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January 20, 2003
FOR IMMEDIATE RELEASE

DO PLANTS KNOW MATH?

Innovative Exhibition and Web Site Offer Explanation for the Stunningly Intricate Spiral Patterns Found in Common Flowers and Vegetables

Editor's note: High-res images (300 dpi) of plant spirals from the exhibition are available. To select, see http://www.math.smith.edu/phyllo/expo and contact Laurie Fenlason with requests [lfenlason@smith.edu].

NORTHAMPTON, Mass.-For more than three centuries botanists and mathematicians have marveled at the complex and beautiful spiral patterns that form as plants develop. As they generate leaves around a stem, or seeds or flowers in a blossom, plants as diverse as broccoli, pinecones, artichokes and water lilies create intricate spirals that follow a well-known mathematical sequence of numbers.


"A prominent theme in science today, whether in biology, math or computer science, is the generation of complex patterns through simple rules," explains Smith College Associate Professor of Mathematics Chris Golé.


"Plants have been succeeding at this throughout their evolution, with great consistency and visual beauty," he adds.


To highlight the mathematical underpinnings of phyllotaxis, which refers to the arrangement of leaves or other botanical elements around a stem, Golé and his Smith colleague Pau Atela, associate professor of mathematics, teamed up with Michael Marcotrigiano and Madelaine Zadik of the Smith College Botanic Garden to produce an unusual exhibition. "Plant Spirals: Beauty You Can Count On" is an exhibition [Web site at www.math.smith.edu/phyllo/expo] accessible to a general audience, that depicts with rare beauty and clarity the geometry and biology of plant spiral formation.


Through a computer animation, scanning electron micrographs and large-scale panels featuring vivid color images and historical contexts, the viewer is guided from the natural phenomena to a recently developed simple mathematical model that reproduces the spiral patterns seen in plants. The model is based on a branch of mathematics known as dynamical systems, which includes chaos theory.


Golé notes that plant spirals often form according to the Fibonacci Sequence [1, 1, 2, 3, 5, 8, 13 ], in which each digit is the sum of the previous two. The spiral helixes visible in plants usually come in two sets winding in opposite directions. The numbers of spirals are most often two consecutive Fibonacci numbers. The flower of an English daisy, pictured in the exhibition, consists of 21 spirals clockwise and 34 counter-clockwise. A pinecone pictured has eight spirals in one direction and 13 in the other, eight and 13 being successors in the Fibonacci sequence.


To understand why Fibonacci numbers predominate in plant spirals, Golé and Atela started with the theories of 19th-century botanist Wilhelm Hofmeister, who observed that a plant's leaves emerge at the least crowded spot around a circular meristem or growing tip. They are then radially displaced from the center. The dynamical systems model developed by Atela, Golé and Scott Hotton of Miami University, based on the recent work of French physicists Stéphane Douady and Yves Couder, suggests that those simple geometric rules are enough to produce the spiral patterns with Golden Angle and Fibonnaci numbers that appear in nature.


"Whether plants 'know' mathematics or not," Atela remarks, "they are clearly programmed to follow a common set of developmental rules, which would suggest that these patterns confer evolutionary advantage."


"That the intricate patterns in nature, such as a leaf arrangement, leopard spots and butterfly wings, may all be regulated by simple and related mechanisms is an intriguing concept," Marcotrigiano adds.


"Plant Spirals" is the debut show in the Church Exhibition Gallery of the Botanic Garden's Lyman Plant House. The exhibition is free and open to the public and will be on view through March 31. The gallery is open daily from 8:30 a.m. to 4:30 p.m. and is wheelchair accessible. The greenhouses are currently closed for renovation. Areas beyond the Church Gallery will reopen to the public on March 1.


The entire campus of Smith College was originally planned and planted 100 years ago as a botanic garden and arboretum, designed by the landscape architecture firm of Frederick Law Olmsted. The Botanic Garden encompasses the 125 contiguous acres of the campus; the Lyman Conservatory, with 12,000 square feet under glass; and a variety of specialty gardens. The garden is open to the public and contains more than 7,000 labeled and mapped plants. Adjacent to the Lyman Conservatory are the rock garden, one of the oldest in America, and the systematics garden, in which plants are arranged by family. Other gardens around the campus include a Japanese viewing pavilion, a wildflower and woodland garden, an herb garden, a terraced rose garden and a formal knot and gazebo garden.


Smith College is consistently ranked among the nation's foremost liberal arts colleges. Enrolling 2,800 students from every state and 55 other countries, Smith is the largest undergraduate women's college in the country.


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