Transmission of the Greek Classics on music ("De institutione musica libri quinque", unfinished) contributed to medieval education. "De arithmetica", begins with modular arithmetic, such as even and odd, evenly even, evenly odd, and oddly even. He then turns to unpredicted complexity by categorizing numbers and parts of numbers. His translations of Euclid on geometry and Ptolemy on astronomy, if they were completed, no longer survive. Boethius made Latin translations of Aristotle's "De interpretation" and "Categories" with commentaries. These were widely used during the Middle Ages. In the Western Provinces (what today is considered the Western Europe's heartland), the collapsing Roman empire lost many Greek manuscripts
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