J. Gielis
De uitvinding van de Cirkel


ISBN:9789062157921
Aantal Pagina's:188 blz.
Prijs: €39,75
Uitgever: Maklu-Uitgevers nv
 

Over het boek:
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Een verzameling abstracte vormen, zoals een rechthoek, cirkel en vierkant, veelhoeken met rechte of gebogen zijden of met scherpe of afgeronde hoeken, bollen, kubussen en piramiden, en vormen uit de natuur, zoals bloemen en bladeren, vogeleieren, schelpen en zeesterren, zijn niet fundamenteel verschillend, maar worden door één en slechts één basisformule weergegeven. Bekende wiskundige vergelijkingen zoals de Stelling van Phytagoras en de vergelijkingen van kegelsneden kunnen worden beschouwd als speciale gevallen.

Onmogelijk?

Wel dit boek gaat over deze geniale en onvoorstelbaar eenvoudige formule. De Superformule biedt een originele en verfrissende kijk op de natuur en wetenschap. Ze werd al op diverse congressen en aan wetenschappelijke instituten wereldwijd voorgesteld en is nu in boekvorm gegoten. Het boek is speciaal geschreven voor een heel breed publiek, met meer dan driehonderd foto''s en meer dan vijftig duidelijke illustraties. Het richt zich tot iedereen die is geïnteresseerd in vormen, structuren en patronen in cultuur of natuur.

Uit www.nature.com:

Maths gets into shape
Is it a starfish? Is it an orchid? No, it''s Superformula.


2 April 2003
JOHN WHITFIELD

One simple equation can generate a vast diversity of natural shapes, a Belgian biologist has discovered. The Superformula, as its creator Johan Gielis has christened it, produces everything from simple triangles and pentagons, to stars, spirals and petals.

"When I found the formula, all these beautiful shapes came rolling out of my computer," says Gielis, at University of Nijmegen, Holland. "It seemed too good to be true - I spent two years thinking ''What did I do wrong?'' and ''How come no one else has discovered it?''" Having spoken to mathematicians, he reckons that he''s found something new.

The Superformula is a modified version of the equation for a circle1. Changing one term in the formula varies the proportions of the shape - moving from a round circle to a long and skinny ellipse. Changing another varies the axes of symmetry - shifting from a circle to triangle, square, pentagon and so on.

Varying both proportion and symmetry together produces shapes with any number of sides, regular and irregular. It can also produce three-dimensional structures, and non-biological shapes such as snowflakes and crystals. "It''s a new way of describing nature," says Gielis.

For centuries, scientists have sought to express natural forms - such as the spiral of a sheep''s horn, the branching of a tree, or a bee''s honeycomb - in mathematical terms.

"Describing form is one of the more intractable problems in biology," says botanist Karl Niklas of Cornell University in Ithaca, New York. Researchers have come up with many ways to describe leaves and shells, for example, but there is little unity: "Things have become cumbersome and idiosyncratic," he says.

The Superformula might provide a single, simple framework for analysing and comparing the shapes of life, believes Niklas. "This is an exciting development."

Gielis has patented his discovery, and is developing computer software based on it. Using one formula to produce shapes will make graphics programs much more efficient, he says. It might also be useful in pattern recognition.

What''s less clear is whether nature uses the formula to generate different shapes. "I''m not convinced this is significant, but it might turn out to be profound if it could be related to how things grow," says mathematician Ian Stewart of the University of Warwick, UK.

Other, more complicated, single equations can produce a similar diversity of shapes, says Stewart. He believes that the Superformula is more likely to provide a useful tool than an insight into how life actually works.

Gielis acknowledge