Fibonacci
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Fibonacci was an Italian mathematician born in Pisa in 1170. He is most famous for introducing the Fibonacci sequence to Western European mathematics in his 1202 book Liber Abaci. The Fibonacci sequence starts with 1, 1, and then each subsequent number is the sum of the previous two numbers. This sequence appears frequently in nature, such as the spiral pattern of seed heads, pinecones, and shells. Fibonacci made other significant contributions through his books including introducing Arabic numerals to Europe and applying mathematics to accounting, commerce, and geometry problems. He has had a lasting legacy as one of the most important mathematicians of the Middle Ages.
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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 :)
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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.
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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)
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Thank you :)
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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.
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Domestic animals such as those found on farms and in homes provide humans with food and companionship. Animals live in a variety of habitats, including on land and in water, and come in different sizes from small to large. They have diverse physical attributes as some have legs, scales, fur, feathers, wings or fins. Animals also demonstrate a range of abilities.
Plants
Plants are living things that feed, grow, and die like other living organisms. They need water, sunlight, air, and soil to survive and have structures like roots, stems, leaves, and sometimes flowers and fruits. Plants come in different forms like trees, bushes, herbs and can exist in the wild or be cultivated.
Science ayuda
El documento proporciona instrucciones sobre recursos educativos disponibles en la página web del Colegio Franciscano La Inmaculada en Cartagena, España. Indica que hay un enlace al blog English Corner en la esquina superior derecha y materiales de ciencias naturales. También explica cómo registrarse en la plataforma SM Savia Digital introduciendo el código de licencia encontrado en los libros de texto.
Senses 1.1
This document describes the five human senses and how they work. It explains that the nose can smell, the mouth can taste, the eyes can see, the ears can hear, and the hands can touch. Each sense is then described in more detail, noting that different senses allow people to experience smells, tastes, textures, sounds at different volumes, and sights.
Cómo crear un reloj de sol 3
El documento describe un taller para crear un reloj de sol durante la Semana de la Ciencia en una escuela secundaria en España. Explica los 10 pasos para construir un reloj de sol, incluyendo trazar una línea, dibujar una semicircunferencia, marcar ángulos, indicar la hora, señalar el norte, dibujar un rombo, agregar solapas y recortar el diseño. El objetivo del taller es enseñar a los estudiantes cómo funciona y se construye un reloj de sol.
The Beatles
The document provides biographies of the four members of the Beatles - John Lennon, Paul McCartney, George Harrison, and Ringo Starr. It details where they were from, how the band was formed, and key facts about each member. It also lists some of the band's most famous albums, including Abbey Road, Help!, Let It Be, and Yellow Submarine.
Saint Francis of Assisi: Biography
Saint Francis of Assisi was born in 1181 in Assisi, Italy. As a young man, he lived a carefree life but had a religious conversion after being imprisoned for a year. He devoted himself to serving God and the poor, rebuilding chapels and preaching. In 1209, he established the Franciscan Order. Saint Francis is renowned for his love of nature and emphasis on poverty. He died in 1226 at the age of 44 while his teachings have had significant and lasting influence.
Archimedes
Archimedes was a famous Greek mathematician and inventor who lived in Syracuse in the 3rd century BC. He made important discoveries in geometry and mechanics, including establishing the science of hydrostatics and formulating Archimedes' principle of buoyancy. He is also credited with inventing the hydraulic screw pump for raising water. The document provides details on Archimedes' life and accomplishments, including using his principle of buoyancy to prove that a golden crown was not pure gold as claimed.
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Fibonacci
- 1. Iván Alarcón Quintana 2 º A E.S.O. “La Inmaculada"
- 2. Index • Life • Mathematical work – Liber Abaci – Sequence Fibonacci – Reflection in nature • Contribution to mathematics • Legacy
- 3. Life • Born in Pisa (1170) • Son of Guglielmo, Nicknamed Bonacci. • He lived with his father in Bejaia (Algiers). • Was there he learned about the numbering system Arabic. • Guest of the Emperor Frederick II • 1240, Pisa granted permanent wage • He died in Pisa (1250)
- 4. Mathematical work • Liber abaci (1202) – Introduced Indorum operandi, today known as Arabic numerals – Defended numbering digits 0-9 and placed value – Applied to accounting, conversion of weights and measures, interest, money exchange, ... – Well received in Europe, had a profound impact
- 5. Mathematical work • Sequence Fibonacci – Known for Indian mathematicians – It was introduced in the West (Liber Abaci) – Starting at 1, each term is the sum of the two previous numbers – But did not mention the proportion Golden • Associated with the beauty in nature according to the Greeks •1 •1 •1 +1 =2 •1 +2 =3 •2 +3 =5 •3 +5 =8 •5 +8 =13 •8 +13 =21 •13 +21 =34 •21 +34 =55 •34 +55 =89 •...
- 6. Mathematical work • Reflection in nature – In the human body: • The length of phalanges (2, 3, 5, 8) • Ratio between hip height and knee height • Ratio between distance from shoulder to fingers and distance from elbow to fingers – The reproduction of rabbits (1, 1, 2, 3, 5,8, ...)
- 7. Mathematical work • Reflection in nature – Nature uses the same pattern to have the seeds in a flower, the petals on the edges, and place the leaves in a stem. They grow in spiral maintaining an angle no matter how much the plant is going to grow, so a leaf will be covered the least possible and will receive the necessary amount of sunlight. Sunflower : 55 coils in one direction and 89 in the other, or, 89 and 144 respectively. Leaves arise following a spiral around the stem
- 8. Mathematical work • Reflection in nature – The galaxies also grow following the suquence of Fibonacci. – The shells of Nautilus are formed according to this pattern.
- 9. Contribution to mathematics • Liber Abaci (Book of the Abacus) – 15 chapters • Practice Geometriae (Practical Geometry) – 7 chapters – Geometry Problems • Letter to Theodore (astrologer of Frederick II) – Resolution of two problems: algebraic and geometricalgebraic • Liber quadratorum (Book of square numbers) – 20 propositions about properties of square numbers
- 10. Legacy • S. Century, stands statue in Pisa. – Today, the historic cemetery Piazza dei Miracoli. • Character in the children's book "Crusade in Jeans" of Thea Beckman. • Math Concepts: – Pisano Period, search Fibonacci, ... • Asteroid 6765 Fibonacci • Art rock band The Fibonaccis