math in nature. fibonacci sequence in nature the sequence begins with numbers 0, 1, 1, 2, 3, 5, 8,...

28

Math in Nature

Upload: derrick-blankenship

Post on 14-Jan-2016

218 views

Category:

Documents

2 download

Report

Download

Tags:

Embed Size (px):

TRANSCRIPT

Page 1: Math in Nature. Fibonacci Sequence in Nature The sequence begins with numbers 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144 and continues

Math in Nature

Page 2: Math in Nature. Fibonacci Sequence in Nature The sequence begins with numbers 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144 and continues

Page 3: Math in Nature. Fibonacci Sequence in Nature The sequence begins with numbers 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144 and continues

Page 4: Math in Nature. Fibonacci Sequence in Nature The sequence begins with numbers 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144 and continues

Page 5: Math in Nature. Fibonacci Sequence in Nature The sequence begins with numbers 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144 and continues

Fibonacci Sequence in NatureThe sequence begins with numbers 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144 and continues.

Page 6: Math in Nature. Fibonacci Sequence in Nature The sequence begins with numbers 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144 and continues

Fibonacci Sequence in NatureThe sequence begins with numbers 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144 and continues.

By observing the spiral arrangement on a pine cone or pineapple we notice that similar to the seed spirals on sunflowers, the numbers of spirals in each direction are consecutive Fibonacci numbers. By looking at the structure of the seed scales in a mature female pine cone you can observe that there are 8 spirals going in one direction and 13 going in the other direction.

http://wikis.swarthmore.edu/math3S08/index.php/Image:Pinecone3.gif

http://wikis.swarthmore.edu/math3S08/index.php/Image:Pinecone2.gif

Page 7: Math in Nature. Fibonacci Sequence in Nature The sequence begins with numbers 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144 and continues

Naturally occurring fractalshttp://www.miqel.com/fractals_math_patterns/visual-math-natural-fractals.html

http://www.miqel.com/fractals_math_patterns/visual-math-natural-fractals.html

Page 8: Math in Nature. Fibonacci Sequence in Nature The sequence begins with numbers 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144 and continues

Page 9: Math in Nature. Fibonacci Sequence in Nature The sequence begins with numbers 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144 and continues

Page 10: Math in Nature. Fibonacci Sequence in Nature The sequence begins with numbers 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144 and continues

Page 11: Math in Nature. Fibonacci Sequence in Nature The sequence begins with numbers 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144 and continues

Nature loves the hexagon…

Page 12: Math in Nature. Fibonacci Sequence in Nature The sequence begins with numbers 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144 and continues

Nature loves the hexagon…

Page 13: Math in Nature. Fibonacci Sequence in Nature The sequence begins with numbers 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144 and continues

Nature loves the hexagon…

Page 14: Math in Nature. Fibonacci Sequence in Nature The sequence begins with numbers 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144 and continues

Page 15: Math in Nature. Fibonacci Sequence in Nature The sequence begins with numbers 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144 and continues

Page 16: Math in Nature. Fibonacci Sequence in Nature The sequence begins with numbers 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144 and continues

Nature loves the hexagon…

Page 17: Math in Nature. Fibonacci Sequence in Nature The sequence begins with numbers 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144 and continues

Math in Art

Page 18: Math in Nature. Fibonacci Sequence in Nature The sequence begins with numbers 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144 and continues

Page 19: Math in Nature. Fibonacci Sequence in Nature The sequence begins with numbers 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144 and continues

Page 20: Math in Nature. Fibonacci Sequence in Nature The sequence begins with numbers 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144 and continues

Page 21: Math in Nature. Fibonacci Sequence in Nature The sequence begins with numbers 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144 and continues

Page 22: Math in Nature. Fibonacci Sequence in Nature The sequence begins with numbers 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144 and continues

Page 23: Math in Nature. Fibonacci Sequence in Nature The sequence begins with numbers 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144 and continues

Page 24: Math in Nature. Fibonacci Sequence in Nature The sequence begins with numbers 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144 and continues

Page 25: Math in Nature. Fibonacci Sequence in Nature The sequence begins with numbers 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144 and continues

Page 26: Math in Nature. Fibonacci Sequence in Nature The sequence begins with numbers 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144 and continues

Page 27: Math in Nature. Fibonacci Sequence in Nature The sequence begins with numbers 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144 and continues

Page 28: Math in Nature. Fibonacci Sequence in Nature The sequence begins with numbers 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144 and continues

Maths in nature fibonacci

The Fibonacci Sequence Under Various Moduliwebspace.ship.edu/msrenault/fibonacci/FibThesis.pdf · The Fibonacci Sequence Under Various Moduli Marc Renault May, ... Chapter 1 Leonardo

Reverse Fibonacci Sequence

Fibonacci sequence

Nspire--iPad App--Fibonacci Sequence

On the origin of the Fibonacci Sequence

FIBONACCI SEQUENCE AND ORDERLINESS AS OBSERVED IN …

Fibonacci Sequence Task 1: Introduction to Fibonacci numbers 13.07.2020 - Year 6... · Fibonacci ¶s work on this problem led him to this sequence of numbers: « Can you figure out

Fibonacci Sequence and Related Numbers

541 Interactive ppt Fibonacci Sequence

FIBONACCI NUMBERS in nature - MSC2010msc2010.org/MSC2010-CD/Printable Posters/fibonacci-poster-sm.pdf · FIBONACCI NUMBERS in nature Fibonacci numbers: After the first two 1’s in

Fun with the Fibonacci Sequence

5.5 The Fibonacci Sequence and the Golden Ratio The Fibonacci Sequence is the sequence … · 2015. 9. 3. · 5.5 The Fibonacci Sequence and the Golden Ratio The Fibonacci Sequence

THE FIBONACCI SEQUENCE Chapter 13: Fibonacci Numbers and ...hans.math.upenn.edu/~rimmer/math170/notes/unit7fibfrombook.pdf · Chapter 13: Fibonacci Numbers and the ... words, the

Fibonacci Sequence A Mathematics Webquest [email protected]

Sequence Spaces De ned by Fibonacci Matrix

Fibonacci Sequence A Mathematics Webquest

THE FIBONACCI SEQUENCE Chapter 13: Fibonacci …rimmer/math170/notes/... · The Fibonacci sequence is infinite, and except for the first two 1s, each number in the sequence is the

Fibonacci sequence and golden ratio

The Fibonacci Sequence in Nature BY SEHYOGUE AULAKH

Fibonacci Sequence, Golden Ratio and Wythoff's Game

INVESTIGATION OF APPLICATIONS OF FIBONACCI SEQUENCE …

THE FIBONACCI SEQUENCE MODULO N

Representations of Palindromic, Prime, and Fibonacci Sequence … · 2015-07-08 · Representations of Palindromic, Prime, and Fibonacci Sequence Patterns Inder J. Taneja1 Abstract

Fibonacci Sequenceslega/250/Spring09/Lecture_Notes/25… · Fibonacci sequence, though not always successive ones. More examples of the Fibonacci sequence used in nature are the patterns

-Fibonacci Sequence and The (-;olden Ratio...-Fibonacci Sequence and The (-;olden Ratio Pamela Cohen and Cheryl Zerafa Fibonacci, or more correctly Leonardo da Pisa, was born in Pisa

Fibonacci Numbers and Nature

The Golden Section and the Fibonacci Sequence - 1

Fibonacci Sequence - University of Torontowordpress.oise.utoronto.ca/robertson/files/2016/07/Fibonacci_Sequ… · a sequence that is found in nature and has been translated into art

Believe It or Not : The Fibonacci Sequence Printing ... It or Not The Fibonacci Sequence_0.pdfTHE GOLDEN RATIO EXAMPLES IN REAL LIFE The Fibonacci sequence is a mathematical series

The Fibonacci Sequence in Nature

The Sequence of Fibonacci Numbers and How They Relate to Nature November 30, 2004 Allison Trask

Geometric Representation of Fibonacci Sequence

Sequences - Lloyd Hutchison Classes 2016lloydhutchison.weebly.com/uploads/5/6/6/0/56603395/mq11_general...Exploring the Fibonacci sequence with CAS The Fibonacci sequence is a sequence

Vortex Mathematics & The Fibonacci Spiral: Unlocking The Fibonacci Sequence