Seeing Math Patterns in Nature
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The document discusses mathematical patterns found in nature, particularly the Fibonacci series and its prevalence in plant growth, such as sunflowers and pinecones. It includes interactive tools, project ideas, and resources for integrating these mathematical concepts into STEM education. The emphasis is on understanding how these patterns can be explored through various educational activities across different grade levels.
Seeing Math Patterns in Nature
- 1. Seeing Math Pa,erns in Nature Mary Van Dyke Green STEM Learning NSTA Conference Richmond, VA October 2014
- 3. • Pack n’ Grow • Pinecones Overview and Pineapples • Sunflowers and Daisies • Fibonacci and non-‐Fibonacci • Phyllotaxis and Branching • Squares and Spirals • Make Your Own Series • Resources
- 4. Pack n’ Grow Hexagonal Pack • Maximum strength with minimum materials Square Pack LaUces
- 5. Pinecones
- 7. h,p://goo.gl/56hbKU How Many Spirals?
- 8. Leonardo of Pisa – son of Bonacci Liber Abaci 1202 c. 1170 – c. 1250 Who Was Fibonacci?
- 9. 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, … F n = F n-‐1 + F n-‐2 where F 0 = 0 and F 1 = 1 0 + 1 = 1 1 + 1 = 2 1 + 2 = 3 2 + 3 = 5 3 + 5 = 8 5 + 8 = 13 8 + 13 = 21 Math – The Fibonacci Series
- 11. Pineapples
- 15. h,p://goo.gl/aUwknV How Many Spirals?
- 16. 90% of Plants Grow in Fibonacci Pa,ern
- 18. Sunflowers
- 19. 1000 seeds 1000 seeds 3000 seeds Efficiency -‐ Sunflower Spiral Pa,erns
- 20. • Wolfram Mathemajca -‐ Interacjve models • Vi Hart -‐ Doodling in Math: Spirals, Fibonacci, and Being a Plant , 3 parts on YouTube Pa,erns and Dynamic Models
- 21. 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/ Interacjve Tools On the Fundamental Theory of Phyllotaxis h,p://demonstrajons.wolfram.com/ OnTheFundamentalTheoremOfPhyllotaxis Fibonacci Tree h,p://demonstrajons.wolfram.com/ FibonacciTree/
- 22. Anomalies – Why?
- 23. Alan Turing’s Sunflowers Global Experiment 2012 Big Data – Cijzen Science
- 25. 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 Roast Sunflower Seeds
- 26. Easy Daisies
- 28. Fibonacci and non-‐Fibonacci Series
- 29. Leaf Arrangement -‐ Phyllotaxis
- 30. Branching
- 31. Branching
- 33. The Pineapple, The Core and The Gherkin…
- 35. Think of a number… Make Your Own Series
- 36. Think of a number… 2. Decide a second number 3. Add the two together Make Your Own Series
- 37. Think of a number… 2. Decide a second number 3. Add the two together 4. Determine the next 12 numbers in your sequence Make Your Own Series
- 38. 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 Make Your Own Series
- 39. 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? Make Your Own Series
- 40. • Fibonacci-‐style Take Homes 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
- 41. 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 NGSS – Hit the Standards
- 42. h,p://goo.gl/HvvLdO Credits and Resources Thank You!
- 43. Contact me: Mary Van Dyke Green STEM Learning maryvandyke4@gmail.com