Inventing the Circle: The Geometry of Nature

Nature has covered the earth with an endless variety of shapes, the most fascinating of which have always been the most basic and most fundamental: the symmetry of a perfectly formed orange, a five-pointed starfish, a honeycomb polygon, an oval egg. To biologists, each natural shape seems somehow unique, but to a mathematician, they are but a close representation of a true circle, or star, or oval, or hexagon.

For centuries, biology and mathematics have existed on separate planes – geometry defined precise formulas for creating a circle, square, star, or any other shape; yet in nature, there is no true shape because all natural shapes are inexact.

But why? If all life forms evolved from single cells, could not all shapes derive from a single geometric equation, a single mathematical formula? And if we could identify this superformula, wouldn’t it change how we visualize virtually everything in our environment? Wouldn’t it revolutionize computer graphics and engineering design?

In 1998, Belgian Botanist Johan Gielis happened upon precisely that equation – that Superformula. Since then, the sheer elegance and simplicity of his discovery has driven Gielis to ask himself again and again, "How could this be? What could be wrong with this idea? How could such a basic and important mathematical concept have gone undiscovered by so many and for so long – literally thousands of years?

Inventing the Circle: The geometry of Nature is a landmark scientific work that takes the reader on an essential journey, exploring the beauty of nature with new eyes through magnificent images, and discovering a fundamental, yet extraordinary concept that may well be the most important mathematical discovery of our time – the Superformula.