Geometry in Nature. Michele Hardwick Alison Gray Beth Denis Amy Perkins. Floral Symmetry Flower Type: Actinomorphic. ~Flowers with radial symmetry and parts arranged at one level; with definite number of parts and size. Anemone pulsatilla Pasque Flower.
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~Flowers with radial symmetry and parts arranged at one level; with definite number of parts and size
~Flowers are three dimensional with basically radial symmetry; parts many o reduced, and usually regular
Narcissus “Ice Follies”
Ice Follies Daffodil
~Flowers with parts spirally arranged at a simple level in a semispheric or hemispheric form; petals or tepals colored; parts numerous
Magnolia x kewensis “Wada’s Memory”
Wada's Memory Kew magnolia
~ Flowers with bilateral symmetry; parts usually reduced in number and irregular
Rose Garden in Washington D.C.
Smithsonian Castle in D.C. (pansies in foreground)
Butterfly Garden D.C. (grape hyacenths in arrangment)
Modern Sculpture Garden D.C.
Butterfly Garden D.C.
National Art Gallery D.C.
Smithsonian Castle D.C.
He worked on his own
He died around 1240.
Cross cut of a bee hive shows a mathematical pattern
Equillateral Triangle Area
Area of Square
Area of hexagon
Wax Cell Wall
1,2,3 Dimensional Planes
Golden Proportional Rectangle
Chamber size is 1.618x larger than the previous
Repeated Squares and Rectangles create the Logarithmic Spiral
Logarithmic Spiral &
Red= length of Segment
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
Whorled Pattern solution
Spiral PatternPatterns of Phyllotaxis:
Single phyllotaxis at each node
Observed in 3 spiral arrangements:
Tapered or Rounded
Tapered or Rounded