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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/ | ||
− | [ | + | [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 |
− | [ ] 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/ | ||
− | [ ] The Ginko Pages Forum : Ginkgo Golden Number (n.d). Retrieved from | + | [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 | http://ginkgopages.blogspot.com/2005/12/ginkgo-golden-number.html | ||
− | [[Walther MA279 Fall2018 topic1|Back to | + | [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:
Videos: