Download presentation
Presentation is loading. Please wait.
Published bySolomon Wiggins Modified over 9 years ago
1
FIBONACCI SEQUENCE & THE GOLDEN RATIO Click this button to continue
2
Please only use your mouse to navigate this power point. To help you navigate, there will be buttons in the lower right hand corner. To go back a slide, click this button: To go forward, click this button: To go to the menu slide, click this button: Click this button to proceed to the next slide.
3
MENU SLIDE Fibonacci Sequence The Golden Ratio Application Quiz
4
FIBONACCI SEQUENCE
5
WHAT IS A SEQUENCE? A sequence is a set of numbers that are in a specific order An infinite sequence goes on forever, and is described by a certain rule (or rules) so that we can find any term of that sequence
6
FIBONACCI SEQUENCE The Fibonacci Sequence is the set of these numbers: 0,1,1,2,3,5,8,13,21,34…
7
FIBONACCI SEQUENCE
9
Simply put, this means that the nth term of the sequence is the sum of the two terms before it.
10
CHECKPOINT!!!!
11
WHAT IS THE 6TH TERM OF THE FIBONACCI SEQUENCE? a.66 b.22 c.55 d.1010
12
CONGRATULATIONS, YOU GOT THE RIGHT ANSWER!! Continue to the next section!
13
SORRY, TRY AGAIN….. Click on the return button to try the question again, or click the home button to navigate back to the information page
14
THE GOLDEN RATIO
17
THIS IS REALLY COMPLICATED!!!!!
18
THE GOLDEN RATIO
19
The Golden Ratio is also used in art, and artist Leonardo Da Vinci used the Golden Ratio (as well as Fibonacci Numbers) in his paintings.
20
THE GOLDEN RATIO Graphic obtained from http://leonardodavincihorseandrider.com/authenticity/leonardo-and-the-golden-spiral/http://leonardodavincihorseandrider.com/authenticity/leonardo-and-the-golden-spiral/ Paintings by Leonardo Da Vinci
21
THE GOLDEN RATIO
22
Simply stated, this means that, starting with the 4 th term of the Fibonacci Sequence, the ratio between two consecutive Fibonacci numbers (with the larger number in the numerator) is approximately the same as the golden ratio!
23
THE GOLDEN RATIO These numbers are Fibonacci numbers. As the Fibonacci numbers get bigger, the ratio between them gets closer to the golden ratio.
24
CHECKPOINT!!!!
25
WHAT PAINTER USED THE GOLDEN RATIO & FIBONACCI NUMBERS IN HIS PAINTINGS? a. Leonardo Da Vinci b. Leonardo DiCaprio c. Claude Monet d. Pierre-Auguste Renoir
26
CONGRATULATIONS, YOU GOT THE RIGHT ANSWER!! Continue to the next section!
27
SORRY, TRY AGAIN….. Click on the return button to try the question again, or click the home button to navigate back to the information page
28
APPLICATION
29
Now this is all fine and dandy, but what does it mean?
30
APPLICATION Amazingly, these numbers actually present themselves to us in nature!
31
APPLICATION
32
CHECKPOINT!!!
33
WHICH OF THE FOLLOWING WERE SHOWN IN THE VIDEO AS BEING OBJECTS FOUND IN NATURE THAT DISPLAY THE GOLDEN RATIO/FIBONACCI SEQUENCE? A. sunflower B. pinecone C. both A&B D. none of the above
34
CONGRATULATIONS, YOU GOT THE RIGHT ANSWER!! Continue to the next section!
35
SORRY, TRY AGAIN….. Click on the return button to try the question again, or click the home button to navigate back to the information page
36
FINAL QUIZ!!!!
37
WHICH OF THE FOLLOWING IS NOT A FIBONACCI NUMBER? A. 2 B. 21 C. 13 D. 4
38
CONGRATULATIONS, YOU GOT THE RIGHT ANSWER!! Continue to the next section!
39
SORRY, TRY AGAIN….. Click on the return button to try the question again, or click the home button to navigate back to the information page
40
WHICH GREEK LETTER IS USED TO REPRESENT THE GOLDEN RATIO?
41
CONGRATULATIONS, YOU GOT THE RIGHT ANSWER!! Continue to the next section!
42
SORRY, TRY AGAIN….. Click on the return button to try the question again, or click the home button to navigate back to the information page
43
FILL IN THE BLANKS: A SEQUENCE IS A SET OF _____THAT ARE IN A _____ORDER A. objects, random B. objects, specific C. numbers, random D. numbers, specific
44
CONGRATULATIONS, YOU GOT THE RIGHT ANSWER!! Continue to the next section!
45
SORRY, TRY AGAIN….. Click on the return button to try the question again, or click the home button to navigate back to the information page
46
IN THE GOLDEN RATIO, THE LETTER PHI CAN BE DEFINED AS
47
CONGRATULATIONS, YOU GOT THE RIGHT ANSWER!! Continue to the next section!
48
SORRY, TRY AGAIN….. Click on the return button to try the question again, or click the home button to navigate back to the information page
49
THE RELATIONSHIP BETWEEN THE GOLDEN RATIO AND THE FIBONACCI SEQUENCE IS THAT A. Starting with the 2nd term of the Fibonacci Sequence, the ratio between two consecutive Fibonacci numbers (with the larger number in the numerator) is approximately the same as the golden ratio.A. Starting with the 2nd term of the Fibonacci Sequence, the ratio between two consecutive Fibonacci numbers (with the larger number in the numerator) is approximately the same as the golden ratio. B. There is no relationship between the two C. Starting with the 4th term of the Fibonacci Sequence, the ratio between two consecutive Fibonacci numbers (with the larger number in the numerator) is approximately the same as the golden ratio.C. Starting with the 4th term of the Fibonacci Sequence, the ratio between two consecutive Fibonacci numbers (with the larger number in the numerator) is approximately the same as the golden ratio. D. The sum of two consecutive Fibonacci numbers divided by their average value equals the golden ratio
50
CONGRATULATIONS, YOU GOT THE RIGHT ANSWER!! Continue to the next section!
51
SORRY, TRY AGAIN….. Click on the return button to try the question again, or click the home button to navigate back to the information page
52
CONGRATULATIONS, YOU FINISHED THE POWERPOINT!
53
REFERENCES Sequences. (n.d.). Sequences. Retrieved October 23, 2013, from http://www.mathsisfun.com/algebra/sequences-series.html Fibonacci Number. (n.d.). Wolfram Alpha. Retrieved October 25, 2013, from http://mathworld.wolfram.com/FibonacciNumber.html Nature, The Golden Ratio, and Fibonacci too.... (n.d.). Nature, The Golden Ratio and Fibonacci Numbers. Retrieved November 9, 2013, from http://www.mathsisfun.com/numbers/nature- golden-ratio-fibonacci.html etareaestudios. (2010, March 11). Nature by Numbers. YouTube. Retrieved November 13, 2013, from http://www.youtube.com/watch?v=kkGeOWYOFoA Da Vinci Horse and Rider. (n.d.). Da Vinci Horse and Rider. Retrieved November 14, 2013, from http://leonardodavincihorseandrider.com/authenticity/leonardo-and-the-golden-spiral/
Similar presentations
© 2025 SlidePlayer.com. Inc.
All rights reserved.