
9The Four Colour Theorem
The Four Colour Conjecture was first stated just
over 150 years ago, and finally proved
conclusively in 1976. It is an outstanding
example of how old ideas combine with new
discoveries and techniques in different fields
of mathematics to provide new approaches to a
problem. It is also an example of how an
apparently simple problem was thought to be
solved but then became more complex, and it
is the first spectacular example where a
computer was involved in proving a mathematical
theorem.
10Laura T
Ancient Babylonia
The Babylonians divided the day into 24 hours,
each hour into 60 minutes, each minute into 60
seconds. This form of counting has survived for
4000 years. To write 5h 25 30, i.e. 5 hours, 25
minutes, 30 seconds, is just to write the
sexagesimal fraction, 5 25/60 30/3600. We adopt
the notation 5 25, 30 for this sexagesimal
number, for more details regarding this notation
see our article on Babylonian numerals. As a base
10 fraction the sexagesimal number 5 25, 30 is 5
4/10 2/100 5/1000 which is written as 5.425 in
decimal notation.
11Laura T
Ancient Babylonia
Perhaps the most amazing aspect of the
Babylonians calculating skills was their
construction of tables to aid calculation. Two
tablets found at Senkerah on the Euphrates in
1854 date from 2000 BC. They give squares of the
numbers up to 59 and cubes of the numbers up to
32. The table gives 82 1,4 which stands for 82
1, 4 1 x 60 4 x 1 64 and so on up to
592 58, 1 58 x 60 1 x 1 3481). The
Babylonians used the formula ab (a b)2  a2
 b2/2 to make multiplication easier. Even
better is their formula ab (a b)2  (a 
b)2/4 which shows that a table of squares is
all that is necessary to multiply numbers, simply
taking the difference of the two squares that
were looked up in the table then taking a quarter
of the answer.
12Egyptian numerals
Laura T
The following hieroglyphs were used to denote
powers of ten
or
Multiples of these values were expressed by
repeating the symbol as many times as needed. For
instance, a stone carving from Karnak shows the
number 4622 as
13Chinese Mathematics
Chinese mathematics has developed greatly since
at least 100 BC. Although the Chinese refer back
to their ancient texts, many of which were
written on strips of bamboo, they are constantly
coming up with ways of working out problems. One
of the earliest Chinese mathematicians was a man
named Luoxia Hong (130BC 30BC). He designed a
new calendar for the Emperor, which featured 12
months, based on a cycle of 12 years. This
inspired many people to design calendars and the
one we have today. The Chinese also came up with
a rule called the Gougu Rule. This is the Chinese
version of Pythagoras. Liu Hui (220AD 280AD)
tried to find pi to the nearest number. He
eventually got to 3.14159, which in those days
was thought to be an incredible achievement.
14Moscow Papyrus arithimetic
The Moscow Papyrus is located in a museum hence
the name. The papyrus was copied by a scribe and
was brought to Russia. The papyrus contains 25
maths problems involving simple equations and
solutions. The problems are not in modern form.
The problem that has generated the most interest
is the volume of a truncated pyramid (a square
based pyramid with the top portion removed). The
Egyptians discovered the formula for this even
though it was very hard to derive.
The Actual author of the equation is unknown. But
this is what he/she discovered
The Moscow Papyrus is 15 feet long and about 3
inches wide.
Alannah
Problem 14 Volume of a truncated Pyramid
15Johannes Widman was a German mathematician who is
best remembered for an early arithmetic book
which contains the first appearance of and
(both adding and subtracting, and positive and
negative) signs in 1498.
Johannes Widman
The plus and minus sign
His book was better than anybody elses because
he had more and a wider range of examples. The
book remained in print until 1526.(28 years after
it was first published.)
Alannah
16Moscow Papyrus Arithmetic
As it name may suggest, the Moscow papyrus is
located in the Museum of Fine Arts in Moscow. In
around 1850BC, the papyrus was copied by an
anonymous scribe and was bought to Russia in the
19th Century. It contains 25 problems containing
simple equations and solutions.
However, the equations are not in modern form.
The problem that generates the most interest is
the calculation of the volume of a truncated
pyramid (a square based pyramid with the top cut
off) The Egyptians seemed to know this difficult
formula.
V (1/3)(a² ab b²)(h)
Alex
17Johannes Widman (1462 1498)
Widman is best known for a book on arithmetic
which he wrote (in German) in 1489AD. This
contains the first appearance of and signs.
This was better than those that had come before
it with a wider range of examples.
The book continued to be published until 1526AD.
Then, Adam Ries amongst others produced
superior books.
Alex
18Chu Shihchieh (Zhu Shijie)
Zhu Shijie was one of the greatest Chinese
mathematicians. He lived during the Yuan
Dynasty. Yang worked on magic squares and
binomial theorem, and is best known for his
contribution of presenting Yang Huis Triangle.
This triangle was the same as Pascals Triangle,
discovered independently by Yang and his
predecessor Jia Xian .Yang was also a friend to
the other famous mathematician Qin Jiushao.
An early form of Pascals triangle
Calum
19Magic squares
In mathematics, a magic square of order n is an
arrangement of n² numbers, usually distinct
integers, in a square, such that the n numbers in
all rows, all columns, and both diagonals sum to
the same constant. A normal magic square
contains the integers from 1 to n². All non
trivial magic squares exist for n3.
An example of a magic square
The equation
Calum
20Johannes Widmann
Johannes Widmann (born c. 1460 in Eger died
after 1498 in Leipzig) was a German mathematician
who was the first to use the addition () and the
subtraction () signs. Widmann attended the
University of Leipzig in the 1480s, and published
Behende und hubsche Rechenung auff allen
Kauffmanschafft, his work making use of the
signs, in Leipzig in 1489.

Calum
21Aristarchus
Charis
Aristarchus of Samos was a Greek mathematician
and astronomer. He was born in about 310BC and
died at around 230BC. He is the first person to
suggest a universe with the Sun at the centre
instead of the Earth.
He tried to work out the sizes of the Sun and the
Moon and how far away they are. He worked out
that the Sun was 20 times further away than the
moon and 20 times bigger. Both these estimates
were too small but the reasoning behind it was
right.
22Blaise Pascal (16231662)
Charis
 Pascal was a French mathematician and physicist.
 His father was a tax official and Pascal made a
calculating machine that did addition and
subtraction to make his work easier.
He wrote about Pascals triangle. Each number is
the sum of the two above it. There are lots of
different patterns in the triangle. Some are
shown on the diagram.
Pascal also worked with Fermat on the theory of
probability, and he wrote about projective
geometry when he was only 16.
23Pythagoras and the Mathematikoi
 Pythagoras was the leader of a Society which
consisted mainly of followers called the
mathematikoi.
 The mathematikoi owned nothing personal and
were vegetarians.
 Any mathematical discoveries they made the
credit was given to Pythagoras.
 Everything we know about Pythagoras and the
mathematikoi was only recorded properly 100 years
later as they apparently wrote none of their
information down.
David
24Trigonometry of Hipparchus
Hipparchus was a Greek mathematician who
invented one of the first trigonometry tables
which he needed to compute the orbits of the Sun
and Moon.
The table on the right represents the Chord
function. The chord of an angle is the length
between two points on a unit circle separated by
that angle.
If one the angles is zero it can be easily
related to the sine function. And the used in the
half angle formula
David
25JAPANESE MATHEMATICS
The system of Japanese numerals is the system of
number names used in the Japanese language. The
Japanese numerals in writing are entirely based
on the Chinese numerals and the grouping of
large numbers follow the Chinese tradition of
grouping by 10,000. Like in Chinese numerals,
there exists in Japanese a separate set of kanji
for numerals called daiji () used in legal and
financial documents to prevent unscrupulous
individuals from adding a stroke or two, turning
a one into a two or a three. The formal numbers
are identical to the Chinese formal numbers
except for minor stroke variations
George
http//en.wikipedia.org/wiki/Japanese_numerals
26John Napier ( 15501617)
 Napier was a Scottish mathematician who studied
math like a hobby as he never had time to spend
on calculations between working on theology.  He is best known, along with Joost Burgi, for his
invention of logarithms  He is also famous for the invention of two
theories  Napiers analogy (used in solving spherical
triangles)  And Napiers bones. (used for mechanically
multiplying, dividing, taking square roots and
cube roots
Hannah
27Pierre de Fermat (1601 1665)
 Fermat was a French mathematician who is best
known for his work on number and theory  One of his last theorems was proven by Andrew
Wiles in 1994.  Whilst in Bordeaux, Fermat produced work on
maxima and minima, which was important. His
methods of doing this were similar to ours ,
however as he has not a professional
mathematician his work was very awkward.  Fermats last theorem was that if you had the
equation xn yn zn  n in this equation can be no more that two.
 When n is more than two the equation does not
work
Hannah
28Hipparchus
Issy
Hipparchus is most known for Trigonometry. He did
not discover this on his own however. Menelaus
and Ptolomy, helped with this.
Even if he did not invent it, Hipparchus is the
first person of whose systematic use of
trigonometry we have documentary evidence. some
historians say. Some even go as far as to say
that he invented trigonometry. Not much is known
about the life of Hipparchus. But it is believed
that he was born at Nicaea in Bithynia, and lived
from 190 BC to 120 BC
29Algebra
Issy
Algebra is a branch of mathematics concerning the
study of structure, relation, and quantity.
Together with geometry, analysis, combinatorics,
and number theory, algebra is one of the main
branches of mathematics. Elementary algebra is
provides an introduction to the basic ideas of
algebra, including effects of adding and
multiplying numbers, along with factorization and
determining their roots. Algebra is much broader
than elementary algebra and can be generalized.
In addition to working directly with numbers,
algebra covers working with symbols, variables,
and set elements. The history of algebra began
in ancient Egypt and Babylon, where people
learned to solve linear (ax b) and quadratic
(ax² bx c) equations, as well as
indeterminate equations such as x² y² z²,
whereby several unknowns are involved. The
ancient Babylonians solved arbitrary quadratic
equations by essentially the same procedures
taught today. They also could solve some
indeterminate equations
30The Roman Abacus
JohnJack
 The Roman Abacus was devised by Roman traders
adapting ideas that had been picked up in Egypt.  The Abacus is made up of grooves in a slate tile
with marbles that run in them.  The Abacus was originally made in Babylon using
stones and ditched made in the dry soil in 2700
BC.  The Abacus was originally made in Babylon using
stones and ditched made in the dry soil in 2700
BC.  Each Abacus used a different scale depending on
the user. Traders often used ones with fractions
up to 1/12.  This would mean that they could subtract quite
accurately eg. To subtract 1/3 you would take a
bead from the 1/4 column and one from the 1/12
column.
31Laura W
 Buffons needle problem
 GeorgesLouis Leclerc, Comte de Buffon lived
from in September 7, 1707 to April 16, 178.  He had many different careers, as a naturalist,
mathematician, biologist, cosmologist and author.  The Lycée Buffon in Paris is named after him.
 The problem he is famous for is
 Suppose we have a floor made of parallel
strips of wood, each the same  width, and we drop a needle onto the floor.
What is the probability that the needle will lie
across a line between two strips  Or in more mathematical terms
 Given a needle of length l dropped on a plane
ruled with parallel lines t units apart, what is
the probability that the needle will cross a
line  For n needles dropped with h of the needles
crossing lines, the probability is
This is useful because it can be rearranged to
get an estimate for pi
32Egyptian Numerals
Kyle
The Egyptians had a writing system based on
hieroglyphs from around 3000 BC. Hieroglyphs are
little pictures representing words. It is easy to
see how they would denote the word bird by a
little picture of a bird but clearly without
further development this system of writing cannot
represent many words. The way round this problem
adopted by the ancient Egyptians was to use the
spoken sounds of words. For example, to
illustrate the idea with an English sentence, we
can see how I hear a barking dog might be
represented by an eye, an ear, bark of
tree head with crown, a dog. Of course
the same symbols might mean something different
in a different context, so an eye might mean
see while an ear might signify sound. The
Egyptians had a bases 10 system of hieroglyphs
for numerals. By this we mean that they has
separate symbols for one unit, one ten, one
hundred, one thousand, one ten thousand, one
hundred thousand, and one million.
33Kyle
The Addition Minus Signs
The plus and minus signs are symbols representing
positive and negative, the meaning of them has
been around since the Egyptian times, but the
actual symbols and were first published by
Johannes Widmann.
Minus
A Jewish tradition that dated from at least from
the 19th century was to write plus using a symbol
like an inverted T. This practice was then
adopted into Israeli schools (this practice goes
back to at least the 1940s) and is still
commonplace today in some elementary schools
(including secular schools) while fewer secondary
schools. It is also used occasionally in books by
religious authors, but most books for adults use
the international symbol . The usual
explanation for the origins of this practice is
that it avoided the writing of a symbol that
looked like a Christian cross. Unicode has this
symbol at position UFB29 Hebrew letter
alternative plus sign
Addition
Jewish Addition Symbol
34CHAOTIC BEHAVIOR
Kyle
In mathematics, chaos theory describes the
behaviour of certain dynamical systems that is,
systems whose states evolve with time that may
exhibit dynamics that are highly sensitive to
initial conditions (popularly referred to as the
butterfly effect). As a result of this
sensitivity, which manifests itself as an
exponential growth of perturbations in the
initial conditions, the behaviours of chaotic
systems appears to be random. This happens even
though these systems are deterministic, meaning
that their future dynamics are fully defined by
their initial conditions, with no random elements
involved. This behaviour is known as
deterministic chaos, or simply chaos. Chaotic
behaviour is also observed in natural systems,
such as the weather. This may be explained by a
chaostheoretical analysis of a mathematical
model of such a system, embodying the laws of
physics that are relevant for the natural system.
35Hieroglyphic numerals in Egypt
 Hieroglyphs were introduced for numbers in
3000BCE. Their number system was based on units
of 10. They used simple grouping to make
different numbers.  The Egyptians
 used different
 images for
 their hieroglyphs.

Horus was Egyptian God who fought the forces of
darkness (in the form of a boar  a pig) and won.
His eye is a symbol for Egyptian Unit Fractions.
Each part of the eye is a part of the whole. All
the parts of eye, however, dont add up to the
whole. This, some Egyptologists think, is the
sign that the knowledge can never be total, and
that one part of the knowledge is not possible to
describe or measure.
Nina
36Pythagoras of Samos
Nina
 Pythagoras was an ancient Greek mathematician.
Pythagoras was born about 569 BC in Samos, Ionia
and died about 475 BC.  Pythagoras invented Pythagorass theorem which is
the idea that in a right angled triangle the two
shorter sides squared and added equals the
longest side (the hypotenuse) squared.  It was thought that the Babylonians 1200 years
earlier knew this before but Pythagoras was the
one to prove it. It is said that this is the
oldest numbertheory document in existence. This
theorem works for every right  angled triangle
37Algebra
Jack G
 While the word algebra comes from Arabic word
(aljabr)its origins are from the ancient
Babylonians. With this system they were able to
discover unknown values for a class of problems
typically solved today by using linear equations,
quadratic equations, and indeterminate linear
equations.  The geometric work of the Greeks, typified in the
Elements, provided the framework for finding the
formulae beyond the solution of particular
problems into more general systems of stating and
solving equations.  The Greek mathematicians Hero of Alexandria and
Diophantus (the father of algebra) made
algebra into a much higher level. People argye
that alKhwarizmi, who founded the discipline of
aljabr, deserves that title instead.
38Algebra
Jack G
 Later, the Indian mathematicians developed
algebraic methods to a high degree of
sophistication. AlKhwarizmi produced the
reduction and balancing (the transposition of
subtracted terms),He gave an explanation of
solving quadratic equations supported by
geometric proofs.  The Indian mathematicians Mahavira and Bhaskara
II, the Persian mathematician AlKaraji and the
Chinese mathematician Zhu Shijie, solved various
cases of cubic, quadratic, quintic and
higherorder polynomial equations using numerical
methods.  Gottfried Leibniz discovered the solution to
simultaneous equations
39Napiers Bones
Paul
 Napiers bones are basically a big multiplication
square.  It was used before calculators for multiplication
of !HUGE! Numbers.  To do a sum using them you arrange the bones in
the order of the number to multiply like in the
example the sum is 467853997.
 Then, starting from the left, you just add all
the numbers in the row, carrying the tens.
http//en.wikipedia.org/wiki/Napier27s_bones
40Nicole
Ahmes
 Ahmes was the Egyptian scribe who wrote the
Rhind Papyrus  one of the oldest known
mathematical documents.
41 Born about 1680 BC in EgyptDied about 1620
BC in Egypt  The Rhind Papyrus, which came to the British
Museum in 1863, is sometimes called the Ahmes
papyrus in honour of Ahmes. Nothing is known of
Ahmes other than his own comments in the papyrus.
 Ahmes claims not to be the author
 of the work, being, he claims, only a
 scribe. He says that the material
 comes from an earlier work of about
 2000 BC.
 The papyrus is our main source of
 information on Egyptian mathematics.
Nicole
42Hieroglyphic Numerals
Hieroglyphics were used by the Egyptians in
around 3000BC. These symbols below are what they
would use as numbers. Although they only have to
write one symbol for one million and we have to
do seven, there is a fault. To write one million
take one they would have to write 54 symbols.
999999
100000
1million or Infinity
1
10
100
1000
10000
Single stroke
Heel bone
Coil of rope
Water Lily
Finger
Man with both hands raised
Michael
Tadpole or frog
43Xenocrates of Chalcedon
Xenorcrates was a Greek philosopher,
mathematician and leader of the platonic army
from 339BC to 314BC. Xenocrates is known to have
written a book On Numbers, and a Theory of
Numbers, besides books on geometry. Plutarch
writes that Xenocrates once attempted to find the
total number of syllables
Birth 396BC, Chalcedon Died 314BC,
Athens Interests logic, physics, metaphysics,
epistemology, mathematics, ethics. Ideas
developed the philosophy of Plato.
that could be made from the letters of the
alphabet. According to Plutarch, Xenocrates
result was 1,002,000,000,000. This possibly
represents the first instance that a
combinatorial problem involving permutations was
attempted. Xenocrates also supported the idea of
indivisible lines (and magnitudes) in order to
counter Zenos paradoxes.
Michael
44Abul Hasan Ahmad ibn Ibrahim AlUqlidisi
Abul Hasan Ahmad ibn Ibrahim AlUqlidisi was an
Arab mathematician who was active in Damascus and
Baghdad. He wrote the earliest surviving book on
the positional use of the Arabic numerals, around
952. It is especially notable for its treatment
of decimal fractions, and that it showed how to
carry out calculations without deletions. While
the Persian mathematician Jamshid alKashi
claimed to have discovered decimal fractions
himself in the 15th century, J. Lennart Berggrenn
notes that he was mistaken, as decimal fractions
were first used five centuries before him by
alUqlidisi as early as the 10th century.
Michael
45Zhu Shijie of China
Ollie
Zhu Shijie was born in the 13th century near
Beijing. Two of his mathematical works have
survived Introduction to Computational
Studies and Jade Mirror of Four
Unknowns. This book brought Chinese algebra to
its highest level and it is his most important
work. He makes use of the Pascal Triangle
centuries before Blaise Pascal brought it to
common knowledge.
46Francesco Pellos 1450 1500 AD
 Francesco Pellos, from Nice, is the earliest
example of the use of the decimal point  He wrote an arithmetic book, called Compendio de
lo Abaco, in 1492.  In this book he makes use of a dot to denote the
division of a number by a power of ten. This has
evolved to what we now call a decimal point.
47Thales (620547BC)Discoverer of deductive
Geometry
Jack S
 Father of deductive geometry
 Credited for five theorems
 1) A circle is bisected by any diameter.
 2) The base angles of an Isosceles Triangle are
equal.  3) The angles between two intersecting straight
lines are equal.  4) Two triangles are congruent if they have
 two angles and one side equal.
 5) An angle in a semicircle is a right angle.
48Bhaskara
Jack S
 Can be called Bhaskaracharya
 meaning Bhaskara the teacher.
 Lived in India.
 Famous for number systems and solving equations
which was not achieved in Europe for several
centuries.  More information at
 http//www.maths.wichita.edu/richardson/
49Hypatia of Alexandria (AD 355 or 370 415)
Rachel
Hypatias father (Theon) was a mathematician in
Alexandria in Egypt and he taught her about
mathematics. From about the year 400 onwards she
lectured on mathematics and philosophy. She also
studied astronomy and astrology and may have
invented astrolabes (which can be used to study
astronomy) . However, there is no proof that she
did this. Although she did not make any
discoveries herself, she helped her father Theon
with some of his works, and was the first woman
to make a significant contribution to the
development of mathematics.
She was believed by some people to practise magic
and was also hated for being a pagan. In AD 415
she was murdered in the street by a group of
monks.
The Crater Hypatia and Rimae Hypatia (features of
the moon) are both named after Hypatia.
http//wwwgroups.dcs.stand.ac.uk/history/Biogra
phies/Hypatia.html
50Julia Hall Bowman Robinson (1919 1985)
Rachel
Julia was born in Missouri in the USA. When she
was nine, she caught scarlet fever, which was
followed by rheumatic fever. In total she missed
two years of school. Over the next year, she had
lessons three mornings a week and managed to get
through four years of education (fifth to eighth
grades). In her last year at school she was the
only girl in her maths and physics classes.
In 1948 she started work on Hilberts tenth
problem (Given a Diophantine equation with any
number of unknown quantities and with rational
integral numerical coefficients To devise a
process according to which it can be determined
in a finite number of operations whether the
equation is solvable in rational integers) and
came up with the Robinson hypothesis. This helped
Yuri Matijasevic to find the final solution to
the problem in 1970.
51Mary Ann Elizabeth Stephansen (1872 1961)
Rachel
She was born in Bergen in Norway on 10 March
1872. She studied at university in Zurich in
Switzerland. She was the only Norwegian to pass
the entrance exam. When she left in 1896 she
became a teacher in Norway, which was unusual for
women at that time. During her time as a teacher
she also worked on partial differential equations.
In 1906 she was appointed to the Norwegian
Agricultural College where she taught maths and
physics. She retired in 1931 and went to live
with her sister Gerda in England.
http//wwwgroups.dcs.stand.ac.uk/history/Biogra
phies/Stephansen.html
52Hieroglyphic numerals in Egypt  Brought in /
3000BC
Rosa
Egyptian hieroglyphics were a symbol for each
power of 10. It did not matter if there was a 0
in the number because of the powers.
This is the number 4622
53Rosa
Roman Numerals
To get a number you put the symbols together in
the correct order unless there is a shorter way
of writing it
Roman Numerals are mainly used for writing dates
and on clocks
For Example  To get some numbers you can put a
smaller number in front of a larger number
indicating a subtraction. E.g. 999 can be written
like this IM which is a lot easier than
DCCCCLXXXXVIIII
54John Napier 15501617
Sam
He is most well known for his inventions of
logarithms but also invented Napiers bones
which are a way of multiplying, dividing, and
taking square and cube roots. The board consists
off 9 rods which have the times table of 19 on
each and the number of the corresponding times
table at the top You turned them so at they top
it made your number then add the numbers in the
row if you are multiplying it by a number with
more than one digit you would do it for both add
a zero on they tens 2 zeros on the hundreds etc
then add together
By Sam allum
55Arabic/Islamic mathematics
Arabic mathematics forgotten brilliance
Recent research has proved the debt that we owe
to Arabic/Islamic mathematics. Certainly many of
the ideas which were previously thought to have
been brilliant new conceptions due to European
mathematicians of the sixteenth, seventeenth and
eighteenth centuries, were actually developed by
Arabic/Islamic mathematicians around four
centuries earlier! In many respects the
mathematics studied today is far closer in style
to that of the Arabic/Islamic contribution than
to that of the Greeks.
56Arabic Numerals
Sameer
 The Indian numerals were not transmitted
directly from India to Europe but rather came
first to the Arabic/Islamic peoples and from them
to Europe. The story of this transmission is not,
however, a simple one. The eastern and western
parts of the Arabic world both saw separate
developments of Indian numerals with relatively
little interaction between the two. By the
western part of the Arabic world we mean the
regions comprising mainly North Africa and Spain.
Transmission to Europe came through this western
Arabic route, coming into Europe first through
Spain.
57Aristarchus Heliocentric Astronomy.
Sophie
 (310BC  BC 210BC)
 He was a Greek mathematician and an astronomer.
He is widely known for proposing the theory that
the universe was suncentred (heliocentric).  He also made some calculations that gave him an
estimation of the sizes and the distance of the
Sun and the Moon, for example, the volume of
Aristarchuss Sun would be almost 300 times
greater than the Earth.
58Ptolemys Almagest.
Sophie
 (85AD 165AD).
 Claudius Ptolemy put a book together called
Mathematical Compilation. It was a book on
everything that people knew about astronomy at
the time.  He thought that the Earth was the centre of
the universe, but surprisingly the calculations
he made were fairly accurate. Up until 1542,
Almagest was still the primary source of
astronomical knowledge.
59Johannes Kepler (1571 1630) Germany
 Kepler was a mathematician who studied astronomy.
In his book, he gave his first 2 laws of
astronomy  The planets move around the Sun in elliptical
orbits.  The radius vector joining a planet to the sun
sweeps out equal areas in equal time.
(1)The orbits are ellipses, with focal
points ƒ1 and ƒ2 for the first planet and ƒ1 and
ƒ3 for the second planet. The sun is placed in a
fixed point ƒ1. (2) The two shaded sectors
A1 and A2 have the same surface area and the time
for planet 1 to cover segment A1 is equal to the
time to cover segment A2. (3) The total orbit
times for planet 1 and planet 2 have a ratio
a13/2 a23/2. Isaac Newton later used
Keplers theory for his gravitational theory.
Sruthi
60Euclid of Alexandria (325BC 265BC)
 Euclid was a Greek mathematician best
 known for his treatise on geometry The
 Elements . This influenced the development
 of Western mathematics for more than 2000
 years.
Sruthi
61Pythagorean Arithmetic and Geometry
 Pythagoras was a Greek philosopher in 500BC. He
is best known for discovering the formula for
finding the hypotenuse on a right angled
triangle, using the other two sides.  Around 518BC, Pythagoras started a school based
on religion and philosophy. The school had many
followers, and was to be found in Crotone in
Southern Italy. Pythagoras had started another
school in Samos, which he abandoned. Pythagoras
named his followers the Mathematikoi. They were
pure mathematicians. They followed strict rules
of respect and humility. They had very few
possessions.
Ben
62Sieve of Eratosthenes
Ben
 Eratosthenes was a Greek philosopher, but was
also an author, poet, athlete, geographer, and
astronomer. He was the first to calculate the
circumference of the Earth.  Eratosthenes was to first to conceive a method of
finding all the prime numbers up to a certain
integer. This link explains more
http//en.wikipedia.org/wiki/Sieve_of_Eratosthenes
. However, a brief explanation is this  1. Think of a continuous list of numbers from two
to some integer.  2. Cross out all multiples of two.
 3. The next lowest, uncrossed number is a prime.
 4. Cross off all of this numbers multiples.
 5. Repeat steps 3 and 4 until you have no more
multiples.
63Buffons (1777) Needle Problem
 Buffons needle problem involves probabilities.
A bunch of needles are scattered on a set of
parallel lines and we need to find the
probability of a needle falling on one of the
lines.
The general formula for the probability is
Total Needles 500 tosses Red needles/ needles on
a line 107 Probability of crossing in this one
is..(107/500)100 0.214100 21.4
Vivek