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[2] Phyllotaxis. (n.d.). Retrieved from http://www.science.smith.edu/phyllo/
 
[2] Phyllotaxis. (n.d.). Retrieved from http://www.science.smith.edu/phyllo/
  
[n] The Fibonacci numbers  (n.d.). Retrieved from http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/fibBio.html
+
[3] The Fibonacci numbers  (n.d.). Retrieved from http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/fibBio.html
  
[n + 1] Honeybees and Family Trees (n.d.). Retrieved from http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/fibnat.html
+
[4] Honeybees and Family Trees (n.d.). Retrieved from http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/fibnat.html
  
[n + 2] Fibonacci’s rabbits  (n.d.). Retrieved from http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/fibnat.html
+
[5] Fibonacci’s rabbits  (n.d.). Retrieved from http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/fibnat.html
  
[ ] Flowers, Fruits, and Leaves (n.d.). Retrieved from
+
[6] Flowers, Fruits, and Leaves (n.d.). Retrieved from
 
http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/fibnat.html
 
http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/fibnat.html
  
[ ] Seed Heads (n.d.). Retrieved from
+
[7] Seed Heads (n.d.). Retrieved from
 
http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/fibnat.html
 
http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/fibnat.html
  
[ ] Fuchsia (n.d.). Retrieved from
+
[8] Fuchsia (n.d.). Retrieved from
 
https://plants.sc.egov.usda.gov/core/profile?symbol=FUCHS&photoID=fuchs_007_ahp.tif
 
https://plants.sc.egov.usda.gov/core/profile?symbol=FUCHS&photoID=fuchs_007_ahp.tif
  
[ ] Michaelmas Daisy (n.d.). Retrieved from
+
[9] Michaelmas Daisy (n.d.). Retrieved from
 
https://www.livinginseason.com/naturalworld/michaelmas-daisy/
 
https://www.livinginseason.com/naturalworld/michaelmas-daisy/
  
[ ] Binet's Formula (n.d). Retrieved from
+
[10] Binet's Formula (n.d). Retrieved from
 
https://artofproblemsolving.com/wiki/index.php?title=Binet%27s_Formula
 
https://artofproblemsolving.com/wiki/index.php?title=Binet%27s_Formula
  
[ ] The Ginko Pages Forum : Ginkgo Golden Number (n.d). Retrieved from  
+
[11] The Ginko Pages Forum : Ginkgo Golden Number (n.d). Retrieved from  
 
http://ginkgopages.blogspot.com/2005/12/ginkgo-golden-number.html
 
http://ginkgopages.blogspot.com/2005/12/ginkgo-golden-number.html
  
[[Walther MA279 Fall2018 topic1|Back to Walther MA279 Fall2018 topic1]]
+
[12] The Golden Angle (n.d). Retrieved from
[[Category:MA279Fall2018Walther]]
+
http://gofiguremath.org/natures-favorite-math/the-golden-ratio/the-golden-angle/
 +
 
 +
[13] Generating Functions and the Fibonacci Numbers (n.d). Retrieved from
 +
https://austinrochford.com/posts/2013-11-01-generating-functions-and-fibonacci-numbers.html
 +
 
 +
[14] Golden Ratio in Phyllotaxis (n.d). Retrieved from http://curiosamathematica.tumblr.com/post/114294953296/golden-ratio-in-phyllotaxis
 +
 
 +
==Other Links to Explore:==
 +
 
 +
Websites:
 +
 
 +
[http://mathworld.wolfram.com/FibonacciNumber.html On the Fibonacci Series]
 +
 
 +
[http://mathworld.wolfram.com/GoldenRatio.html On the Golden Ratio]
 +
 
 +
Videos:
 +
 
 +
[https://www.youtube.com/watch?v=sj8Sg8qnjOg On the Golden Ratio]
 +
 
 +
[https://www.youtube.com/watch?v=dTWKKvlZB08 On the Golden Ratio and its Irrationality]
 +
 
 +
[[Walther MA279 Fall2018 topic1|Back to Home]]
 +
<br><br>[[Category:MA279Fall2018Walther]]

Latest revision as of 22:36, 2 December 2018

References

[1] Košmrlj, A. (n.d.). Spirals and Phyllotaxis. Lecture. https://www.princeton.edu/~akosmrlj/MAE545_S2017/lecture12_slides.pdf

[2] Phyllotaxis. (n.d.). Retrieved from http://www.science.smith.edu/phyllo/

[3] The Fibonacci numbers (n.d.). Retrieved from http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/fibBio.html

[4] Honeybees and Family Trees (n.d.). Retrieved from http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/fibnat.html

[5] Fibonacci’s rabbits (n.d.). Retrieved from http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/fibnat.html

[6] Flowers, Fruits, and Leaves (n.d.). Retrieved from http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/fibnat.html

[7] Seed Heads (n.d.). Retrieved from http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/fibnat.html

[8] Fuchsia (n.d.). Retrieved from https://plants.sc.egov.usda.gov/core/profile?symbol=FUCHS&photoID=fuchs_007_ahp.tif

[9] Michaelmas Daisy (n.d.). Retrieved from https://www.livinginseason.com/naturalworld/michaelmas-daisy/

[10] Binet's Formula (n.d). Retrieved from https://artofproblemsolving.com/wiki/index.php?title=Binet%27s_Formula

[11] The Ginko Pages Forum : Ginkgo Golden Number (n.d). Retrieved from http://ginkgopages.blogspot.com/2005/12/ginkgo-golden-number.html

[12] The Golden Angle (n.d). Retrieved from http://gofiguremath.org/natures-favorite-math/the-golden-ratio/the-golden-angle/

[13] Generating Functions and the Fibonacci Numbers (n.d). Retrieved from https://austinrochford.com/posts/2013-11-01-generating-functions-and-fibonacci-numbers.html

[14] Golden Ratio in Phyllotaxis (n.d). Retrieved from http://curiosamathematica.tumblr.com/post/114294953296/golden-ratio-in-phyllotaxis

Other Links to Explore:

Websites:

On the Fibonacci Series

On the Golden Ratio

Videos:

On the Golden Ratio

On the Golden Ratio and its Irrationality

Back to Home

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