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Geometry in Nature

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Geometry in Nature

Michele Hardwick

Alison Gray

Beth Denis

Amy Perkins

~Flowers with radial symmetry and parts arranged at one level; with definite number of parts and size

Anemone pulsatilla

Pasque Flower

Caltha introloba

Marsh Marigold

www.hort.net/gallery/view/ran/anepu

http://www.anbg.gov.au/stamps/stamp.983.html

~Flowers are three dimensional with basically radial symmetry; parts many o reduced, and usually regular

Narcissus “Ice Follies”

Ice Follies Daffodil

Aquilegia canadensis

Wild Columbine

http://www.hort.net/gallery/view/amy/narif

http://www.hort.net/gallery/view/ran/aquca

~Flowers with parts spirally arranged at a simple level in a semispheric or hemispheric form; petals or tepals colored; parts numerous

Nymphaea spp

Water Lilly

Magnolia x kewensis “Wada’s Memory”

Wada's Memory Kew magnolia

www.hort.net/gallery/view/nym/nymph

www.hort.net/gallery/view/mag/magkewm

~ Flowers with bilateral symmetry; parts usually reduced in number and irregular

Cypripedium acaule

Stemless lady's-slipper

Pink lady's-slipper

Moccasin flower

http://www.hort.net/gallery/view/orc/cypac

Tulip : Haplomorphic

Rose Garden in Washington D.C.

Smithsonian Castle in D.C. (pansies in foreground)

My Backyard

Pansy: Haplomorphic

Butterfly Garden D.C. (grape hyacenths in arrangment)

Modern Sculpture Garden D.C.

Butterfly Garden D.C.

Azalea: Actinomorphic

National Art Gallery D.C.

Smithsonian Castle D.C.

Hyacinth: Zygomorphic

- Born in Pisa, Italy
Around 1770

He worked on his own

Mathematical compositions.

He died around 1240.

- This is a brief introduction to Fibonacci and how his numbers are used in nature.

- Many Plants show Fibonacci numbers in the arrangement of leaves around their stems.
- The Fibonacci numbers occur when counting both the number of times we go around the stem.

- Top plant can be written as a 3/5 rotation
- The lower plant can be written as a 5/8 rotation

- Fibonacci numbers:
- Fibonacci series is formed by adding the latest 2 numbers to get the next one, starting from 0 and 1
- 0 1
- 0+1=1 so the series is now
- 0 1 1
- 1+1=2 so the series continues

- This is just a snapshot of Fibonacci numbers and a very small introduction, if you would like more information on Fibonacci.Check out this website…
- www.mcs.surrey.ac.uk/personal/r.knott/

Cross cut of a bee hive shows a mathematical pattern

Equillateral Triangle Area

0.048

Area of Square

0.063

Area of hexagon

0.075

Wax Cell Wall

0.05mm thick

1,2,3 Dimensional Planes

First Dimension

Linear Spiral

Second Dimension

Golden Proportional Rectangle

Third Dimension

Chamber size is 1.618x larger than the previous

Logarithmic Spiral

Repeated Squares and Rectangles create the Logarithmic Spiral

Logarithmic Spiral &

Geometric sequence

Red= length of Segment

Green= radii

Dots= create 85 degree spiral

Height Of Butterfly Is Divided By The Head

Total Height Of Body Is Divided By The Border Between Thorax & Abdomen

Bilateral: single plane divides organism into two mirror images

Radial: many planes divide organism into two mirror images

Tentacles have ratio of 1.618

Sand-Dollar & Starfish are structured similarly to the Icosahedron.

Design of Five-Fold Symmetry is very strong and flexible, allowing for the virus to be resilient to antibodies.

phyllos = leaf

taxis = order

http://ccins.camosun.bc.ca

www.ams.org

http://members.tripod.com

Whorled Pattern

Spiral Pattern

http://members.tripod.com

http://members.tripod.com

- 2 leaves at each node
- n = 2

http://members.tripod.com

- The number of leaves may vary in the same stem
- n = vary

http://members.tripod.com

Single phyllotaxis at each node

http://members.tripod.com

Observed in 3 spiral arrangements:

Vertically

Horizontally

Tapered or Rounded

Vertically

http://members.tripod.com

Horizontally

http://members.tripod.com

Tapered or Rounded

www.ams.org

http://ccins.camosun.bc.ca