Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
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 Caltha introloba Marsh Marigold www.hort.net/gallery/view/ran/anepu http://www.anbg.gov.au/stamps/stamp.983.html Floral Symmetry Flower Type: Stereomorphic ~Flowers are three dimensional with basically radial symmetry; parts many o reduced, and usually regular Narcissus “Ice Follies” Aquilegia canadensis Ice Follies Daffodil Wild Columbine http://www.hort.net/gallery/view/amy/narif http://www.hort.net/gallery/view/ran/aquca Floral Symmetry Flower 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 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 Floral Symmetry Flower Type: Zygomorphic ~ Flowers with bilateral symmetry; parts usually reduced in number and irregular Cypripedium acaule Stemless lady'sslipper Pink lady'sslipper Moccasin flower http://www.hort.net/gallery/view/orc/cypac Pansy: Haplomorphic Azalea: Actinomorphic National Art Gallery D.C. Smithsonian Castle D.C. Hyacinth: Zygomorphic Biography of Leonardo Fibonacci Born in Pisa, Italy Around 1770 He worked on his own Mathematical compositions. He died around 1240. Fibonacci Numbers This is a brief introduction to Fibonacci and how his numbers are used in nature. 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. Fibonacci Top plant can be written as a 3/5 rotation The lower plant can be written as a 5/8 rotation Common trees with Fibonacci leaf arrangement This is a puzzle to show why Fibonacci numbers are the solution 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 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/ Why the Hexagonal Pattern? Cross cut of a bee hive shows a mathematical pattern Efficiency Equillateral Triangle Area 0.048 Area of Square 0.063 Area of hexagon 0.075 Strength of Hive Wax Cell Wall 0.05mm thick Golden Ratio Golden Ratio = 1.618 Golden Ratio Nautilus Shell 1,2,3 Dimensional Planes Golden Ratio Nautilus Shell First Dimension Linear Spiral Golden Ratio Nautilus Shell Second Dimension Golden Proportional Rectangle Golden Ratio Nautilus Shell Golden Ratio Nautilus Shell Third Dimension Chamber size is 1.618x larger than the previous Golden Ratio Human Embryo Logarithmic Spiral Golden Ratio Logarithmic Spiral Repeated Squares and Rectangles create the Logarithmic Spiral Golden Ratio Spider Web Logarithmic Spiral & Geometric sequence Red= length of Segment Green= radii Dots= create 85 degree spiral Golden Ratio Gazelle Golden Ratio Height Of Butterfly Is Divided By The Head Total Height Of Body Is Divided By The Border Between Thorax & Abdomen Butterflies Bilateral vs. Radial Symmetry Bilateral: single plane divides organism into two mirror images Radial: many planes divide organism into two mirror images Golden Ratio Starfish Tentacles have ratio of 1.618 Five-Fold Symmetry Five-Fold Symmetry Sand-Dollar & Starfish are structured similarly to the Icosahedron. Five-Fold Symmetry Design of Five-Fold Symmetry is very strong and flexible, allowing for the virus to be resilient to antibodies. Phyllotaxis: phyllos = leaf taxis = order http://ccins.camosun.b c.ca www.ams.org http://members.tri pod.com Patterns of Phyllotaxis: Whorled Pattern http://members.trip od.com Spiral Pattern http://members.tripo d.com Whorled Pattern: http://members.tripod.com 2 leaves at each node n=2 Whorled Pattern: http://members.tripod.com The number of leaves may vary in the same stem n = vary Spiral Pattern: Single phyllotaxis at each node http://members.tripod.com Phyllotaxis and the Fibonacci Series: Observed in 3 spiral arrangements: Vertically Horizontally Tapered or Rounded Phyllotaxis and the Fibonacci Series: Vertically http://members.tripod.com Phyllotaxis and the Fibonacci Series: Horizontally http://members.tripod.com Phyllotaxis and the Fibonacci Series: Tapered or Rounded www.ams.org http://ccins.camosun.bc.ca