Non-Euclidean geometry that are both perpendicular to a third line: Euclidean geometry, named after the Greek mathematician Euclid, includes some of the oldest known mathematics, and geometries that deviated from this were not widely accepted as legitimate until the 19th century. The debate that eventually led to the discovery of the non-Euclidean geometries began almost as soon as Euclid's work "Elements" was written. In the "Elements", Euclid began with a limited number of assumptions (23 definitions, five common notions, and five postulates) and sought to prove all the other results (propositions) in the work. The most notorious of the postulates is often
The Fractal Geometry of Nature The Fractal Geometry of Nature The Fractal Geometry of Nature is a 1982 book by the Franco-American mathematician Benoît Mandelbrot. "The Fractal Geometry of Nature" is a revised and enlarged version of his 1977 book entitled "Fractals: Form, Chance and Dimension", which in turn was a revised, enlarged, and translated version of his 1975 French book, "Les Objects Fractals: Forme, Hasard et Dimension". "American Scientist" put the book in its one hundred books of 20th century science. As technology has improved mathematically accurate, computer-drawn fractals have become more detailed. Early drawings were low-resolution black and white; later drawings were higher