Unit 9 Pi Assignment

Unit 9 Pi Assignment
"PI" Assignment 1. Max makes certain statements and claims to belief, which he repeats many
times. First, Math (number) is the language of the universe. Second, Nature can be expressed in
these numbers. Third, if you graph (or otherwise represent) these numbers, patterns will emerge.
Fourth, if you can discover these patterns, you can find the key to understanding the apparent chaos,
and you can predict everything. What is your opinion of Max's core beliefs? Do they really apply to
the universe? Could a mathematical pattern be something like the DNA if the universe? Max's
beliefs cannot be valid in terms of defining the universe. If mathematics would be able to create
patterns that can help to understand the universe it would have helped solve ... Show more content
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Faith comes in, as a person believes that there is a number that can solve almost everything from
religion to the stock market. People therefore have a belief of a certain particular number, which can
help them sought out problems especially the Rabbis who deal are looking for a key, which is
associated with the 216–digit number. 3. The complete title of the film is "Pi: Faith in Chaos". How
does the concept of chaos apply to the film? The film has much chaos especially those related with
the uncertainty of various issues like the state of the stock market. Chaos are present in the world
especially where people are uncertain about various things. The Rabbis do not have the answer to
where the key was and the businesspersons require the code to predict the stock market. The many
chaos in the movie are thus brought about by lack of a solution, which most people think is in the
216 numbers that have not been found fully. 4. Suppose that there is a mathematical pattern that
allows one to comprehend the order of the universe. How would that impact the question of free will
and
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Leonardo Bonacci : An Italian Mathematician
Intro:
Leonardo Bonacci was an Italian mathematician during the middle ages. He is better known as
Fibonacci or Leonardo de Pisa. There is very little known about Fibonacci's life except for what he
wrote down in his books. The details of his education, early life and family are vague. Since his
books are written mainly about his work in mathematics he does not elaborate on his personal life.
Date of Birth/Death & Family:
Leonardo Bonacci was born around 1175 to a wealthy Italian merchant and the consul for Pisa
named Gugleilmo Bonacci. His mother, Alessandra Bonacci, was not a big part of his life due to the
fact that she passed away when he was only nine years old. Leonardo "Fibonacci" Bonacci also had
a brother named, Bonaccinghus, ... Show more content on Helpwriting.net ...
When Liber abaci was published in 1202, Europeans begin to learn and use Arabic numerals as
opposed to Roman numerals. In the year 1212, thousands of people head to Jerusalem to rescue the
Holy Land from the Muslims. Most of those people were children who ended up being killed or sold
into slavery. Furthermore, in 1217 the Fifth Crusade begins and later in 1228 The Sixth Crusade
begins in order for the Holy Roman Emperor Frederick 2 to gain control of Jerusalem. In western
Africa, Sumaguru Knate, raids and conquers the area. A couple of years before Leonardo Bonacci's
death, the Aztecs settle in a region that is known today as Chapultepec. On the year of Fibonacci's
death, Conrad 4 becomes the new Holy Roman Emperor after Frederick 2 dies. In additionThe
Seventh Crusade met defeat at the hands of Egyptian forces led by the new Caliph, Turanshah, at the
Battle of Fairskur on April 6th 1250. Turanshah captures Louis IX whom he released only after the
payment of a ransom. Later, in 1258, a crisis developed in England over a new series of taxes levied
by Henry III. Rebellious barons led by Simon de Montfor demanded a program of reforms be
enacted by the "Mad Parliament". There would be a council of fifteen who would have veto power
over the actions of the king. Finally, ten years after Fibonacci's death, Kublai becomes the grand
Khan of the Mongols and is favored by the army at Shan–tu, in China. At the end of the 13th century
The

The Fibonacci Numbers
The Fibonacci numbers also known as the Fibonacci sequence is a set of numbers where after the
first two numbers, every number is the sum of the two preceding numbers. It begins in most
examples at one however it has been shown to start with zero, the first ten numbers in the sequence
are 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89. This sequence is an important mathematical figure that is seen
in many other theorems in mathematics and also the surrounding natural world. This sequence first
appears in Indian mathematics and even in Indian poetry, this quote by Gopala an Indian poet from
around 1135 states that "For example, for a meter of four lengths, variations of meters of two and
three being mixed, five happens this also works out with examples 8, 13, 21]... In this way, the
process should be followed in all mātrā–vṛttas". To deconstruct this it is necessary to match the
numbers of the sequence mentioned in the quote with the numbers that exist in the sequence, Gopala
mentions the sequence of two numbers creating the next in the sequence, 2 & 3 to 5 and then 8 & 13
to 21, that the meters in Indian poetry add together just as it is in the fibonacci sequence. When this
idea travels outside of India it is first posed in the book Liber Abaci written by Fibonacci, whose
real name was Leonardo Bonacci. Leonardo was born in Pisa around the year 1175, his father was a
wealthy Italian merchant who bought along his son on his journeys around the Mediterranean world,
in these travels

Important Discoveries And Contributions That Were Made By...
Abstract: – The many concepts we currently have in the field of mathematics are thanks to great
mathematicians from different cultures throughout time. An important era when great mathematical
discoveries were made was during Medieval Times, or the Middle Ages. In this paper we discuss
important discoveries and contributions that were made by three famous mathematicians of this time
period including French Nicole Oresme, German Jordanus Nemorarius and Italian Leonardo Pisano,
better known for his nickname of Fibonacci.
Key–Words: – Medieval, Mathematics, Fibonacci, Arithmetic, Sequence
1 Introduction
Mathematics has grown and expanded its many concepts thanks to mathematicians from different
societies throughout time. A very important era in history is considered to be the Medieval Times, or
the middle ages. According to reference [6], "People use the phrase 'Middle Ages' to describe
Europe between the fall of Rome in 476 CE and the beginning of the Renaissance in the 14th
century." The Middle Ages, or Medieval Times, are known for their famous art, architecture,
crusades among other things, but there were also mathematical contributions happening during this
time period.
Mathematical concepts that we know and use nowadays are thanks to contributions made from
different mathematicians throughout time. The Medieval Times are no exception since great men
living in this era contributed to the beautiful subject of mathematics. Some of the many intelligent
minds from this era

Effects Of Fibonacci Sequence In Nature
"Fibonacci Sequence in Nature" Introduction: Nature is interesting, wonderful and fascinating. In a
state of equilibrium, animals, plants, insects, and many other things create amazing habitats suited to
their environment and living condition. This is just one of many reasons why nature is so wonderful
and fills one with curiosity and fascination. For example, the design of a shell for a shell gives them
protection and survive in though environment where they have to deal with several different
predators. There are significant amount of species that has ability to camouflage which helps them
to create fascinating habitats. A reindeer eyeballs turn blue during winter to help them see at lower
light levels. Reindeers evolved and adjusted themselves ... Show more content on Helpwriting.net ...
This kind of spiral is often called as Fibonacci spiral or the Golden spiral. To have the Fibonacci
spiral, we need equation formulated from polar equation. Point A: A(x) = (r(x) cos⁡
x, r(x) sin⁡
x) When
x=0, A(0) = (r(0) cos⁡
0, r(0) sin⁡
0) = (1×1, 0) = (1, 0) Point B: B(x) = (r(x) cos⁡
x, r(x) sin⁡
x) When
x=π/2 B(π/2) = (r(π/2) cos⁡
〖π/2〗, r(π/2) sin⁡
〖π/2〗) = (1.618 × 0, 1.618 × 1) = (0, 1.618) When
x=π C(π) = (r(π) cos⁡
π, r(π) sin⁡
π) = (–2.618 × 1, –2.618 × 0) = (–2.618, 0) From the previous Table 2
F_n÷F_(n–1) = φ (1.618) (1≤φ≤2) φ= 1.618 φ^2= 2.618 φ^3= 4.236 From here, we recognize a
pattern, you just need to multiply φ for next coordinate. Therefore, D(0, –4.236) E(6.854, 0) F(0,
11.089) and so on... Coordinates are shown as this, Graph 2 Graph 2 When the lines are connected,
it shows Graph 3. Graph 3 (Extracted) The squares are formed with Fibonacci sequence where it
begins

Golden Ratio In Facial Beauty
The Golden Ratio and Symmetry in Facial Beauty What is beauty? Is it perceived by whoever looks
upon the person, or is it some mathematical formula that can be scientifically explained and proved
by fact? By researching the topic of perceived beauty and observing multiple proofs, experiments,
and photographs it has been concluded that the "perfect face" can be found within the golden ratio.
While the quote "beauty is in the eye of the beholder" speaks a truth, so does the golden ratio in
determining exactly how aesthetically beautiful one is. The golden ratio can be found in many
different places including but not limited to nature, Greek architecture, and even people. The Golden
Ratio is made up of the Fibonacci numbers. These numbers go in a certain sequence where every
number, with an exception of the first two digits, is equal to the sum of the previous two numbers.
So, this sequence begins with the following numbers 1, 1, 2, 3, 5, 8, 13, 21 in that order and
continues in that specific pattern (Bourne n.a). Phi, another name for the golden ratio using the
symbol Φ, is the decimal made up of a single Fibonacci number divided by the previous sum before
it. By using the infinite decimal of phi, you can create the golden ratio. To put phi into simpler
terms, the golden ratio divides the line at a point, so that the ratio of the lengths of the two sides
(a/b) is equal to the ratio sum of the opposite pair of sides (c+d) to the longest side (c). To bring it all
together into entirety, the equation would look similar to this– a/b = (c+d)/c (P Prokopakis et al
2013). When the golden rule is applied to faces, beauty mostly depends on how proportioned and
spaced facial features are on the face. Individual attractiveness is optimized when the face's vertical
distance between the eyes and the mouth is approximately 36% of its length, and the horizontal
distance between the eyes is approximately 46% of the face's width. The distance between the
hairline and the chin is the length ratio, while the distance between the pupils of one's eyes is the
width ratio (Prokopakis 2013). In an experiment previously done, they tested the prediction that
facial symmetry can be attractive by manipulating the symmetry of

Leonardo Fibonacci : The Life Of Leonardo Pisano
Have you ever noticed the patterns in nature? Leaves alternating on a branch, or the stripes or spots
on an animal? Scientists always look at our world and try to figure out how things come to be. Turns
out, a 12th century mathematician taught scientists about the patterns in nature, while also making
history with his numerical theories.
Leonardo da Pisa, or Leonardo Pisano, was born around 1170 in Pisa, Italy. His original name was
Leonardo Fibonacci, but since famous Italian people were normally named based on where they're
from, he is referred to as Leonardo da Pisa, which means "from Pisa". This was later changed by
historians to the Latin version, Pisano. Leonardo sometimes called himself, in his writing anyway,
Leonardo Bigollo, which means "traveller" in Tuscany. He felt Bigollo was a more personal name,
one he could choose for himself. He never used the name "Fibonacci" for himself. It was likely
made up in 1838, long after he died, by Guillaume Libre. "Fibonacci" is a shortened term for "filius
Bonacci", which literally translates to "son of Bonaccio" (Knott, "Who was Fibonacci?").
Pisano's father, Guglielmo Bonaccio, was a successful merchant. He was appointed consul for a
community of Pisan merchants in a North African port. Pisano's mother, Alessandra, died when he
was 9, so he had no choice but to follow his father to Africa. There, his father sent Pisano to study
with an Arab master nearby. He met with many merchants, learning how they completed arithmetic.
He

The Golden Ratio And Fibonacci
INTRODUCTION
In this report I will discuss the Golden Ratio and the Fibonacci sequence .I will provide work done
on the exercises and give data and information from the exercises. This report will be based on 3
exercises given to me :
(1) Get Golden Ratio with derived Formula.
(2) Get Golden Ratio using successive approximation technique.
(3) Get Golden Ratio from Fibonacci series.
[1]The Golden Ratio according to Hom.E(2013) "is a special number found by dividing a line into
two parts so that the longer part divided by the smaller part is also equal to the whole length divided
by the longer part."
[1]"This special number has a unique symbol of phi which is a Greek letter."
[1]"The value of this number is 1.618.The golden ratio is often displayed or ... Show more content
The program had to compute y=x^2–x–1 for x = –2 to x=+2
Assumptions made were that a u shaped graph would appear due to the type of equation given.
Exercise 3
The problem to be solved in this exercise is to get the Fibonacci sequence in the right order to get
the first 50 values.
The relationship given in order for us to get the sequence was :
"fn=fn–1+fn–2"
"f0=0 and f1=1"
The program had to generate the first 50 values for the sequence.
Input/Output data (Exercise 1)
The data type necessary for this exercise is Float as we will expect decimal places and not whole
numbers.
The Output data for this ="Phi".
For this exercise there was no input data needed as we were given all the values.
There was a data range of a number between 1–2.
Exercise 2
The data type used for this exercise was double float
The Output = y .Due to the range of –2 to 2 the value of y will have 5 different values.
There was a range of –2 to 2 when substituting x.
Exercise 3
The data type used was integer
The Output = Fn. The Input = F2=F1+F0,n=1.

Table 1 (Exercise 1)
Variable Data Type Value Range Description X Float 1 – 2 This is "Phi"
Table 2 (Exercise

##bol Symbols : The Concept Of Eternal Return By Carl Jung
Spiral Symbol Amplification Paper
Carl Jung thought that the form of a spiral represented the idea of "eternal return" in the pattern of
human thought and insisted that the archetypal symbol represented the cosmic force (Bobroff, p.
27). Various ancient cultures viewed the spiral as a symbol for journey, growth, and evolution. From
timeless edifices to contemporary architecture, one can observe the spiral form in building
structures; such as staircases, domes, and spires. One doesn't have to look very hard to see spirals in
their everyday lives, take the golden ratio for example. The golden ratio can be expressed in the
naturally occurring patterns in various plants and will also reflect the Fibonacci number sequence in
the same manner. A pine cone is a perfect illustration of this, as are many succulents. Who knew that
a simple image could represent so much, to so many, so differently.
For the sake of this paper, when referring to the spiral symbol, I am referencing the simple image of
a curve that radiates from a point, moving further away as it revolves around the original position in
a circular orientation. I remember the first time I saw it. I recall the corkscrew shape carved in the
center of a dilapidated stone, slowly letting my eyes move with the coil, as it guided me outward
towards the edges of the boulder and then eventually guided my awareness to my surroundings. I
never expected my first impression of the spiral symbol to be so profound. Ever since that day, so
many years ago, the spiral symbol has shadowed my existence in the most unexpected ways and in
the most peculiar places. I have seen this symbol in my travels immersed in many vibrant cultures,
far from one another. These recurring observations led me to ask a paramount question.
What is the cultural significance behind the spiral symbol in various societies throughout time?
Specifically, what are the similarities that connect these broad civilizations to the spiral symbol and
how can one establish an interconnection between the symbol and the collective unconscious? TS
AND TRANSITION SENTENCE The spiral is among one of the oldest known pictograph symbols
on the planet; as it is often associated with representing the individual's

Ever Since People Started Walking The Earth, They Used
Ever since people started walking the earth, they used different items found in nature known as
symbols to represent various meanings. Over time people passed down these symbols to the next
generation; they either get altered because of the progression of time, or new ones form as a result of
this progression. Today objects have different meaning to different people because of the changes
made throughout history. In his novel, The Da Vinci Code, Dan Brown reveals to his audience that
objects such as art, literature, people, and sciences could be viewed in multiple perspectives. In The
Da Vinci Code, art is viewed differently by careful examination of details revealing the messages
behind it. Leonardo Da Vinci's paintings are examples ... Show more content on Helpwriting.net ...
Not only are the visual arts important, the use of film moreover elevates the idea of objects seen in
different points of view. Popular Disney movies for example appeal to the young generations, but
there is more background information than children see on television. Snow White alludes to the
Bible story of Adam and Eve; the Little Mermaid used symbols from Isis, Eve, Pisces, and Mary
Magdalene (Brown 282–283). Films and artwork seen from an innocent mind are not always
accredited for their talent of mixing history with fiction. While the fine arts are significant to
proving the point of objects seen in different perspectives, literature also impacts this idea. During
the course of the novel, Brown use different works of literature to demonstrate the fact that the
world has to be viewed in different angles. An example of how Brown uses literature is
Shakespeare's plays. Shakespeare is well known for his plays such as A Midsummer Night's Dream,
The Merchant of Venice, and Romeo and Juliet, but he also known for his use of the meter, iambic
pentameter. "For centuries, iambic pentameter had been a preferred poetic meter of outspoken
literati across the globe, from the ancient Greek writer Archilochus to Shakespeare, Milton, Chaucer,
and Voltaire––bold souls who chose to write their social commentaries in a meter that many of the
day believed had mystical properties." (Shakespeare in The Da Vinci Code." Shakespeare
Newsletter). Iambic pentameter also relates to the

Mathematics In Music : The Relationship Of Mathematics And...
Math can be seen in all aspects of life, whether you notice it is prevalent or not. As a result, almost
every aspect of life can be boiled down to a specific group of mathematical concepts. Similarly, art
forms, especially music, can be analyzed through the eye of math and therefore be fully inspected,
observing how certain chords and notes sound more harmonious than others.
Mathematics and music have a closer relationship than most people realize. Mathematics and music
are directly related and their relationship can be seen in every measure of musical theory. In fact,
when Einstein was having trouble with a mathematical problem, he would play the piano or violin.
He was able to substantiate the connection between the two hemispheres of his brain and increase
his brainpower by focusing on his troubling problem (left brain) while playing his instrument (right
brain). Every chord, time signature, and even dotted half notes contain mathematical concepts, one
of them being the Fibonacci sequence. The Fibonacci sequence consists of adding two numbers to
get the following number. This sequence is prevalent in the scales of a piano, for one scale of a
piano contains 8 white keys and 5 black keys which aligns with the sequence 0, 1, 1, 2, 3, 5, 8, 13,
21, 34,...
The beginning of the concept of integrating math into music stemmed from the discovery of the 12th
root of 2. This seemingly simple math problem unlocked the mystery of the chromatic scale. The
12th root of 2, figured

How Did Leonardo Da Vinci Get His Ideas From?
Leonardo Da Vinci was the great painter and inventor of the 15th century. Throughout his life he
made different works of art including La Gioconda, The Last Supper, and his famous Annunciation
painting. From an early age he learned to paint in Florence in the open world of Italy. He then later
formulated his scientific discoveries, and invented bizarre contraptions to solve all kinds of different
problems. One question that still remains is where did Leonardo Da Vinci get all his ideas from?
The world that Leonardo lived in was a world filled with nature, cities, and animals. Leonardo Da
Vinci's art work and inventions were inspired by his environment.
Near the town of Vinci, a boy named Leonardo was born on April 15, 1452 (Chew). From the ...
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He has influenced many people and even mankind as a whole, but what influenced him? Back in the
15th century there wasn't much to be around except a small town or nature. For Leonardo his
situation was filled with a variety of everything. He went from the small towns of Vinci, to the big
cities of Florence. Leonardo took the best from nature and from the cities around him to develop his
great paintings and great inventions. In his paintings Leonardo used Fibonacci and other drawing
techniques that are fundamentally built into nature. An example of Fibonacci in nature is the shell of
the chambered Nautilus with its almost perfect proportions (Parveen). Another thing leonardo used
from nature was its plant life and wild animals. Something Leonardo drew a lot in his notebooks and
paintings were different kinds of plant life and animals. Lastly Leonardo was not a man to indulge in
riches and other worldly things, but rather would sit in a small estate in the wild and paint all that he
could see. After all La Gioconda was supposedly painted outside showing his interest in drawing the
surroundings around him perfectly. As for his inventions, Leonardo always drew most of his
inventions next to his inspiration, such as animals, in his notebook. A great example would be his
flying machine with a drawing of a bird showing the outline of its

Definition Of Honor
The word Honor is defined in the dictionary to mean high respect; esteem. My definition of honor is
a role model that I have high respect for because of the way he or she conducts their life. Leonardo
Pisano, better known as Fibonacci, as he got older, was born in 1170 in Pisa which is a city in Italy.
He was the son of Guilielmo and Alessandra Pisano. His mother, Alessandra, past away when he
was only nine. With Fibonacci's mother dead and being an only child, he followed wherever his
father went. They spent time traveling between North Africa and Italy. Fibonacci had no formal
education. He received his education through his travels.
One of his greatest accomplishments was the discovery of the Fibonacci Sequence. The Sequence is
... Show more content on Helpwriting.net ...
Like the Practica Geometriae. This book is about techniques in survey, the measurement and
partition of areas and volumes, and other topics in practical geometry. Another book by Fibonacci is
Flos which solved problems posed by Johannes of Palermo. Liber Quadratorum, written in 1225
AD, is a number theory book, which examines methods to find the Pythagorean Triples. Two of his
books that were lost, they were Di minor guisa, and the Commentary on Book X of Euclid's
Elements.
Some of Fibonacci's awards were the statue that the republic of Pisa made for Fibonacci in the 19th
Century, since he helped spread the arabic numeral system. The statue is in the city of Camposanto.
He also got a salary for the arabic numeral system and the Fibonacci Sequence. The impact of
Fibonacci's work towards the world is that the Arabic numeral system has been used instead of the
Roman Numerals. In addition, the impact the Fibonacci Sequence has had on the world to help us
understand animal species. I do not think Fibonacci is a definition of honor to me, due to the fact
that he is not a role model to me. I have respect for him and his wonderful contributions to math and
science, however, he would not fit my criteria of

The Fibonacci Contributions In Indian Poetry
The Fibonacci numbers, also known as the Fibonacci sequence is a set of numbers where after the
first two numbers, every number is the sum of the two preceding numbers. The sequence is usually
shown in the following format; 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89...etc, although it has been shown to
start with zero. This sequence is an important mathematical figure that is seen in many other
theorems in mathematics and it was helped to push for a better form of mathematics by the man
whose name was eventually attributed to the number sequence and also the surrounding natural
world and attempts have been made to connect it with the human world, through anatomy and the
stock market. This sequence first appears in Indian mathematics and even in Indian poetry, this
quote by Gopala an Indian poet from around 1135 states that "For example, for a meter of four
lengths, meter variations of two and three being mixed, results in five this also works out with
examples eight and thirteen with gives twenty one, In this way, the process should be followed in all
mātrā–vṛttas". Gopala mentions the sequence of two numbers creating the next in the sequence, 2 &
3 to 5 and then 8 & 13 to 21, that the meters in Indian poetry add together just as it is in the
Fibonacci sequence. This sequence will spread throughout India passing between poets and
mathematicians and then outwards towards the Middle East and then on to Europe where it will be
taught to the man whose name becomes attached to this

The Pros And Cons Of Field Trip To The Aquarium
Have you or another fellow teacher been wondering about what field trip to take that will enhance
your pupil's mind? Or have you been engulfed in the side effects of worry and/or stress? Well not to
worry. The Aquarium and Leonardo are here. They both have very amazing things in them that your
students will like. Such as things flying across the room right in front of you. I'm sure one, or both,
of these locations will be the right field trip for you and your school. But, before you zoom to the
computer, then to the printer and finally to the copy machine, you need to know that there and the
pros of the building, but also some cons. That doesn't mean that your scholar won't enjoy the future
field tip, it just means that some extra safety precautions should be taken.
The Aquarium and Leonardo have many tremendous things hidden inside, but they both also have
remarkable architecture like a huge fin on the outside or glass in a cool circular shape. This provides
excitement for the kids when they first see the place. The excitement that sparks in first seeing the ...
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This is a place for observers where they can look and learn about animals all over the world that
they would probably never see in their lifetime. That includes of penguins, sloths, sharks, different
types of birds, monkeys, otters and many other things. In the place you can actually find a theater
where they play movies of animals and other seasonal movies. They get so many visitors that come
back, so that gives us a clue that it is a great place that so many people want to come back. Maybe it
is because every room you go to has a different ecosystem with their accompanying animals in is, or
maybe because in each ecosystem the air temperature changes to the air temperature it would
usually be. Or maybe because birds fly freely around the Aquarium. All of these variables would
make any observer fill with

Example Of Fibonacci Sequence
1. Introduction
Fibonacci sequence is one of the most famous and perhaps the most interesting number patterns in
mathematics. Far from being just a curiosity, this sequence recurs in structures found throughout
nature – from the arrangement of whorls on a pinecone to the branches of certain plant stems. Other
than nature, numerous examples of the Fibonacci sequence as well as its derivative, the Golden
Ratio can be found in art, a stock market, and other areas of society and culture. In the paper, some
of the interesting facts of Fibonacci number are discussed.
1.1. About Fibonacci
Fibonacci, the "greatest European mathematician of the middle ages", lived between 1170 and 1250
in Italy. Leonardo Pisano Bogollo was his real name and "Fibonacci" was his nickname, which
roughly means "Son of Bonacci". In 1200 he used the knowledge he had gained on his travels to
write Liber Abaci (published in 1202) in which he ... Show more content on Helpwriting.net ...
1.2. The Rabbit Problem and Fibonacci Sequence
Among many problems contained in Leonardo's book Liber Abaci, the most famous was his over
800 years old rabbit population problem which he stated as follows:
This is indeed a celebrated problem in mathematical biology dealing with how many pairs of baby
rabbits will be produced in a year from a single pair of adult rabbits. Consequently, the rabbit
population will grow rapidly provided no rabbit ever dies and in every month each pair reproduces a
new pair which becomes productive from the second month onwards. This problem led Fibonacci to
discover in 1202 a new sequence of numbers as
1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377...
These numbers are called the Fibonacci numbers, which have been named by the nineteenth–century
French mathematician, Edouard Lucas (1842–1891), and the recurrence relation defines
with the two initial values and

Da Vinci a Man of Math
Leonardo Da Vinci, Man of Math Ask any given person who the most famous artist during the
Renaissance was and the result would be nearly unanimous in the answer of "Leonardo Da Vinci".
But why is that? Yes, there is the Mona Lisa and The Last Supper to his name, but his legacy has
extended beyond the world of paint and into other modern popular realms: of best–selling books
(The Da Vinci Code by Dan Brown) and even world renowned video games (Assassin's Creed II).
For each reproduction of his character, the modern world seems to want more of Leonardo. His
ability to wield a paintbrush is undeniable, but other artists from this time could arguably be his
equal, or perhaps even better in skill; so the question remains: why is it that these ... Show more
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He rationalizes that each eye produces the image of the object viewed in a different location, which
produces depth; though the problem with this phenomenon is that it is not producible through paint.
There is only one canvas for which the viewer to see, but they are looking at an image through two
eyes. Being able to get around this drawback of paint frustrated the man to no end. Ultimately, he
knew that there was no way around the fact that a painting could never be an exact copy of what the
eyes can see, but he never stopped trying to fake it as best he could. The device he came up with was
brilliant, and simple: to blur the objects in the background in order to give a lifelike focus on the
object which he wanted the viewer to look at. This had never been done before, as there was
emphasis on making sure every nuance of detail was correct. Leonardo understood that by looking
at each object in his field of view separately created a fake observation, since when he was actually
focused on one subject, his eyes could not focus on the area around them. With the desire to
understand proportion, there was a curiosity for geometry, and by learning the methods behind this
math form, Leonardo's work benefitted greatly. By collaborating on De divina proportione with
mathematician Fra Luca Pacioli when he was younger, we are able to infer that Leonardo held an
interest in furthering his knowledge of math for his personal

Why Is Mathematics Invented By Humans?
With mathematics seemingly being intuitive and the basis of the universe around us it would seem a
given that mathematics has always been there, that it is a physical concept which we can completely
understand and one that has set rules that cannot change. However this is not the case and we only
have to look just over two thousand years into the past to see the use of Roman Numerals, where
numbers were represented by letters or four thousand years in the past to see the unrealistic yet
beautiful base–60 number system used by the Babylonians to realise that whilst the overall concept
is the same, to group things of the same amount together, the way that we express it is vastly
different.
To address the question, "To what extent was mathematics invented by humans?" we first need to
deal with the most simple concept of mathematics, the natural numbers; 1, 2, 3, 4, 5, 6, 7.. There is
nothing simpler in maths then this, but it took us nearly 165,000 years to even produce a primitive
tally stick, the Lebombo bone. Yet it was these numbers more than anything that enabled us to take
control of the world around us and let our presence be felt across the globe. But what is a number? It
appears to be a fairly easy question yet it is very hard to answer as it is not shown in the physical
world, it is an abstraction, a human mental concept, one that is derived from reality but is not
actually real, but one which allowed humans to develop and discover new areas of mathematics and

American Film Title Designer: Kyle Cooper
Kyle Cooper is an American film title designer how is responsible for creating some of the most
invitational and evocative title sequences. Designing title sequences for film and television with a
unique style and ability to invoke an emotional response through his imagery and use of narrative.
He is often compared to Saul Bass and his Typography approach to titles sequences, In the title's for
Saul Bass Psycho, he get across the nature of his main character with slicing up uneven Type and
shapes moving vertical and horizontal causes a sense of unease and discomfort. The use of
Typographic method acting, to animate the words shows the emotional effect of type and how it can
reflect the film.
Kyle cooper's titles are more that just a title they give an emotional response in a audience with his
bark and bold and unforeseen style that draws you in and hooks you
His most admired work comes from the 1995 title sequence of the American film "Seven". Not since
Saul Bass's title sequence to The Man With the Golden Arm and Vertigo have credits attracted such
attention.
But Cooper was already a title–sequence expert at this stage with more than 40 credits to his name
"Each film is a different problem to solve so each is different" Kyle cooper
Typeface has got to be a character through the narrative. It should really carry a part of the story.
The first scene we are presented with a black screen, with the sounds of Dinah Washington singing
'A Stranger on Earth' being played

Leonardo Fibonacci Research Paper
Leonardo Fibonacci Autobiography
Fibonacci was an Italian number theorist. It is believed that Leonardo Pisano Fibonacci was born in
the 13th century, around 1170 and that he died in 1250. Fibonacci was born in Italy very little is
known about him or his family, He did however obtain is education in Bougie, Algeria, where his
father was a warehouse official. Fibonacci was known as the greatest European mathematician of
the middle ages. Fibonacci traveled extensively throughout Europe as well as Egypt and Syria.
During his travels, he observed and analyzed the arithmetical systems employed in commerce and
learned the Hindu–Arabic numerals. Fibonacci was one of the first people to introduce Europe to the
Hindu–Arabic number system, which is the system we still use today. This was the system that
replaced the Roman Numeral system. Leonardo also wrote a book that was completed in 1202, on
how to do arithmetic in the decimal system, it was called Liber abbaci (Book of Calculating) the
book persuaded many European mathematicians of his day to use this "new" system. ... Show more
In his book, Liber abaci he introduced the Hindu–Arabic place–valued decimal system and the use
of Arabic numerals into Europe. He introduced us to the bar we use in fractions, before this, the
numerator had quotations around it. The square root notation is also a Fibonacci method. Though he
was primarily an arithmetician and an algebraist, Fibonacci also wrote a book on geometry entitled
Practica geometriae (1220), which seems to be based on Euclid's lost work On the Division of
Figures. In this work, Fibonacci uses algebraic methods to solve many arithmetical and geometrical
problems. Fibonacci was influenced by many merchants throughout the

Comparing A Piece Of Renaissance Art: The Mona Lisa By...
For my mathematical exploration I will be comparing a piece of Renaissance art with a modern logo
and showing the mathematical principles each artist utilized to create a harmonious and balanced
composition. This exploration entails a discussion of geometric forms, the Fibonacci Spiral, and the
Golden Ratio. Probably the most famous piece of artwork from the Renaissance, The Mona Lisa by
Leonardo da Vinci is considered by many artists and mathematicians to not only be an amazing
piece, but also an amazing use of mathematics. For reference, a picture of the Mona Lisa is to the
right. In composition, Leonardo helped to create balance by placing the portrait within a central
triangle. This triangle can be apparent when looking at the subject,

Does Cognitive Bias Influence The Patterns We Exist?
"Humans are pattern seeking animals and we are adept at finding patterns whether they exist or not"
(adapted from Michael Shermer). Discuss knowledge questions raised by this idea in two areas of
knowledge.
My knowledge question is to what extent does cognitive bias influence the patterns we see in life?
Cognitive bias is defined as pattern of distortion in perception and a deviation from rational
decision; irrationality Decision–making, belief and behavioral biases. If a person was to look into
human sciences and mathematics as ways of knowing, he or she would determine that cognitive bias
is present every time a person sees a pattern. However, they are unable to see the bias for themselves
because of the selectivity of perception. Human sciences will be beneficial in answering this
question because looking at studies and experiments previously done on the subject would give
insight into cases in which people use cognitive bias. Fallacies such as the bandwagon effect and the
ambiguity effect could be seen in experiments to help prove or disprove the claim. Mathematics as
an area of knowledge is helpful because it uses logic and reason through values and shapes to
present patterns and it is the most common form of patterns. Also in math we can look at imaginary
and irrational numbers as well as geometry to determine if cognitive bias causes pareidolia in logical
patterns.
My claim for human sciences is that human sciences show

Attraction Research Paper
When you are attracted to someone you believe that it is because you think they caught your eye or
how charming they are, but there is a science that gives the deeper reasoning to why you are
attracted to someone. Smell, fertility, masculinity, and the golden ratio are all factors in attraction.
Science has affected who our ancestors chose for mates and now it is affecting us.
Smell? Yes, smell is actually a big factor in mating. Pheromones are a type of scent–bearing
chemical secreted in sweat and other bodily fluids. A type of pheromone called a releaser includes
the compounds androstenone, androstadienone and androstenol and may be involved in attraction.
"In one study, female participants were tasked with the unpleasant directive to smell ... Show more
Yes, math. It is proven that humans are more attracted to other humans if their bodies and faces are
more proportional. What determines if humans are in proportion is the Golden Ratio. The Golden
Ratio originates from Greece and is based on Fibonacci Numbers created by Leonardo Fibonacci in
1200 AD, which is a series of numbers in which each number is the sum of the two numbers before
it , for example 1, 1, 2, 3, 5, 8, 13, 21 and so on. If you divide every number by the one in front of it
you get decimals that are very close to each other for example: 1.60, 1.61, 1.62. This is where we get
Phi from (1.6180339887) . The Golden Ratio is 1:1.6180339887. It wasn't until the 1900's that
American mathematician Mark Barr used the Greek letter phi (Φ) for this proportion.
Artists also use the golden ratio to make paintings. Leonardo Da Vinci created many drawings that
revolved around the Golden Ratio. His drawings consist of a circle, a square, and the length from
navel to head and navel to the foot. The golden ratio doesn't only exist in humans, but also
Architects throughout history have used this ratio to make buildings. Pyramids, The Parthenon, and
Notre Dame in Paris are all made with the golden ratio. We also see this in nature in tree branches,
shells, and honey

The Different Names of Fibonacci Essay
The Different Names of Fibonacci
In 1175 AD, one of the greatest European mathematicians was born. His birth name was Leonardo
Pisano. Pisano is Italian for the city of Pisa, which is where Leonardo was born. Leonardo wanted to
carry his family name so he called himself Fibonacci, which is pronounced fib–on–arch–ee.
Guglielmo Bonnacio was Leonardo's father. Fibonacci is a nickname, which comes from filius
Bonacci, meaning son of Bonacci. However, occasionally Leonardo would us Bigollo as his last
name. Bigollo means traveler. I will call him Leonardo Fibonacci, but if anyone who does any
research work on him may find the other names listed in older books. Guglielmo Bonaccio,
Leonardo's father, was a customs ... Show more content on Helpwriting.net ...
The four books that still exist are Liber abbaci, Practica geometriae, Flos, and Liber quadratorum.
Leonardo had written several other books, which unfortunately were lost. These books included Di
minor guisa and Elements. Di minor guisa contained information on commercial mathematics. His
book Elements was a commentary to Euclid's Book X. In Book X, Euclid had approached irrational
numbers from a geometric perspective. In Elements, Leonardo utilized a numerical treatment for the
irrational numbers. Practical applications such as this made Leonardo famous among his
contemporaries. Leonardo's book Liber abbaci was published in 1202. He dedicated this book to
Michael Scotus. Scotus was the court astrologer to the Holy Roman Emperor Fredrick II. Leonardo
based this book on the mathematics and algebra that he had learned through his travels. The name of
the book Liber abbaci means book of the abacus or book of calculating. This was the first book to
introduce the Hindu–Arabic place value decimal system and the use of Arabic numerals in Europe.
Liber abbaci is predominately about how to use the Arabic numeral system, but Leonardo also
covered linear equations in this book. Many of the problems Leonardo used in Liber abacci were
similar to problems that appeared in Arab sources. Liber abbaci was divided into four sections. In
the second section of this book, Leonardo focused on

Pow 16: Spiralaterals
A spiralateral is a series of line segments that form a shape that resembles a spiral. You make
spiralaterals by picking a spot on a piece of graph paper to be the starting point of the spiralateral.
Then take a set of three numbers and using that point go up the first number of squares on the graph
paper, go right the second number of squares, down the third number of squares and left the first
number of squares going in that pattern until the line meets the starting point. So if you were using
the numbers 1, 2, and 3 you would do what is shown in the diagram below. You go up one square,
then you go right two squares, next you go down three squares and start the sequence again but
while going in that direction. So after you go down three ... Show more content on Helpwriting.net
...
For example using the numbers 1–2–3 again, the three combinations where the numbers are in
ascending order, so 1–2–3, 2–3–1, and 3–1–2 will be facing one way and the sequences 1–3–2, 2–1–
3, and 3–2–1 will be a mirror image of the original number sequences spiralateral. The way I know
that this is true is because I used two of my number sequences and drew them out and then I
checked

Triangular Number Of Triangular Numbers
Triangular Numbers
Eli Nazarian
Ms. Ramson
H Algebra 2A
October 21, 2014
A triangular number is a number that counts the amount of objects that form when they are put
together to form an equilateral triangle (a triangle with all equal sides). The most common object
used to form a triangle are dots. When the dots create an equilateral triangle, the number of dots
seen in the triangle represent the triangular number. Overall, the sequence is generated from a
pattern of dots which form a triangle.
The first row contains a single dot and each subsequent row contains more dots than the previous
one. The sequence of triangular numbers are: 1, 3, 6,10, 15, 21... and so on.
When working with multiple triangles, each triangle is assigned a triangle number. For example,
triangle one (T1) has a triangular number of one. Triangle three has a triangular number of six. The
letter T, followed but a number represents a certain triangle.
The formula to calculate the amount of object using a stated length is:
Tn(th)= n(n+1) 2
T represents triangle number. N represents the length of the three sides of the equilateral triangle. If
a number (and only whole numbers) were plugged in for N. The final answer of the problem would
equal the number objects (dots) in the equilateral triangle.
Example: n= length of 6 Formula: Tnth= n(n+1) 2
Plug in 6 for n. T6th=6(6+1) 2
Solve. T6th= 6(7) T6th=42 T6th=21. 2 2
The

Analysis Of The Book ' Fibonacci Rabbits '
Leonardo Fibonacci was an Italian mathematician who lived from 1170 to 1240. While Fibonacci
was growing up, he was sent to study mathematics with an Arab master. Once he finished studying,
he began to travel to other countries to study their mathematics and calculations (Encyclopedia
Britannica). In 1202, Fibonacci published his book that was entitled Liber Abaci or Book of the
Counting. In this book, he used Hindu–Arabic numbers. This is the number system that we are using
today. Prior to his writing, many people did not know or use this system of numbers. In the
beginning, Fibonacci talked about how this system worked, basically how to use, write, and
compute with these numbers. He taught this by focusing on real life examples ... Show more content
The formula used is F_n= F_(n–2)+F_(n–1). In order to calculate the nth term another formula,
known as Binet's formula, is used. It states F_n=(φ–(–φ)^(–n))/√5 where φ=(1+√5)/2≈1.61803. The
Fibonacci sequence has led to many mathematical advances over time, and it is used in many
different areas of life. It is an important part of life due to its ever present appearances throughout
nature, mathematics, pop culture, and business. The Fibonacci Sequence is most important in the
world of mathematics. It is found in other discoveries like Pascal's triangle and Cassini identities.
One area of mathematics that overlaps with the Fibonacci Sequence is the Golden Ratio which is
typically used when discussing the ratio of distances (wolfram alpha). The ratio is approximately
1.6180. It is found by this formula φ= (1+√5)/2≈1.61803 . The ratio has been surrounded by mystery
since the time of the ancient Greeks. Many scholars look at the Parthenon statues (built by Phidias,
from 490–430 BC) and believe that they were built using the Golden Ratio. Euclid, during his
lifetime, became the first to define this ratio. He defined it as "extreme and mean ratio" (Wikipedia).
Credit is generally given to Phidias hence the symbol phi is used when denoting the ratio (UIUC).
The Golden Ratio is similar to the ratio between each consecutive Fibonacci number.
Fibonacci numbers also overlap with Pascal's Triangle, which is found on the right. The triangle is
formed by adding the

06
Chapter 6: Additional Database Objects
TRUE/FALSE
1. A sequence serves as a nickname for a database object.
ANS: F PTS: 1 REF: 158
2. A database index allows users and application programs to quickly locate specific records.
ANS: T PTS: 1 REF: 158
3. A synonym is an alternate name assigned to a database object.
4. When a positive value is assigned to the INCREMENT BY clause of the CREATE SEQUENCE
command, numeric values are generated in descending order.
ANS: F PTS: 1 REF: 161
5. When a negative value is assigned to the INCREMENT BY clause of the CREATE SEQUENCE
command, numeric values are generated in descending order.
6. The START WITH clause is used to identify the ... Show more content on Helpwriting.net ...
_________________________
5. The default value for the INCREMENT BY clause is two. _________________________
ANS: F one 1

PTS: 1 REF: 161
6. The default beginning value for a sequence is one. _________________________
7. Both a minimum and maximum value can be defined for a(n) sequence.
_________________________
8. The lowest possible value for an increasing sequence is 1. _________________________
9. The CYCLE option prevents a sequence from regenerating previous values.
_________________________
ANS: F, NOCYCLE
PTS: 1 REF: 162
10. The GENERATE option can be used to have a sequence pre–generate a set of numbers before
they are requested by a user. _________________________
ANS: F, CACHE
PTS: 1 REF: 162
11. The CURRVAL pseudocolumn is used to generate the next value in a sequence.
_________________________
ANS: F, NEXTVAL
PTS: 1 REF: 165
12. Sequence settings can be altered using the ALTER SEQUENCE command.
_________________________
13. The INCREMENT BY setting for a sequence cannot be changed with the ALTER SEQUENCE
command. _________________________
ANS: F, START WITH

PTS: 1 REF: 167
14. A sequence can be deleted from the database using the DROP SEQUENCE command.
_________________________
15. Indexes are usually

Fractals: Stonehenge, the Pyramids of Giza, the Parthenon
My infatuation in fractals began freshmen year at Greeley after taking a Seminar with one of the
seniors. I'm not sure exactly when simple interest turned to a kind of obsession, but during that
lesson something seemed to click. It seemed as if this was the universe's answer to everything; the
mystery was solved, however complex the answer was to understand. I'm still not sure if I was
misunderstanding the lesson, or if I had somehow seen it for what it really was; a pattern to describe
the way the universe works. Nevertheless, that day followed me, and I tried to understand more
about fractals through the resources I already had at my disposal–– through courses I was taking.
Sophomore year, through my European History and ... Show more content on Helpwriting.net ...
If you look at yourself, the ratios for phi can be found anywhere. The ratio of your forearm to your
hand, and each of the segments of your finger to the next ideally would equal phi (Human Hand &
Foot). The idea that even your own body abides by this law is strange to imagine, which is what led
me to want to understand these concepts. I began by exploring the different places fractals could
appear and was quickly drawn to the theories of the universe. I soon found that the entire universe
being a fractal was very unlikely because it conflicted with Einstein's Theory of Relativity, so I
turned away from that area of research. I next turned to the applications of fractals only to realize
that I was missing the mathematical concepts. My goal was to find which is the cause and which is
the effect– does nature follow these numbers and concepts that we make up, or did we make up all
of these things to better understand how nature behaves. In math, fractals are a geometric figures but
they come from the world of sequences. They are the result of a graphical representation of the
iterations of polynomial equations. The most famous graph, the Mandelbrot Set, is the graphical
solution of z=z2+c where c is a constant and z is the resulting number from the previous iteration.
To make this more clear, lets substitute the variables for numbers. If my c value is three and my z
value starts at one, the first iteration would tell me that z1=4, the next time you iterate your

Rhetorical Analysis- Snuggie
The Snuggie Commercial tied to Monroe's Motivated Sequence xxxxxxxxxxxxx Governors State
University Abstract This paper focuses on an analysis of the Snuggie commercial. The author will
cover the five steps that make up the Monroe's Motivated Sequence and illuminate how the
commercial is organized according to these steps. The Snuggie Commercial tied to Monroe's
Motivated Sequence The Snuggie is a soft, cozy, one piece blanket with sleeves that is available in 3
different colors. Awareness of this product is now worldwide due to its widely spread television
commercials and advertisements. The Snuggie commercial is not one of the favored commercials in
television today. It does not contain much to gain the ... Show more content on Helpwriting.net ...
Following Satisfaction is Visualization in the Monroe's Motivated Sequence. The commercial uses
Visualization to allow the viewer to see how the snuggie is used in a situation that may be relate to
themselves. It shows all members of a family using the Snuggie. It shows an older lady knitting, a
mother reading to her daughter, a man watching television, a lady making coffee, a child

Mathematical and Musical Harmony
For most people, mathematics is an unsolvable puzzle characterized by the impression of numbers
and calculations taught in school. It is often associated with feelings of rejection and disinterest. To
the general population mathematics appears to be to be strictly rational, abstract, cold and soulless.
Music, however, is involved with emotion, with feelings, and with life. It exists in all daily routines.
Everyone has sung a song, pressed a key on a piano, or blown into a flute, and therefore, in some
sense, made music. People can easily interact with it. Music is a way of expression and a part of
everyone's existence. The incentive for investigating the connections between these two apparent
opposites therefore is in the least ... Show more content on Helpwriting.net ...
This proportion can not only be found in geometric forms (for example the length of a diagonal
related to the length of an edge in a regular pentagon), but also in nature (for example the length of
the trunk in relation to the diameter of some particular trees, such as the
Norway spruce). Due to its consideration as well–balanced, beautiful and dynamic, the golden
section has found various applications in the arts, especially in painting and photography, where
important elements often divide a picture's length or width (or both) following the golden
proportion. However, such a division is not necessarily undertaken consciously, but results from an
impression of beauty and harmony. Diverse studies have discovered that this same concept is also
very common in musical compositions. The golden section–expressed by Fibonacci ratios–is either
used to generate rhythmic changes or to develop a melody line Examples of deliberate applications
can be found in the widely used 'Schillinger System of Musical Composition' or concretely in the
first movement of Béla Bartók's piece 'Music for Strings, Percussion and Celeste', where, for
instance, the climax is situated at bar 55 of 89. Furthermore, Rothwell's study has revealed examples
of the golden proportion in various musical periods. While the characteristics of the examined
compositions varied greatly, the importance of

Research Paper On Leonardo Fibonacci
Leonardo is a well known mathematician, due to his invention in the math community; Such as the
Fibonacci sequence and the Fibonacci Spiral. Leonardo's country of origin is Italy, where he grew
up. Fibonacci made tons of mathematical inventions to improve the world and I'm going to tell you
all about Fibonacci. Leonardo Fibonacci was born in 1170 in Pisa, Italy; Growing up in the wealthy
family of the Bonacci. Even though Fibonacci's first name is Leonardo, nobody in the Modern Era
called him that. Fibonacci's father was the Secretary of the Republic for Pisa, in the province of
Tuscany. Fibonacci's father was ordered to a post in Bugia, where he took Leonardo. Leonardo
studied the customs of the area and began his mathematical knowledge with

Mathematics and Music: The Collision of Science and Art Essay
The concept of the Renaissance man is somewhat of a lost ideal, replaced by the specialized
philosophy of the industrial era. From the 14th to 17th centuries; however, it would be common to
find a man with a profound knowledge of both the Arts, music, poetry, literature, art, and the
Sciences, mathematics, physics, chemistry, biology. The Renaissance man embraced all forms of
knowledge, and through a deep passion for both the Arts and Sciences, used each discipline to
expand the other. Unfortunately, in the 21st century, this same philosophy is far gone. Where these
two fields once were used together to create an ultimate beauty, they are now pitted against each
other by many scholars. It is not uncommon now for a mathematician or ... Show more content on
Helpwriting.net ...
To understand what exactly these ratios are we must first understand; what is the set of Fibonacci
numbers? Mathematically, the Fibonacci Series is defined Fn = Fn–1 + Fn–2 with seed values F1 =
1 and F2 = 1. Seed values are values from which an equation is allowed to work. Without seed
values there would be no basis for the equation, and therefore no way to expand upon it. This
sequence is named after Leonardo Fibonacci who, in 1202 A.D., introduced the sequence to Europe.
The first ten numbers are as follows: 1,1,2,3,5,8,13,21,34,55. These numbers are closely connected
to something called the Golden Ratio, or Phi, the value of this ratio in three significant figures is
1.61. Interestingly, when dividing a Fibonacci number by the number directly before it in the
sequence, the ratio of successive numbers gets closer to Phi.
The Golden Ratio has been considered by many aesthetic philosophers to be the most pleasing
proportion for works of art and architecture. It is well documented how the Golden Ratio has been
utilized in pieces of art and architecture; however, it also finds its place in music. For example, Erik
Satie, a French composer, utilized the golden ratio to write several pieces. The golden ratio is also
found in the musical piece Reflections in the Water written by Debussy. In this piece the climax of
the song sits at Phi, or approximately 61% into the song, and each sequences of keys

Research Paper On Bottleneck Analysis
Bottleneck analysis:
Bottleneck analysis is a technique to analyze the point of congestion of the work. Bottleneck creates
the longer cycler time. In this analysis we use any technique to improve the overall performance of
the system. Bottleneck limits the production capacity and we use some work force or workstation to
overcome that problem.
 Trend analysis
 Correlation
 Comparison
 Elimination drill down
 Pattern matching
MOST (Maynard operation sequence technique):
Maynard is a technique which is based on motion time system. It is used to set the standard time for
the industry in which a performer performs its task. In this system the motion is calculated in TMU's
known as time measurement units. 1 hour is equal to 100000 TMU.
An ... Show more content on Helpwriting.net ...
Gain control over the tool manually
2) Put tool in place
Take the tool to the place where it will be used either directly or by moving the body
Place tool in usage position
3) Use tool
Apply some tool action
4) Put tool aside
Gain the tool for more use, put down the tool aside, return the tool to its original location or put it on
in new location either directly or by moving body.
Tool sequence model:
Get tool Put Tool Use Tool Put Tool Aside Return
A B G A B P * A B P A
(*) May be one of the following;
F=Fasten
L=Loosen
C= cut
S= surface treat
M=measure
R= record

T=think
For e.g. before welding two plates a welder obtains a square and check the angle that is correct the
square is located three steps away from the workstation. The time would be: A6B0G1 A6B0P1
M10A6B0E1 A0
(The sum of all values)*10=Normal

Is3350 Unit 2 Assignment
5 x 36 = 180 Jeremy has 5 strips & each is 36 in long so 5 x 36 = 180 The next thing we have to do
is find the perimeter of the small triangle & that comes out to be 58 in. The rectangles are similar
so.. perimeter of big rectangles equals scale factor times perimeter of small rectangle equals scale
factor times 58 & it results with 4.5. the perimeter of the big rectangle is 261. so now all we do is
use addition for the perimeters which is what gave you the total length & then use subtraction for
180 & the answer comes out to be 139 Based off the picture I can assume that it will expand by the
factor of one over four & then it's probably going to become 25 percent larger. Instead of TU
crossing the x – axis at one it's going to be at 1.25. As far as the relationship i'm not 100% positive if
it's going to expand to at least 25 percent or shrink 25 percent of the squares default size. ... Show
more content on Helpwriting.net ...
I'm going to assume that they're parallel & if this is the case they will probably always be parallel
regardless of how much that they shrunk or got bigger. I think that the two figures are not similar &
I'm going to prove why. All i did for this one was basically calculate the slopes because I didn't want
to over think the question. Based off the figures let's calculate the following slopes... DE from the
left hand figure JK from the right hand figure. After we calculated the slopes we find out that DE is
–2 & JK is –1 so that would mean their not similar mainly because the angles are not

Leonardo Pisano Research Paper
Leonardo Pisano commonly referred to as Fibonacci revolutionized education and economics by
reviving ancient mathematics and creating his own theories (Stetson, University). Through some of
his well known books are mathematical advancements and broken barriers in the world of
mathematics. His desire to learn more and ability to travel led him to create important mathematical
advancements that changed history forever (Henderson, H).
Leonardo Pisano was born in Italy somewhere between 1170–1175 and studied in North Africa. His
father was a merchant who traveled around the world. During these trips he would often be
accompanied by Fibonacci who even at a young age was amazed by the different mathematical
institutions. During these trips he observed ... Show more content on Helpwriting.net ...
Without the Fibonacci sequence or Fibonacci numbers we would not be able to understand
symmetry and spirals in Nature as in depth as we know today. We also would not be able to solve
consecutive sequences with the quickness that we do so today. By developing the Fibonacci
sequence and introducing Hindu–Arabic number systems and algebra theory to Europe, Leonardo
Fibonacci had a far–reaching effect on the evolution of the study and application of mathematics in
Western civilization (O'Neill, Christopher). If Fibonacci had not incorporated these elements in his
book or theorems we would live in a completely different

What Is Metronome?
Singing has lots to do with math. The rhythm, the beat, the notes, and even the strum of a string has
a mathematical formula.
There are full notes, half notes, and quarter notes. A full note is 1 as a half note is 1/2 and a quarter
note is 1/4.
A metronome is a device used for timekeeping. It was design to tick when the "hand" similar to that
of a clocks, moved to one side of the metronome. Using math it can keep instruments from playing a
note to early or too soon. If an instrument is played at the wrong time not only does it sound bad, but
the singer may not be able to adjust to the new pace.
On a music sheet you can see five horizontal lines with notes scattered across them. These lines are
called the staff or a stave. Each line and space is given a letter. A note on A will sound different from
one on C. ... Show more content on Helpwriting.net ...
The twelve–tone technique sets all 12 tones on the chromatic scale. The twelve tones not only make
music sound better but also easier to play than a higher number of tones. Singers earn about $37,889
per year. A salary of $14,352 – $100,524 and a bonus of $0.00 – $5,068. Profit sharing is $1,224 for
singers. The total pay is about $17,667 – $202,903. The hourly rate for a singer is $11.15 – $102.02
with an hourly tip of $0.57 – $37.75.
Singers have to preform in front of audiences or be recorded in a recording studio. They must learn
and rehearse songs, but that doesn't mean a little math isn't involved. Math is everywhere and a part
of everyday life. From school all the way to

Leonardo Fibonacci Research Paper
Leonardo Fibonacci was one of the greatest mathematicians to contribute to the math in the western
world we know of today. Often referred to as "Fibonacci", he was considered to be "the most
talented Western Mathematician of the middle ages."
Born to Guglielmo Bonacci of Pisa, a wealthy Italian merchant in 1170, Fibonacci travelled with
him as a young boy. It was in Buga (now known as Bejaia, Algeria) that Fibonacci learned about the
Hindu–Arabic numeral system.
In 1202, a book called the Liber Abaci (Book of Albacus or Book of Calculation) was birthed from
the many merchants that Fibonacci learned systems of arithmetic from as he travelled the
mediterranean coast. This popularized the Hindu–Arabic numerals in Europe.
Fibonacci was ... Show more content on Helpwriting.net ...
Examples include the Brahmagupta– Fibonacci identity, the Fibonacci search technique, and the
Pisano Period. Beyond mathematics, namesakes of Fibonacci include the astroid 6765 Fibonacci and
the art rock band, The Fibonaccis.
Furthermore, Fibonacci's contributions even though not as revolutionary as other scholars, made
ripples in the mathematics world. While Fibonacci spent time with Fredrick II, he dedicated his
Liber quadratorum (Book of Square Numbers) to Fredrick. Devoted entirely to Diophantine
equations of the second degree (containing squares) the Liber quadratorum is considered Leonardo's
most creative work was in congruent numbers – numbers that give the same remainder when
divided by a given number.
Leonardo Fibonacci's achievements and his shortcomings all came to a stop when his success of a
life ended in the estimated period of time between 1240 and 1250. It is also estimated that his death
took place in Pisa, Italy.
Except for his role in spreading the use of the Hindu–Arabic numerals, Leonardo's contribution to
mathematics has been largely overlooked. Thankfully, his contributions are available to the wester
world of

The Golden Mean in Anatomy
The Golden Mean in Anatomy The Golden Mean is a mysterious number that has been found in
plants, humans, art and even architecture. It was first discovered and studied by ancient
mathematicians in Egypt a very long time ago. In the study of mathematics one realizes that many
patterns often occur. None have been more relevant or fascinating that the golden ratio. The golden
ratio has many names and is often referred to as the golden section, golden mean, golden proportion
and golden cut. The golden mean has been studied and taught for centuries and is still the most
interesting and fascinating things to study. The golden ratio has inspired thinkers like no other
component in mathematics.
While studying the golden mean it becomes evident ... Show more content on Helpwriting.net ...
This ratio gives someone wanting to re–create the human features a very accurate way to measure
the size and distances needed between parts of the body. It is incredible to see the relation and
impact mathematics has on everything in the world. Many famous pieces of art that depict humans
have been known to use the golden ratio in their creations. Leonardo de Vinci used the human body
proportioned according to the golden ratio when producing such incredible works such as Mona
Lisa, and The Last Supper.
The Golden Mean and Christianity
When studying the golden ratio it is evident that there is symmetry in the entire universe. When
studying this subject from a Christian world view it is very easy to see the act of god in the creation
of it all. Everything in nature is fixated around this magical number and this is described as Gods
fingerprints upon nature. When looking at nature using the sequence it is evident that there is a
mathematically precise correlation in the world. This correlation can be seen every day when
looking at nature, humans and even astronomy. This to many is proof of a creator.
The argument against Christianity is that everything in the universe happened by a random chance.
If this was true and the world was created by an absolute random occurrence then why would this
number and sequence occur in almost everything on earth? This sequence is the answer and rebuttal
to an atheist's

Unit 9 Pi Assignment

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Unit 9 Pi Assignment