geometry in nature michele hardwick alison gray beth denis amy perkins
TRANSCRIPT
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Geometry in Nature
Michele Hardwick
Alison Gray
Beth Denis
Amy Perkins
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Floral SymmetryFlower Type: Actinomorphic
~Flowers with radial symmetry and parts arranged at one level; with definite number of parts and size
www.hort.net/gallery/view/ran/anepu
Anemone pulsatilla
Pasque Flower Caltha introloba
Marsh Marigold
http://www.anbg.gov.au/stamps/stamp.983.html
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Floral SymmetryFlower Type: Stereomorphic
~Flowers are three dimensional with basically radial symmetry; parts many o reduced, and usually regular
http://www.hort.net/gallery/view/ran/aqucahttp://www.hort.net/gallery/view/amy/narif
Narcissus “Ice Follies”
Ice Follies Daffodil
Aquilegia canadensis
Wild Columbine
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Floral SymmetryFlower Type: Haplomorphic
~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
www.hort.net/gallery/view/nym/nymph
Magnolia x kewensis “Wada’s Memory”
Wada's Memory Kew magnolia
www.hort.net/gallery/view/mag/magkewm
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Floral SymmetryFlower Type: Zygomorphic
~ 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
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Tulip : HaplomorphicRose Garden in
Washington D.C.
My Backyard
Smithsonian
Castle in D.C.
(pansies in
foreground)
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Pansy: Haplomorphic
Butterfly Garden D.C.
Modern Sculpture Garden
D.C.
Butterfly Garden D.C. (grape
hyacenths in arrangment)
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Azalea: Actinomorphic
Hyacinth: Zygomorphic
National Art Gallery D.C.
Smithsonian Castle D.C.
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Biography of Leonardo Fibonacci Born in Pisa, Italy
Around 1770
He worked on his own
Mathematical compositions.
He died around 1240.
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Fibonacci Numbers This is a brief introduction to Fibonacci
and how his numbers are used in nature.
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For Example 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.
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Fibonacci Top plant can be
written as a 3/5 rotation
The lower plant can be written as a 5/8 rotation
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Common trees with Fibonacci leaf arrangement
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This is a puzzle to show why Fibonacci numbers are the solution
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Answer 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
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Fibonacci 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/
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Why the Hexagonal Pattern?
Cross cut of a bee hive shows a mathematical pattern
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Efficiency
Equillateral Triangle Area
0.048
Area of Square
0.063
Area of hexagon
0.075
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Strength of Hive
Wax Cell Wall
0.05mm thick
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Golden Ratio
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Golden Ratio = 1.618
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Golden Ratio Nautilus Shell
1,2,3 Dimensional Planes
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Golden Ratio Nautilus Shell
First Dimension
Linear Spiral
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Golden Ratio Nautilus Shell
Second Dimension
Golden Proportional Rectangle
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Golden Ratio Nautilus Shell
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Golden Ratio Nautilus Shell
Third Dimension
Chamber size is 1.618x larger than
the previous
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Golden Ratio Human Embryo
Logarithmic Spiral
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Golden Ratio Logarithmic Spiral
Repeated Squares and Rectangles create the Logarithmic Spiral
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Golden Ratio Spider Web
Red= length of Segment
Green= radii
Dots= create 85 degree spiral
Logarithmic Spiral &Geometric sequence
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Golden Ratio Gazelle
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Golden Ratio Butterflies
Height Of Butterfly Is Divided By The Head
Total Height Of Body Is Divided By The Border Between Thorax & Abdomen
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Bilateral vs. Radial Symmetry
Bilateral: single plane divides organism into two mirror images
Radial: many planes divide organism into two mirror images
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Golden Ratio Starfish
Tentacles have ratio of 1.618
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Five-Fold Symmetry
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Five-Fold Symmetry
Sand-Dollar & Starfish are structured similarly to the Icosahedron.
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Five-Fold Symmetry
Design of Five-Fold Symmetry is very strong and flexible, allowing for the virus to be resilient to antibodies.
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Phyllotaxis:phyllos = leaf
taxis = order
http://members.tripod.co
m
www.ams.orghttp://ccins.camosun.bc.ca
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Patterns of Phyllotaxis: Whorled Pattern Spiral Pattern
http://members.tripod.co
m
http://members.tripod.com
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Whorled Pattern:
2 leaves at each node n = 2
http://members.tripod.com
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Whorled Pattern:
The number of leaves may vary in the same stem
n = vary
http://members.tripod.com
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Spiral Pattern:
Single phyllotaxis at each node
http://members.tripod.com
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Phyllotaxis and the Fibonacci Series:
Observed in 3 spiral arrangements:
Vertically
Horizontally
Tapered or Rounded
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Phyllotaxis and the Fibonacci Series:
Vertically
http://members.tripod.com
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Phyllotaxis and the Fibonacci Series:
Horizontally
http://members.tripod.com
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Phyllotaxis and the Fibonacci Series:
Tapered or Rounded
www.ams.org http://ccins.camosun.bc.ca
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