Before the Polish-born French-American mathematician Benoit Mandelbrot made his mark on the world, scientists liked to forget about the imperfections and irregularities of nature. The study of perfect squares, triangles and planes had dominated their field for over 2,000 years, since the Greek geometer Euclid wrote maths' oldest treatise "Elements" and provided us with the tools to measure these flawlessly smooth shapes. Early question about how to measure the real shape of a tree, a coastline or anything with a rough edge could not be tackled by Euclidean geometry and had therefore been ignored. But Mandelbrot changed all this when he invented fractal geometry, which enables us to measure roughness. "My whole career has been one long, ardent pursuit of the concept of roughness", he says. "The roughness of clusters in the physics of disorder, of turbulent flows, of exotic noises, of chaotic dynamical systems, of the distribution of galaxies, of coastlines, of stock-price charts and of mathematical constructions."
It is clear from the passage that, before Mandelbrot's concepts attracted the attention of the scientific world, ______.
mathematics followed the lead of Euclid and concentrated on regular shapes
everyone felt that Euclidean geometry was inadequate
scientists relied on Euclidean geometry to measure trees and exotic noises
Mandelbrot almost lost confidence in the concept of roughness
Mandelbrot was careful to limit the scope of his studies into roughness
It is clear from the passage that Mandelbrot _____.
only began to work on the concept of roughness at a later stage in his career
finds the concept of roughness immensely exciting, and apparent in widely different areas
worked on the concept of roughness because he wanted to prove that Euclid's theories were contradictory
didn't discover fractal geometry but worked to extend its uses
has still to convince the scientific world of the value of fractal geometry
One point made in the passage is that Euclidean geometry _____.
has led to a better appreciation of the irregularities in nature
has had to be modified in the light of new discoveries
has been shown to be invalid
is not universally applicable
doesn't deserve the respect it has enjoyed for 2,000 years
According to the passage, fractal geometry _____.
makes possible the measurement of anything with a rough edge
is actually, as regards method, very similar to Euclidean geometry
is merely an extension of Euclidean geometry
is well on the way to replacing Euclidean geometry entirely
is just one of several remarkable innovations propounded by Mandelbrot