The Fibonacci Sequence. Leonardo Fibonacci (1170 – 1250) First from the West, but lots of evidence...

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The Fibonacci Sequence

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Transcript of The Fibonacci Sequence. Leonardo Fibonacci (1170 – 1250) First from the West, but lots of evidence...

Page 1: The Fibonacci Sequence. Leonardo Fibonacci (1170 – 1250) First from the West, but lots of evidence from before his time.

The Fibonacci Sequence

Page 2: The Fibonacci Sequence. Leonardo Fibonacci (1170 – 1250) First from the West, but lots of evidence from before his time.

The Fibonacci Sequence

Leonardo Fibonacci(1170 – 1250)

First from the West, but lots of evidence from before his time

Page 3: The Fibonacci Sequence. Leonardo Fibonacci (1170 – 1250) First from the West, but lots of evidence from before his time.

The Fibonacci Sequence

1, 1, 2, 3, 5, 8, 13, …

The current term is found by adding the previous two

Page 4: The Fibonacci Sequence. Leonardo Fibonacci (1170 – 1250) First from the West, but lots of evidence from before his time.

The Fibonacci Sequence

Originated from a question he had about rabbit population

Page 5: The Fibonacci Sequence. Leonardo Fibonacci (1170 – 1250) First from the West, but lots of evidence from before his time.

The Fibonacci Sequence

What’s special about it?

If we continue the sequence… and take the limit of the ratio to infinity…

Page 6: The Fibonacci Sequence. Leonardo Fibonacci (1170 – 1250) First from the West, but lots of evidence from before his time.

The Fibonacci Sequence

We find a ratio that is approximately 1.61803399

This is known as the GOLDEN Ratio

Page 7: The Fibonacci Sequence. Leonardo Fibonacci (1170 – 1250) First from the West, but lots of evidence from before his time.

The Fibonacci Sequence

This ratio can be found in nature…

Page 8: The Fibonacci Sequence. Leonardo Fibonacci (1170 – 1250) First from the West, but lots of evidence from before his time.
Page 9: The Fibonacci Sequence. Leonardo Fibonacci (1170 – 1250) First from the West, but lots of evidence from before his time.
Page 10: The Fibonacci Sequence. Leonardo Fibonacci (1170 – 1250) First from the West, but lots of evidence from before his time.

The Golden Rectangle

Page 11: The Fibonacci Sequence. Leonardo Fibonacci (1170 – 1250) First from the West, but lots of evidence from before his time.
Page 12: The Fibonacci Sequence. Leonardo Fibonacci (1170 – 1250) First from the West, but lots of evidence from before his time.
Page 13: The Fibonacci Sequence. Leonardo Fibonacci (1170 – 1250) First from the West, but lots of evidence from before his time.

The Fibonacci Sequence

This ratio can be found in art…

Page 14: The Fibonacci Sequence. Leonardo Fibonacci (1170 – 1250) First from the West, but lots of evidence from before his time.
Page 15: The Fibonacci Sequence. Leonardo Fibonacci (1170 – 1250) First from the West, but lots of evidence from before his time.
Page 16: The Fibonacci Sequence. Leonardo Fibonacci (1170 – 1250) First from the West, but lots of evidence from before his time.
Page 17: The Fibonacci Sequence. Leonardo Fibonacci (1170 – 1250) First from the West, but lots of evidence from before his time.

And many other places…


GENERAL ARTICLE ATaste of Functional Programming – 2madhavan/courses/pl2009/... · fibonacci :: Int -> Int fibonacci 0 = 1 fibonacci 1 = 1 fibonacci n = fibonacci (n-1) + fibonacci

GENERAL ARTICLE ATaste of Functional Programming – 2madhavan/courses/pl2009/... · fibonacci :: Int -> Int fibonacci 0 = 1 fibonacci 1 = 1 fibonacci n = fibonacci (n-1) + fibonacci

Leonardo Fibonacci nació en Pisa, Italia, en 1170. Cuando su padre trabajaba en la costa norteafricana, Fibonacci estuvo en contacto con la cultura árabe.

Leonardo Fibonacci nació en Pisa, Italia, en 1170. Cuando su padre trabajaba en la costa norteafricana, Fibonacci estuvo en contacto con la cultura árabe.

cs2110Fibonacci - Cornell University · FIBONACCI NUMBERS GOLDEN RATIO, RECURRENCES Lecture 26 CS2110 –Spring 2019 Fibonacci (Leonardo Pisano) 1170-1240? Statue in Pisa Italy Announcements

cs2110Fibonacci - Cornell University · FIBONACCI NUMBERS GOLDEN RATIO, RECURRENCES Lecture 26 CS2110 –Spring 2019 Fibonacci (Leonardo Pisano) 1170-1240? Statue in Pisa Italy Announcements

DOCUMENT RESUME Harnett, T. Some Ideas About Number … · suggested by the thirteenth century mathematician Leonardo of Pisa (about 1170-1250), who is called Fibonacci since he was

DOCUMENT RESUME Harnett, T. Some Ideas About Number … · suggested by the thirteenth century mathematician Leonardo of Pisa (about 1170-1250), who is called Fibonacci since he was

PowerPoint Presentation Fibonacci...1170-1250 Leonardo Da Pisa / Leonardo Bonacci 0 1 1 2 3 5 8 13 21 34 55 … Dari deret angka ini, ternyata tersembunyi rasio Tuhan. Rasio Tuhan

PowerPoint Presentation Fibonacci...1170-1250 Leonardo Da Pisa / Leonardo Bonacci 0 1 1 2 3 5 8 13 21 34 55 … Dari deret angka ini, ternyata tersembunyi rasio Tuhan. Rasio Tuhan

Keplers Wege zum Goldenen Schnitt Beschreibung GERMAN · PDF filevorhergehenden ist, nennt man heute Fibonacci-Reihe (nach dem Mathematiker Leonardo Fibonacci aus Pisa, 1170 – ca.

Keplers Wege zum Goldenen Schnitt Beschreibung GERMAN · PDF filevorhergehenden ist, nennt man heute Fibonacci-Reihe (nach dem Mathematiker Leonardo Fibonacci aus Pisa, 1170 – ca.

cesargallegos.files.wordpress.com · pág.111 Capítulo 2 Números Reales Fibonacci, matemático italiano (1170 - 1250) Introducción La idea de número aparece en la historia del

cesargallegos.files.wordpress.com · pág.111 Capítulo 2 Números Reales Fibonacci, matemático italiano (1170 - 1250) Introducción La idea de número aparece en la historia del

L PISA , also known as FIBONACCI (1170–1250)...The term “FIBONACCI sequence” for the sequence 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, … is due to the French mathematician EDOUARD

L PISA , also known as FIBONACCI (1170–1250)...The term “FIBONACCI sequence” for the sequence 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, … is due to the French mathematician EDOUARD

漫談 Fibonacci sequence 唐學明 2013.12.13.. Introduction Leonardo Pisano Bogollo, (c. 1170 – c. 1250) also known as Leonardo of Pisa, Leonardo Pisano, Leonardo.

漫談 Fibonacci sequence 唐學明 2013.12.13.. Introduction Leonardo Pisano Bogollo, (c. 1170 – c. 1250) also known as Leonardo of Pisa, Leonardo Pisano, Leonardo.

Leonardo de Pisa Fibonaccí (1170-1250 )

Leonardo de Pisa Fibonaccí (1170-1250 )

Por Miguel Ángel Díaz. Fibonacci o Leonardo de Pisa Nacido en Pisa (Italia) en 1170.

Por Miguel Ángel Díaz. Fibonacci o Leonardo de Pisa Nacido en Pisa (Italia) en 1170.

Page 1 Dt.17-12-2013 TPBO - B Guruva Reddy (Div.No.Xl) Hording No. B Rate per Unit 2550 1250 1250 2550 2550 1250 1250 1250 1250 1250 1250 1250 2550 Demand Encroach ment Tax private

Page 1 Dt.17-12-2013 TPBO - B Guruva Reddy (Div.No.Xl) Hording No. B Rate per Unit 2550 1250 1250 2550 2550 1250 1250 1250 1250 1250 1250 1250 2550 Demand Encroach ment Tax private

TARTALOM · 2016. 6. 14. · Felfedezés 1202 : Leonardo Fibonacci (1170?–1250?) Főműve: Liber Abacci Fibonacci sorozata rekurencia képlettel: f1 = f2 =1, fn = fn – 1 + f n

TARTALOM · 2016. 6. 14. · Felfedezés 1202 : Leonardo Fibonacci (1170?–1250?) Főműve: Liber Abacci Fibonacci sorozata rekurencia képlettel: f1 = f2 =1, fn = fn – 1 + f n

UNDERSTANDING N A T U R E - theunsecretsociety.net · 2 Understanding Nature ... the next chapter discusses rhythms in numbers. ... as the Italian scientist Leonardo Fibonacci (1170

UNDERSTANDING N A T U R E - theunsecretsociety.net · 2 Understanding Nature ... the next chapter discusses rhythms in numbers. ... as the Italian scientist Leonardo Fibonacci (1170

cs2110Fibonacci - Cornell University · 4/29/18 1 FIBONACCI NUMBERS GOLDEN RATIO, RECURRENCES Lecture 25 CS2110 –Spring 2018 Fibonacci (Leonardo Pisano) 1170-1240? Statue in Pisa

cs2110Fibonacci - Cornell University · 4/29/18 1 FIBONACCI NUMBERS GOLDEN RATIO, RECURRENCES Lecture 25 CS2110 –Spring 2018 Fibonacci (Leonardo Pisano) 1170-1240? Statue in Pisa

Type 1170 1400 1411 - MOSER ConsumerType 1170 / 1400 / 1411 Gebrauchsanweisung Haarschneidemaschine Typ 1170 / 1400 / 1411 de Operating instructions Hair clipper type 1170 / 1400

Type 1170 1400 1411 - MOSER ConsumerType 1170 / 1400 / 1411 Gebrauchsanweisung Haarschneidemaschine Typ 1170 / 1400 / 1411 de Operating instructions Hair clipper type 1170 / 1400

LA MAGIA DEL LONTANO EST INCONTRA IL GENIO DEL VICINO OVEST Leonardo Pisano detto Fibonacci (Pisa,settembre 1170 – Pisa, 1240 ) fu un matematico italiano.

LA MAGIA DEL LONTANO EST INCONTRA IL GENIO DEL VICINO OVEST Leonardo Pisano detto Fibonacci (Pisa,settembre 1170 – Pisa, 1240 ) fu un matematico italiano.

Brother PT-1100, 1130, 1170, 1180, 11q, 1160, 1250, St1150 Service Manual

Brother PT-1100, 1130, 1170, 1180, 11q, 1160, 1250, St1150 Service Manual

FIBONACCI NUMBERS GOLDEN RATIO, … NUMBERS GOLDEN RATIO, RECURRENCES Lecture 23 CS2110 – Fall 2016 Fibonacci (Leonardo Pisano) 1170-1240? Statue in Pisa Italy

FIBONACCI NUMBERS GOLDEN RATIO, … NUMBERS GOLDEN RATIO, RECURRENCES Lecture 23 CS2110 – Fall 2016 Fibonacci (Leonardo Pisano) 1170-1240? Statue in Pisa Italy

L PISA , also known as FIBONACCI (1170–1250)

L PISA , also known as FIBONACCI (1170–1250)