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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

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 SymmetryFlower Type: Stereomorphic

~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

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

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 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

Rose Garden in Washington D.C.

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

My Backyard

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

Modern Sculpture Garden D.C.

Butterfly Garden D.C.

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

Answer solution

- 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 solution

- 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? solution

Cross cut of a bee hive shows a mathematical pattern

Golden Ratio solution

Golden Ratio = 1.618 solution

Golden Ratio solutionNautilus Shell

1,2,3 Dimensional Planes

Golden Ratio solutionNautilus Shell

Golden Ratio solutionHuman Embryo

Logarithmic Spiral

Golden Ratio solutionLogarithmic Spiral

Repeated Squares and Rectangles create the Logarithmic Spiral

Golden Ratio solutionSpider Web

Logarithmic Spiral &

Geometric sequence

Red= length of Segment

Green= radii

Dots= create 85 degree spiral

Golden Ratio solutionGazelle

Golden Ratio solutionButterflies

Height Of Butterfly Is Divided By The Head

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

Bilateral vs. Radial Symmetry solution

Bilateral: single plane divides organism into two mirror images

Radial: many planes divide organism into two mirror images

Golden Ratio solutionStarfish

Tentacles have ratio of 1.618

Five-Fold Symmetry solution

Five-Fold Symmetry solution

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

Five-Fold Symmetry solution

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

Phyllotaxis: solution

phyllos = leaf

taxis = order

http://ccins.camosun.bc.ca

www.ams.org

http://members.tripod.com

Whorled Pattern solution

Spiral Pattern

Patterns of Phyllotaxis:http://members.tripod.com

http://members.tripod.com

Whorled Pattern: solution

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

http://members.tripod.com

Phyllotaxis and the Fibonacci Series: solution

Observed in 3 spiral arrangements:

Vertically

Horizontally

Tapered or Rounded

Phyllotaxis and the Fibonacci Series: solution

Tapered or Rounded

www.ams.org

http://ccins.camosun.bc.ca

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