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Leonardo Pisano Fibonacci was an influential Italian mathematician born in 1170. He introduced the decimal numeral system and Hindu-Arabic numerals to Western Europe through his book Liber Abaci. In this book, he also described the Fibonacci sequence where each number is the sum of the previous two numbers. This sequence has applications in mathematics and patterns seen in nature. Fibonacci made important contributions to number theory and introduced notations still used today such as the bar in fractions and square root symbols.

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Maths in nature fibonacci

The document discusses how patterns in nature can be modeled mathematically through concepts like the Fibonacci sequence and golden ratio. It provides several examples of how these concepts appear in structures like pine cones, sunflowers, nautilus shells, galaxies, and even the human body. The Fibonacci sequence describes the breeding patterns of rabbits introduced by Leonardo Fibonacci in the 13th century, and the ratios between its numbers approach the golden ratio - a number linked to patterns in architecture, music, and nature.

Fibonacci The Man of Numbers

This the power point presentation I made and used for my presentation in History of Math. Pardon me for not being able to cite ALL of my references through out the presentation. (one day I will). It is not detailed and perfect, but I am hoping that in a way, it may help you a hint on where to start to study about him and his works.
Information known about his life and SOME of his contributions will be found in this books. I merely focused on his first book, liber abbaci, so if you wish to see more of his contributions, look out for his other writings. (there are lots of articles online about him, just look for them and read them)
Fibonacci, the most famous mathematician from Pisa, Italy during the medieval period, is the man behind the fibonacci sequence and the popularization of the Hindu-Arabic Numeral System to Europe. Learn some things about him and his contributions through this.
Thank you :)

541 Interactive ppt Fibonacci Sequence

The document discusses the Fibonacci sequence and its relationship to the golden ratio. It begins by introducing Leonardo of Pisa, who helped spread the use of the modern number system and knowledge of the Fibonacci sequence. The sequence is defined as a pattern where each number is the sum of the two preceding ones, starting with 1, 1, 2, 3, 5, etc. This sequence appears throughout nature and can be seen in spirals of shells, pinecones, and sunflowers. The ratio of consecutive Fibonacci numbers approaches the golden ratio, about 1.618, an irrational number important in art and architecture considered aesthetically pleasing. The golden ratio can also be observed in proportions of the human body.

Fibonacci Sequence and Golden Ratio

The document discusses Fibonacci numbers and the golden ratio, explaining how Fibonacci discovered the Fibonacci sequence by modeling rabbit populations and how ratios between numbers in the sequence converge on the golden ratio. It provides many examples of how the golden ratio appears frequently in nature, art, architecture, and the human body, demonstrating its aesthetic appeal and role in design.

Fibonacci sequence

The Fibonacci sequence is a series of numbers where each number is the sum of the two preceding numbers. The sequence begins with 0 and 1 and progresses as 0, 1, 1, 2, 3, 5, 8, etc. This mathematical pattern is found throughout nature, appearing in aspects like petal arrangements, sunflower seeds, and seashell spirals. The Fibonacci sequence was first studied by Indian mathematicians around 200 BC and introduced to Western Europe by Leonardo Fibonacci in 1202 based on patterns in rabbit populations.

Fibonacci sequence

This document discusses the Fibonacci sequence, a number pattern discovered over 8,000 years ago by Italian mathematician Leonardo Fibonacci. The sequence is 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, etc. where each number is the sum of the two preceding numbers. It explains that many aspects of nature exhibit this pattern, like the number of petals on plants or the spiral pattern of seeds inside a sunflower. Activities are provided for students to explore properties of the sequence, like the sum of numbers above a chosen line or multiplying certain numbers together.

History of mathematics

The history of mathematics began with early civilizations developing basic arithmetic and geometry. Some of the earliest and most influential mathematical texts came from ancient Mesopotamia, Egypt, China, and India. Greek mathematics built upon earlier traditions and introduced deductive reasoning and mathematical rigor. Key Greek mathematicians included Thales, Pythagoras, Plato, Euclid, Archimedes, and Apollonius, who made seminal contributions to geometry, number theory, and the early study of functions and calculus. Following this Golden Age of Greek mathematics, mathematical advances continued within the Islamic world and medieval Europe.

Maths in nature

This document discusses the relationship between mathematics and nature. It provides examples of symmetry, patterns, ratios and shapes found in nature that relate to mathematical concepts like the golden ratio, pi, the Fibonacci sequence, fractals and perfect shapes. These natural phenomena were inspiration for mathematical discoveries made by ancient civilizations. Symmetry is seen in structures like starfish and flowers, while spirals in shells, pinecones and sunflowers relate to the Fibonacci sequence. The human body and works of art also exhibit mathematical proportions. Overall, the document argues that mathematics is deeply embedded throughout nature.

Fibonacci series and Golden ratio

The document discusses the Fibonacci sequence and the golden ratio. It begins by introducing the Fibonacci sequence of numbers: 1, 1, 2, 3, 5, 8, etc., where each number is the sum of the previous two. It then explains that the ratios of successive numbers in the sequence converge on the golden ratio, approximately 1.618. The golden ratio is found throughout nature, such as in the proportions of the human body and in vegetation. The document also provides methods for constructing a golden rectangle using squares and diagonals, with a final ratio matching the golden ratio.

medieval European mathematics

The document discusses medieval mathematics from the 12th-14th centuries. It provides biographies of several important medieval mathematicians including Fibonacci, who introduced the Fibonacci sequence to Western Europe and studied rabbit populations. It also discusses Nicole Oresme who proved the divergence of the harmonic series and Giovanni di Casali who analyzed accelerated motion graphically. The document notes that during this time, Europeans learned mathematics from Arabic sources that had been translated to Latin.

Golden ratio and Fibonacci series

In this presentation, we see that how golden ratio and Fibonacci series are calculated or working? and What is the problem faced by Fibonacci in Fibonacci series.

Nine patterns in nature by CuriOdssey

CuriOdyssey is exploring nine visual patterns found in nature in a series of blog posts and in our upcoming new exhibit, THE NATURE OF PATTERNS. The patterns we will delve into are:
1. Symmetries (mirror & radial)
2. Fractals (branching)
3. Spirals
4. Flow and chaos
5. Waves and dunes
6. Bubbles and foam
7. Arrays and tiling (tessellations)
8. Cracks
9. Spots & stripes
These beautiful patterns are seen throughout the natural world, from atomic to the astronomical scale.
Philip Ball's book, "Patterns in Nature" was a source of inspiration. We recommend it to discover more about nature's incredible patterns.

Fibonacci Series

The Fibonacci sequence is an integer sequence where each number is the sum of the two preceding ones, starting from 0 and 1. It was invented by Leonardo Fibonacci in his book Liber Abaci in 1202. The sequence is closely related to the golden ratio and appears throughout nature in patterns of spirals in shells, flowers, pinecones, and galaxies. It has also been used in art, architecture, and mathematics due to its aesthetic appeal from approximating the golden ratio.

Vedic addition

Vedic Mathematics is a system of mathematics that allows problems to be solved quickly and efficiently. It is based on the work of Sri Bharathi Krishna Thirthaji Maharaja (1884 – 1964), who devised the system from a close study of the Vedas. The Vedas are ancient scriptures of India that deal with many subjects. It is based on 16 sutras (aphorisms) from the Vedas that provide a principle or a rule of working to solve a problem. These sutras may be ancient in origin, but are still relevant to modern day mathematics.

evolution of number system

The document discusses the history and development of number systems. It describes how ancient cultures like the Sumerians, Egyptians, Greeks, Romans, and Indians all developed early number systems to suit their needs. The most commonly used system today, the Hindu-Arabic numeral system, can be traced back to developments in India in the 5th century where place-value notation and the concept of zero were introduced. This system was then adopted and modified by Arabs and Europeans.

Mathematics in nature

The document discusses how mathematics is present in nature. It provides examples of symmetry, shapes, parallel lines, and the Fibonacci spiral that can be observed in the natural world. Radial and bilateral symmetry are seen in structures like flowers and the human body. Common shapes found in nature include spheres, hexagons used by bees to build hives efficiently, and cones formed by volcanoes. Parallel lines can be seen in dune formations, and the Fibonacci spiral appears in nautilus shells. The document aims to show how nature demonstrates mathematical concepts and patterns.

Maths in nature

Patterns in nature are visible regularities that recur in different contexts and can be mathematically modeled. Early philosophers studied natural patterns like symmetries, spirals, and waves. The Fibonacci sequence, where each number is the sum of the previous two, is found throughout nature in patterns of seeds, shells, and other biological structures that follow the golden ratio of approximately 1.618. Many natural phenomena exhibit self-similar fractal patterns related to the Fibonacci sequence and golden ratio.

Fibonacci Sequence

The Fibonacci sequence appears frequently in nature. It is seen in patterns of plant leaves, flower petals, pinecones, shells, and other biological settings. Many plants and flowers display spirals corresponding to Fibonacci numbers. The ratio of numbers in the sequence approaches the golden ratio, which is also found in natural patterns. The Fibonacci sequence has applications in mathematics, computer science, architecture, and art due to its prevalence in natural forms and patterns.

Word Problems with Inequalities

The document provides examples of word problems involving inequalities. It gives steps to follow, such as defining variables, writing inequalities, solving, and checking answers. Several examples are worked through, applying these steps to problems about numbers, rates, areas, and time. The examples demonstrate how to set up and solve linear inequalities to find possible values that satisfy the given relationships.

Maths in nature fibonacci

Maths in nature fibonacci

Fibonacci The Man of Numbers

Fibonacci The Man of Numbers

541 Interactive ppt Fibonacci Sequence

541 Interactive ppt Fibonacci Sequence

Fibonacci Sequence and Golden Ratio

Fibonacci Sequence and Golden Ratio

Fibonacci sequence

Fibonacci sequence

Fibonacci sequence

Fibonacci sequence

History of mathematics

History of mathematics

Maths in nature

Maths in nature

Fibonacci series and Golden ratio

Fibonacci series and Golden ratio

5.4 mutually exclusive events

5.4 mutually exclusive events

medieval European mathematics

medieval European mathematics

Golden ratio and Fibonacci series

Golden ratio and Fibonacci series

Nine patterns in nature by CuriOdssey

Nine patterns in nature by CuriOdssey

Fibonacci Series

Fibonacci Series

Vedic addition

Vedic addition

evolution of number system

evolution of number system

Mathematics in nature

Mathematics in nature

Maths in nature

Maths in nature

Fibonacci Sequence

Fibonacci Sequence

Word Problems with Inequalities

Word Problems with Inequalities

Fibonacci

Leonardo de Pisa, Leonardo Pisano o Leonardo Bigollo (c. 1170 - 1250), también llamado Fibonacci, fue un matemático italiano, famoso por haber difundido en Europa el sistema de numeración arábiga actualmente utilizado, el que emplea notación posicional (de base 10, o decimal) y un dígito de valor nulo: el cero; y por idear la sucesión de Fibonacci.
El apodo de Guglielmo (Guillermo), padre de Leonardo, era Bonacci (simple o bien intencionado). Leonardo recibió póstumamente el apodo de Fibonacci (por filius Bonacci, hijo de Bonacci). Guglielmo dirigía un puesto de comercio en Bugía (según algunas versiones era el cónsul de Pisa), en el norte de África (hoy Bejaia, Argelia), y de niño Leonardo viajó allí para ayudarlo. Allí aprendió el sistema de numeración árabe.
Consciente de la superioridad de los numerales árabes, Fibonacci viajó a través de los países del Mediterráneo para estudiar con los matemáticos árabes[1] más destacados de ese tiempo, regresando cerca de 1200. En 1202, a los 32 años de edad, publicó lo que había aprendido en el Liber Abaci (libro del ábaco o libro de los cálculos). Este libro mostró la importancia del nuevo sistema de numeración aplicándolo a la contabilidad comercial, conversión de pesos y medidas, cálculo, intereses, cambio de moneda, y otras numerosas aplicaciones. En estas páginas describe el cero, la notación posicional, la descomposición en factores primos, los criterios de divisibilidad. El libro fue recibido con entusiasmo en la Europa ilustrada, y tuvo un impacto profundo en el pensamiento matemático europeo.
Leonardo fue huésped del Emperador Federico II, que se interesaba en las matemáticas y la ciencia en general. En 1240, la República de Pisa lo honra concediéndole un salario permanente (bajo su nombre alternativo de Leonardo Bigollo).
Conocido por Fibonacci, hijo de Bonaccio, no era un erudito, pero por razón de sus continuos viajes por Europa y el cercano oriente, fue el que dio a conocer en occidente los métodos matemáticos de los hindúes.
•
Su quinta obra
En el año 1225 publica su cuarto y principal libro: Liber Quadratorum 'El Libro de los Números cuadrados', a raíz de un desafío de un matemático de la corte de Federico II (Teodoro) que le propuso encontrar un cuadrado tal que si se le sumaba o restaba el número cinco diera como resultado en ambos casos números cuadrados. Curiosamente, el año de publicación del libro es un número cuadrado.
Fibonacci comienza con los rudimentos de lo que se conocía de los números cuadrados desde la antigua Grecia y avanza gradualmente resolviendo proposiciones hasta dar solución al problema de análisis indeterminado que le habían lanzado como desafío.
En la parte original de la obra introduce unos números que denomina congruentes (Proposición IX) y que define, en terminología actual, como c = m.n (m² - n²), donde m y n son enteros positivos impares, m > n. De esta forma, el menor de ellos es 24. Enuncia y muestra que el producto de un número congruente por un cuadrado es otro número congruente.
Utiliza estos números como herramientas para sus posteriores proposiciones y los hace intervenir en una identidad que es conocida como Identidad de Fibonacci (Proposición XI). La identidad es: [1/2(m²+n²)]² ± mn (m² - n²) = [1/2(m² - n²) ± mn]². Esta permite pasar con facilidad de un triángulo rectángulo a otro.
Leonardo de Pisa utiliza frecuentemente las proposiciones precedentes como lemas para las siguientes, por lo que el libro lleva un encadenamiento lógico. Sus demostraciones son del tipo retórico y usa segmentos de recta como representación de cantidades. Algunas proposiciones no están rigurosamente demostradas, sino que hace una especie de inducción incompleta, dando ejemplos prácticos y específicos, pero su dominio algorítmico es excelente y todo lo que afirma puede ser demostrado con las herramientas actuales. No se encuentran errores important

Alan turing

Alan Turing fue un matemático británico que nació en 1912 y murió en 1954. Describió una máquina calculadora capaz de realizar cálculos mediante instrucciones lógicas, anticipando los ordenadores modernos, y creó procesos para descifrar mensajes alemanes durante la Segunda Guerra Mundial. También definió un método para determinar si una máquina podía pensar como un ser humano.

Alan Turing

Alan Turing was a British mathematician, logician, cryptanalyst and computer scientist. He made major contributions to mathematics, cryptanalysis and computer science. During World War II, Turing worked at Bletchley Park where he played a pivotal role in cracking Nazi Germany's Enigma code. This helped the Allies win the war. Later in life, Turing was prosecuted for homosexuality, which was illegal in the UK at that time, and he tragically died at the young age of 41 in 1954. He is now recognized as one of the most influential scientists of the 20th century.

Alan Turing

This document summarizes Alan Turing's seminal 1950 paper "Computing Machinery and Intelligence" which proposed what is now known as the Turing Test. The Turing Test involves an interrogator determining which of two entities, a human or computer, they are communicating with via teletyped responses. Turing argued that if a computer could successfully pass as human, it should be considered thinking. The document outlines Turing's description of the "Imitation Game" protocol and responses to philosophical counterarguments against the possibility of machine thought. It concludes by noting the impact of Turing's work on artificial intelligence and philosophy of computing.

Alan Turing

Alan Turing fue un matemático, informático teórico, criptógrafo y filósofo inglés nacido en 1912 que realizó contribuciones fundamentales en los campos de la computación teórica, la inteligencia artificial y la criptografía. Durante la Segunda Guerra Mundial trabajó descifrando códigos nazis en Bletchley Park. Más tarde propuso la Prueba de Turing para evaluar la inteligencia de las máquinas. Sin embargo, su carrera se vio truncada cuando fue procesado y conden

Fibonacci

The document discusses how the Fibonacci sequence appears frequently in nature. It introduces Leonardo Fibonacci, the Italian mathematician who documented the sequence, and describes how the sequence is formed by adding the previous two numbers. It then gives several examples of how the Fibonacci sequence shows up in patterns of plant life like flowers, fruit, vegetables, and phyllotaxis. Finally, it explains how the Golden Ratio, a ratio derived from the Fibonacci sequence, is commonly found in art, architecture, nature, and proportions of the human body.

Fibonacci

Fibonacci

Alan turing

Alan turing

Alan Turing

Alan Turing

Alan Turing

Alan Turing

Alan Turing

Alan Turing

Fibonacci

Fibonacci

Fibonacci Numbers

Leonardo Pisano Fibonacci was an Italian mathematician from the 13th century known for introducing the decimal numeral system and the Fibonacci sequence to Western Europe. The Fibonacci sequence is a series of numbers where each subsequent number is the sum of the previous two, starting with 0 and 1. This sequence appears frequently in nature, such as in the spiral pattern of flower petals, seed heads, pinecones, and branching in trees and galaxies. It is also used in computer programming, poetry meter, and as a technical analysis tool in finance to determine support and resistance levels in stock prices.

Fibonacci Sequence 1

The document discusses the Fibonacci sequence and how it relates to rabbit populations and flower patterns. It explains who Fibonacci was, how the sequence works, and how the population of rabbits in a hypothetical town grows each month in a way that matches the Fibonacci sequence. It also gives examples of how spiral patterns in flowers like daisies and sunflowers correspond to Fibonacci numbers.

Leonardo de pisa (Santiago y José Manuel)

Leonardo Fibonacci was an Italian mathematician born around 1170 in Pisa, Italy. He introduced the Indo-Arabic numeral system to Europe, which uses positional notation with the numbers 0 through 9. He is also known for the Fibonacci sequence, where each number is the sum of the two preceding numbers. Fibonacci wrote several books on mathematics, including one at age 32 introducing the concept of zero and the Indo-Arabic numeral system to Europe. He died around 1250 in Pisa.

Patterns in Nature

What patterns can we find in nature? Plants, flowers and fruits have all kinds of patterns, from petal numbers that are in the Fibonacci sequence, to symmetry, fractals and tessellation.

Fibonacci Sequence 2

1- The story "Rabbits, Rabbits Everywhere" is about a town named Chee that is overrun by rabbits after the wizard gets angry for not receiving food from the Pied Piper. A girl named Amanda discovers the rabbits are increasing according to the Fibonacci sequence.
2- The Fibonacci sequence is a pattern of numbers where each number is the sum of the previous two numbers, starting with 1, 1, 2, 3, 5, etc. It was popularized by the Italian mathematician Fibonacci in his 1202 book Liber Abaci.
3- The Fibonacci sequence can be seen in nature, such as the number of petals on flowers following the sequence rather than being divisible by

leonardofibonacci-140918135347-phpapp02.pdf

- Leonardo Fibonacci was an Italian mathematician born around 1170 who is credited with introducing the Hindu-Arabic numeral system (base-10 system using 0-9 symbols) to Western Europe through his book Liber Abaci, published in 1202.
- In Liber Abaci, he described the decimal number system and arithmetic operations like addition, subtraction, multiplication, and division using this system. This helped popularize the use of this more efficient "new" system in Europe over the traditional Roman numeral system.
- Fibonacci is also known for the Fibonacci sequence of numbers where each number is the sum of the previous two, which arises from a rabbit breeding problem he posed in Liber Abaci

Fibonacci Sequence 4

The document discusses the Fibonacci sequence, which is a series of numbers where each subsequent number is the sum of the previous two. It begins with Leonardo Fibonacci introducing the sequence to Western mathematics. It then describes how the sequence appears in nature, such as in the spiral of shells. Specifically, it examines how the Fibonacci sequence relates to the number of bones in the human hand. The palm and knuckles correspond to the early numbers in the sequence, demonstrating how this mathematical concept appears throughout our bodies.

Early European Mathematics

Early European Mathematicians:
> Fibonacci
> Pascal
> Regiomontatus
> Luca Pacioli
> Leonardo Da Vinci
> Francois Viete
> John Napier
> Johannes Kepler
> Isaac Newton

Fibonacci Numbers.pptx

The Fibonacci sequence is a series of numbers where each subsequent number is the sum of the previous two. It begins with 0 and 1, and the next terms are generated by adding the two numbers before it: 0, 1, 1, 2, 3, 5, 8, etc. The Fibonacci sequence appears throughout nature in patterns of plant growth, spirals in shells, and branching patterns in trees. It also shows up in galaxies, hurricanes, pinecones, and the human body, demonstrating mathematics in the natural world.

Fibonacci en

The document discusses the Fibonacci sequence and the Golden ratio. It describes how Leonardo Fibonacci introduced Arabic numerals to Europe and discovered a rabbit population problem that led to the famous Fibonacci sequence. The sequence is defined as Fn=Fn-1+Fn-2, where each number is the sum of the previous two. The ratio of consecutive numbers approaches the Golden ratio φ ≈ 1.618. This ratio has been found throughout nature and was considered aesthetically pleasing, appearing in architecture and art from ancient times through the Renaissance.

Fibonaaci sequence.pptx

This is the Fibonacci Series PPT.
It contains 9 pages in total
Explanation done in easy and simplest method
Thank you

mathematicians.docx

Isaac Newton was considered one of the greatest scientists of all time. He made huge impacts in many fields including inventing calculus, building the first reflecting telescope, and establishing classical mechanics with his work "Philosophiæ Naturalis Principia Mathematica." Newton decomposed white light into colors and formulated the three laws of motion. The world would be very different without Newton's contributions to science and technology.

Fibonacci Numbers (abridged)

The document discusses Fibonacci numbers, which are a sequence of numbers where each number is the sum of the two preceding ones. Some key points:
- The sequence was introduced by Leonardo Fibonacci in 1202 and appears in aspects of nature like plant growth.
- Applications include computer algorithms and graphs used for interconnecting systems. Fibonacci numbers also appear in musical compositions and arrangements.
- There are closed-form expressions and matrix representations for calculating Fibonacci numbers. The ratio of consecutive numbers approaches the golden ratio.

Fibonaccis Decimal System

Fibonacci introduced the decimal system to replace the Roman numeral system because Roman numerals lacked a symbol for zero. The decimal system is now used daily for measurements, statistics, percentages, and algebra. Fibonacci also studied fractions and created the fraction bar that is still used today to represent parts of a whole. While we write fractions differently now, placing them to the right of the whole number, Fibonacci originally wrote fractions to the left, showing how far the concept of fractions has developed since his time.

Fibonacci

This is about Fibonacci, a famous mathematician who lived hundreds of years ago. He discovered number patterns in all aspects of nature.

MEM RES.docx

During the Dark Ages in Europe from the 4th to 12th centuries, mathematical study stagnated while Chinese, Indian, and Islamic mathematicians advanced the field. European knowledge was limited until the 12th century when trade with the East began spreading foreign ideas and practical needs drove more study of arithmetic. The 15th century printer furthered mathematics education, and figures like Fibonacci, Oresme, and Regiomontatus made important contributions that advanced European mathematics.

MEM RES.docx

During the Dark Ages in Europe from the 4th to 12th centuries, mathematical study stagnated while Chinese, Indian, and Islamic mathematicians advanced the field. European knowledge was limited until the 12th century when trade with the East began spreading foreign ideas and practical needs drove more study of arithmetic. The 15th century printer furthered mathematics education, and figures like Fibonacci, Oresme, and Regiomontatus made important contributions that advanced European mathematics.

Problem Solving with Patterns

This presentation presents three common sequences-the Arithmetic sequence, the Geometric sequence and the Fibonacci sequence.

Fibonacci Sequence 3

The document summarizes several projects done by students on Fibonacci sequences in nature. It discusses how the seed patterns in sunflowers, the number of petals in many flowers, the branching patterns in daisies, and the spiral patterns in pineapples can all be described by the Fibonacci sequence. It also provides biographical information on Leonardo Fibonacci and summaries of the students' projects on sunflowers, pineapples, daisies, and a book about rabbits.

ZERO.ppt

The document discusses the origins and importance of the number zero. It notes that zero was independently discovered by the Mayans and Indians, with the Indians representing it as a dot and the Mayans using a pair of wedges. The concept of zero spread to the Arabic world and was represented as a circle. It was introduced to Europe in the 9th century by an Italian mathematician. The document emphasizes that life would be much more complicated without zero, as it is a fundamental part of modern number systems like binary used in computers.

Fibonacci Numbers

Fibonacci Numbers

Fibonacci Sequence 1

Fibonacci Sequence 1

Leonardo de pisa (Santiago y José Manuel)

Leonardo de pisa (Santiago y José Manuel)

Patterns in Nature

Patterns in Nature

Fibonacci Sequence 2

Fibonacci Sequence 2

leonardofibonacci-140918135347-phpapp02.pdf

leonardofibonacci-140918135347-phpapp02.pdf

Fibonacci Sequence 4

Fibonacci Sequence 4

Early European Mathematics

Early European Mathematics

Fibonacci Numbers.pptx

Fibonacci Numbers.pptx

Fibonacci en

Fibonacci en

Fibonaaci sequence.pptx

Fibonaaci sequence.pptx

mathematicians.docx

mathematicians.docx

Fibonacci Numbers (abridged)

Fibonacci Numbers (abridged)

Fibonaccis Decimal System

Fibonaccis Decimal System

Fibonacci

Fibonacci

MEM RES.docx

MEM RES.docx

MEM RES.docx

MEM RES.docx

Problem Solving with Patterns

Problem Solving with Patterns

Fibonacci Sequence 3

Fibonacci Sequence 3

ZERO.ppt

ZERO.ppt

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- 2. Childhood It is believed that Leonardo Pisano Fibonacci was born in the 13th century, in 1170. Fibonacci was born in Italy but obtained his education in North Africa. Very little is known about him or his family and there are no photographs or drawings of him. Much of the information about Fibonacci has been gathered by his autobiographical notes which he included in his books.
- 3. Accomplishments Fibonacci is considered to be one of the most talented mathematicians for the Middle Ages. Few people realize that it was Fibonacci that gave us our decimal number system, which was replaced by Roman Numeral system as times advanced.
- 4. Liber abaci Liber abaci is his book were he shows how to use our current numbering system all from what he discovered. Here is an example problem form his book :A certain man put a pair of rabbits in a place surrounded on all sides by a wall. How many pairs of rabbits can be produced from that pair in a year if it is supposed that every month each pair begets a new pair, which from the second month on becomes productive?
- 5. Liber abaci continued The problem that you just read was the problem that lead to this following discovery of the introduction of the Fibonacci Numbers the Fibonacci Sequence. The sequence is 1, 1, 2, 3, 5, 8, 13, 21, 34, 55... This sequence, shows that each number is the sum of the two preceding numbers. It is a sequence that is seen and used in many different areas of mathematics and science. The sequence is an example of a recursive sequence. The Fibonacci Sequence defines the curvature of naturally occurring spirals, such as snail shells and even the pattern of seeds in flowering plants.
- 6. Contributions Fibonacci is famous for his contributions to number theory. 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, previous to this, the numerator has quotations around it. The square root notation is also a Fibonacci method.