Seeing Math Patterns in Nature

Seeing Math Pa,erns in Nature

Mary Van Dyke Green STEM Learning

NSTA Conference Richmond, VA

October 2014

Play and Pa,erns

Overview

•  Pack n’ Grow •  Pinecones and Pineapples •  Sunflowers and Daisies •  Fibonacci and non-‐Fibonacci •  Phyllotaxis and Branching •  Squares and Spirals •  Make Your Own Series

•  Resources

Pack n’ Grow

Hexagonal Pack •  Maximum strength

with minimum materials

Square Pack LaUces

Pinecones

How Many Spirals?

How Many Spirals? h,p://goo.gl/56hbKU

Who Was Fibonacci?

Liber Abaci 1202 Leonardo of Pisa – son of Bonacci c. 1170 – c. 1250

Math – The Fibonacci Series

F n = F n-‐1 + F n-‐2 where F 0 = 0 and F 1 = 1

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, …

0 + 1 = 1 1 + 1 = 2 1 + 2 = 3 2 + 3 = 5 3 + 5 = 8 5 + 8 = 13 8 + 13 = 21

Pinecone Projects

Pineapples

How Many Spirals?

How Many Spirals? h,p://goo.gl/aUwknV

90% of Plants Grow in Fibonacci Pa,ern

Sunflowers at School

Sunflowers

Efficiency -‐ Sunflower Spiral Pa,erns 1000 seeds 1000 seeds 3000 seeds

Pa,erns and Dynamic Models

•  Wolfram Mathemajca -‐ Interacjve models

•  Vi Hart -‐ Doodling in Math: Spirals, Fibonacci, and Being a Plant , 3 parts on YouTube

Interacjve Tools

Wolfram Mathemajca Demonstrajons

Search “phyllotaxis” for about a dozen models h,p://demonstrajons.wolfram.com/search.html?query=phyllotaxis

Phyllotaxis Spirals in 3D

h,p://demonstrajons.wolfram.com/PhyllotaxisSpiralsIn3D/

On the Fundamental Theory of Phyllotaxis h,p://demonstrajons.wolfram.com/OnTheFundamentalTheoremOfPhyllotaxis

Fibonacci Tree

h,p://demonstrajons.wolfram.com/FibonacciTree/

Anomalies – Why?

Big Data – Cijzen Science

Alan Turing’s Sunflowers Global Experiment 2012

Sunflower Projects

Roast Sunflower Seeds

Roast In-‐Shell Sunflower Seeds Brush or pick seeds off seedhead Soak and Salt •  Cover unshelled seeds with salt water ( ¼

to ½ cup of salt per two quarts of water •  Soak overnight •  Drain off water, pat seeds dry (Or: Skip saljng and soaking and roast unsalted) Roast •  Preheat oven to 300 º F •  Spread seeds evenly on baking sheet •  Bake for 30 – 40 minutes •  Check and sjr occasionally •  Cool before eajng •  Store when cool in airjght container

Easy Daisies

Fibonacci and non-‐Fibonacci Series

Leaf Arrangement -‐ Phyllotaxis

Branching

Phyllotacjc Architecture 2012

The Pineapple, The Core and The Gherkin…

Squares and Spirals

Make Your Own Series

Think of a number…


Think of a number… 2.  Decide a second number 3.  Add the two together


Think of a number… 2.  Decide a second number 3.  Add the two together 4.  Determine the next 12 numbers in your sequence


Think of a number… 2.  Decide a second number 3.  Add the two together 4.  Determine the next 12 numbers in your sequence 5.  Name your series of numbers


Think of a number… 2.  Decide a second number 3.  Add the two together 4.  Determine the next 12 numbers in your sequence 5.  Name your series of numbers

6. What are the ra4os of each of your consecujve numbers divided by the next larger number in the sequence?

7. What are your conclusions about the ra4o of consecujve numbers in your sequence – as numbers get larger?

Take Homes

•  Fibonacci-‐style math sequences are prevalent in nature and design

•  90% of plant species grow in a Fibonacci way

•  Why? Efficiency for growth, leaf arrangement, branching, flower and seed arrangement

•  Correlajons with Fibonacci-‐style sequences include breeding pa,erns and sound/music

•  You can study these pa,erns at all grade levels with STEM integrated projects with art and design components

NGSS – Hit the Standards

Seeing Math Pa,erns in Nature Projects:

•  Ask and Define Problems

•  Plan and Carry Out Invesjgajons •  Analyze and Interpret Data •  Develop and Use Models

•  Construct Explanajons and Design Solujons

•  Engage in Evidence-‐based Argumentajon

•  Use Math and Computajonal Thinking

•  Obtain, Evaluate, and Communicate Informajon

Thank You!

h,p://goo.gl/HvvLdO Credits and Resources

Contact me: Mary Van Dyke

Green STEM Learning [email protected]

Seeing Math Patterns in Nature

Education

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