MATHEMATICS IN

NATUREPresented by:

Jay Gallagher & Laura Lieberman

Definition of Mathematics

“Mathematics is the science of patterns and order” (Van De Walle, 2004)

Study of PatternsThe National Council of Teachers of Mathematics suggests

that,

“The study of patterns should start at a very early age with rich and interesting experiences to facilitate a better understanding of the concepts related to functions and algebra that students will encounter later in upper middle school and throughout secondary school”

Recognizing

PATTERNS INNATURE

is a rich and interesting way for

elementary and middle school

students to study mathematics

Patterns in Nature

“The natural world contains an infinite variety of patterns. Patterns are found in plants and animals. All living things create patterns. Patterns are constantly being created by simple physical laws”

Flower Patterns

Flower Patterns

Patterns can be – Described in numbers

and words– Repeated– Compared

Can you describe and compare these patterns?

Are any patterns repeated?

Fibonacci Numbers

• Leonardo Fibonacci is famous for a pattern or series of numbers

• The series starts with 0 and 1• Every subsequent number in the series

is the sum of the previous two numbers

0,1,1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987,...

Fibonacci Numbers in Nature• “Flowers often have a Fibonacci number of petals, daisies

can have 34, 55 or even as many as 89 petals!”

• “The patterns of seeds in a sunflower appear to be spiraling outwards. There are a Fibonacci number of spirals. This pattern keeps the seeds uniformly packed no matter how large the seed head.”

• Pinecone Spirals: These two numbers, 8 and 13, are consecutive numbers in the Fibonacci series

Nature WalkLet’s take a nature walk to

examine more patterns in nature

Patterns in Objects

Patterns in Actions

• Ducks in a Row• Migration Routes of

Monarch Butterflies• Weather Patterns• Conservation and

the water cycle• Time

Patterns in Characteristics

Patterns in Sounds

• Cricket sounds

• Bird Sounds

• Waves

Studying patterns will lead to …

• Variables and Equations

• Variables as pattern generalizations

And other problems to solve…

Problems Using Patterns

The surface area of one cube is 6 units:

By understanding the relationship in patterns, problems that involve patterns, like the one below can be solved!

This is how one student solved the problem:

M.C. Escher• Escher uses patterns in his artwork

that connects mathematics and nature

.

Visit http://www.mcescher.com/

Recommended BooksLots & Lots of Zebra Stripes:

Patterns in Nature, by Stephen R. Swinburne

Nature’s Paintbrush: The Patterns and Colors Around You, by Susan Stockdale

Nature’s Patterns, by Joyce R. Becker

Right in Your Own Backyard: Nature Math (I Love Math), by Time Life Book Series

Plant Math, by Patricia Whitehouse

Images and References• http://www.indoorooss.qld.edu.au/04studgl/fibonacci/webs/nature.html• http://www.pvplc.org/photocontest/photo99/photos/twofriends.jpg• http://raysweb.net/patterns/index.html• http://www.tomtezak.com/• http://atschool.eduweb.co.uk/sirrobhitch.suffolk/patterns_nature/animals.htm• http://www.greeneclipse.net/thewavfiles/animal_e.html• http://www.blazingpaddles.on.ca/photography/tips/mud.htm• http://illuminations.nctm.org/imath/across/connections/pattern/index.html• http://www.intermath-uga.gatech.edu/topics/algebra/patterns/links.htm• http://www.nctm.org• http://www.mcescher.com• http://www.accessexcellence.org/AE/AEC/AEF/1995/welch_patterns.html• http://www.42explore.com/patterns.htm• http://www.uen.org/themepark/html/patterns/naturepatterns.html