Leonardo Fibonacci Research Paper

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
... Get more on HelpWriting.net ...

##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 ...
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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

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

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.
пЃ¶Trend analysis
пЃ¶Correlation
пЃ¶Comparison
пЃ¶Elimination drill down
пЃ¶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

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
1Introduction
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

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 О¦, 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

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) cosвЃЎx, r(x) sinвЃЎx) When x=0, A(0) = (r(0) cosвЃЎ0, r(0) sinвЃЎ0) = (1Г—1, 0) = (1, 0) Point B: B(x) = (r(x)
cosвЃЎx, r(x) sinвЃЎx) When x=ПЂ/2 B(ПЂ/2) = (r(ПЂ/2) cosвЃЎгЂ–ПЂ/2гЂ—, r(ПЂ/2) sinвЃЎгЂ–ПЂ/2гЂ—) = (1.618 Г— 0, 1.618 Г— 1) =
(0, 1.618) When x=ПЂ C(ПЂ)= (r(ПЂ) cosвЃЎПЂ, r(ПЂ) sinвЃЎПЂ) = (–2.618 Г— 1, –2.618 Г— 0) = (–2.618, 0) From the previous Table 2
F_nГ·F_(n–1) = П† (1.618) (1в‰¤П†в‰¤2) П†= 1.618 П†^2= 2.618 П†^3= 4.236 From here, we recognize a pattern, you just need to multiply П† 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

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 on Helpwriting.net ...
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=(П†–(–П†)^(–n))/в€
љ5 where П†=(1+в€
љ5)/2в‰€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 П†= (1+в€
љ5)/2в‰€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

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 on Helpwriting.net ...
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)
VariableData TypeValue RangeDescription XFloat1– 2 This is "Phi"
Table 2 (Exercise

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 content on Helpwriting.net ...
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 (О¦) 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

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

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 content on Helpwriting.net ...
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

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

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

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
... Show more content on Helpwriting.net ...
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

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 content on Helpwriting.net ...
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

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

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

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,

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 mДЃtrДЃ–vб№›ttas". 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

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

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

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

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

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

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
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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 BГ©la BartГіk'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

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
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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

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... Show more content on Helpwriting.net ...
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. Hismother, 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

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

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 on Helpwriting.net ...
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

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

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

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 mДЃtrДЃ–vб№›ttas". 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

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 6Formula: Tnth= n(n+1) 2
Plug in 6 for n. T6th=6(6+1) 2

Solve.T6th= 6(7)T6th=42T6th=21. 22
The

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
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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

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 LeonardoFibonacci, 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

06
Chapter 6: Additional Database Objects
TRUE/FALSE
1.A sequence serves as a nickname for a database object.
ANS:FPTS:1REF:158
2.A database index allows users and application programs to quickly locate specific records.
ANS:TPTS:1REF:158
3.A synonym is an alternate name assigned to a database object.
ANS:TPTS:1REF:158
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:FPTS:1REF: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.
ANS:TPTS:1REF:161
6.The START WITH clause is used to identify the... Show more content on Helpwriting.net ...

_________________________
ANS:TPTS:1REF:161
5.The default value for the INCREMENT BY clause is two. _________________________
ANS:F one 1
PTS:1REF:161
6.The default beginning value for a sequence is one. _________________________
ANS:TPTS:1REF:161
7.Both a minimum and maximum value can be defined for a(n) sequence. _________________________
ANS:TPTS:1REF:161
8.The lowest possible value for an increasing sequence is 1. _________________________
ANS:TPTS:1REF:162
9.The CYCLE option prevents a sequence from regenerating previous values. _________________________
ANS:F, NOCYCLE
PTS:1REF: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:1REF:162

11.The CURRVAL pseudocolumn is used to generate the next value in a sequence. _________________________
ANS:F, NEXTVAL
PTS:1REF:165
12.Sequence settings can be altered using the ALTER SEQUENCE command. _________________________
ANS:TPTS:1REF:167
13.The INCREMENT BY setting for a sequence cannot be changed with the ALTER SEQUENCE command. _________________________
ANS:F, START WITH
PTS:1REF:167
14.A sequence can be deleted from the database using the DROP SEQUENCE command. _________________________
ANS:TPTS:1REF:169
15.Indexes are usually

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