Skip to main content
Read page text
page 10
The Origins of Fractals Fractal geometry is an extension of classical geometry. It does not replace classical geometry, but enriches and deepens its powers. Using computers, fractal geometry can make precise models of physical structures - from sea-shells to galaxies. . ........... . . .. .. .. .. ........••... ... . .... . . . . .. . ... . .... . .........•.... . .. .. .. .. ................ =·=··==·= ......... ... . .. . . . . ... . .. ......... . .. .. . ......... ............. . -..... . ............. ... . .... . . . . .. . ... . .... . .....•.•••... . .. .. .. .. .......•••... fRA.c.TAL GEOME.TRY''f-_.--'~\"<--""-------' f5A NEW LANGUAGE We will now trace the historical development of this mathematical discipline and explore its descriptive powers in the natural world, then look at the applications in science and technology and at the implications of the discovery. 8
page 11
Classical Geometry r-· ···· Euclid of Alexandria (c. 300 Be) laid down the rules which were to define the subject of geometry for millennia to come. The shapes that Euclid studied - straight lines and circles - proved so successful in explaining the universe that scientists became blind to their limitations, denouncing patterns that did not fit in Euclid's scheme as "counterintuitive" and even "pathological" . .-..~~~~~~~ .... A steady undercurrent of ideas, starting in the 19th century with discoveries by Karl Weierstrass (1815-97), Georg Cantor (1845-1918} and Henri Poincare (1845-1912), led inexorably towards the creation of a whole new kind of geometry, with the power to describe aspects of the world inexpressible in the basic language of Euclid. 9

Page Text

View plaintext

The Origins of Fractals

Fractal geometry is an extension of classical geometry. It does not replace classical geometry, but enriches and deepens its powers. Using computers, fractal geometry can make precise models of physical structures - from sea-shells to galaxies.

. ........... . . .. .. .. .. ........••... ... . .... . . . . .. . ... . .... . .........•.... . .. .. .. .. ................ =·=··==·= ......... ... . .. . . . . ... . .. ......... . .. .. . ......... ............. . -..... . ............. ... . .... . . . . .. . ... . .... . .....•.•••... . .. .. .. .. .......•••...

fRA.c.TAL GEOME.TRY''f-_.--'~\"<--""-------'

f5A NEW LANGUAGE

We will now trace the historical development of this mathematical discipline and explore its descriptive powers in the natural world, then look at the applications in science and technology and at the implications of the discovery.

8

read next page

My Bookmarks

Buy this Book
Skip to main content