Ron Eglash Home Page. Architecture Unit 6. The PLATONIC SOLIDS "Let no one destitute of geometry enter my doors.
" Plato (c. 427 - 347 B.C.E.) Slide 6-1: RAPHAEL: School of Athens American Catalgo, p. 126, #21061. Fresco, Vatican, Stanza della Signurata, the Pope's Private Library We now move forward in time about 150 years, still staying in Greece, from Pythagoras to Plato, himself a Pythagorean. J. S. Bach + Fractals = New Music. By MALCOLM W.
BROWNEPublished: April 16, 1991 FOR anyone craving a stripped-down version of Bach -- one from which three-quarters of the master's notes have been cut away -- help is on the way. A scientist and his musician son have devised a system to condense music to its underlying essence. In a paper published yesterday in The Proceedings of the National Academy of Sciences, Dr. Kenneth J. Mathematics and fiber arts. Mathematical ideas have been used as inspiration for a number of fiber arts including quilt making, knitting, cross-stitch, crochet, embroidery and weaving.
A wide range of mathematical concepts have been used as inspiration including topology, graph theory, number theory and algebra. Some techniques such as counted-thread embroidery are naturally geometrical; other kinds of textile provide a ready means for the colorful physical expression of mathematical concepts. Quilting[edit] The IEEE Spectrum has organized a number of competitions on quilt block design, and several books have been published on the subject. Notable quiltmakers include Diana Venters and Elaine Ellison, who have written a book on the subject Mathematical Quilts: No Sewing Required. Latin letters used in mathematics. Many letters of the Latin alphabet, both capital and small, are used in mathematics, science and engineering to denote by convention specific or abstracted constants, variables of a certain type, units, multipliers, physical entities.
Certain letters, when combined with special formatting, take on special meaning. Below is an alphabetical list of the letters of the alphabet with some of their uses. The field in which the convention applies is mathematics unless otherwise noted. Aa[edit] Bb[edit] Cc[edit] Dd[edit] D represents the digit "13" in hexadecimal and other positional numeral systems with a radix of 14 or greater diffusion coefficient or diffusivity in dimensions of [length^2 / time]d represents the differential operatorthe unit day of time (86,400 s)the difference in an arithmetic sequence (e.g. Ee[edit] Ff[edit] Gg[edit] G represents g represents: the generic designation of a second functionthe acceleration due to gravity on Earth. Chronology of computation of π. Quaternion Group Q8 and Yi Jing (I Ching) Hexagrams - un knol de Suresh Emre.
In mathematics the quaternion group is formed by the basis quaternions .
The multiplication table is given by compare the table above to the Yi Jing (I Ching) hexagrams below. Suzhou numerals. The Suzhou numerals or huama is a numeral system used in China before the introduction of Arabic numerals.
History[edit] The Suzhou numeral system is the only surviving variation of the rod numeral system. The rod numeral system is a positional numeral system used by the Chinese in mathematics. Bifurcation diagram. In mathematics, particularly in dynamical systems, a bifurcation diagram shows the possible long-term values (equilibria/fixed points or periodic orbits) of a system as a function of a bifurcation parameter in the system.
It is usual to represent stable solutions with a solid line and unstable solutions with a dotted line. Bifurcations in 1D discrete dynamical systems[edit] Logistic map[edit] Animation showing the formation of bifurcation diagram An example is the bifurcation diagram of the logistic map: Foundations of Mathematics By David Hilbert (1927) David Hilbert (1927) Source: The Emergence of Logical Empiricism (1996) publ.
Garland Publishing Inc. The whole of Hilbert selection for series reproduced here, minus some inessential mathematical formalism. Brouwer's Cambridge Lectures on Intuitionism. Lej Brouwer (1951) Lectures on Intuitionism Source: Brouwer's Cambridge Lectures on Intuitionism (1951) publ.
Cambridge University Press, 1981. Cubic function. Where a is nonzero; or in other words, a function defined by a polynomial of degree three.
The derivative of a cubic function is a quadratic function. The integral of a cubic function is a quartic function. Euler's Letters to a German Princess. List of topics named after Leonhard Euler. In mathematics and physics, there are a large number of topics named in honor of Leonhard Euler, many of which include their own unique function, equation, formula, identity, number (single or sequence), or other mathematical entity. Unfortunately, many of these entities have been given simple and ambiguous names such as Euler's function, Euler's equation, and Euler's formula. Euler's work touched upon so many fields that he is often the earliest written reference on a given matter. Physicists and mathematicians sometimes jest that, in an effort to avoid naming everything after Euler, discoveries and theorems are named after the "first person after Euler to discover it".[1][2] Cardinality of the continuum. Or The real numbers are more numerous than the natural numbers .
Moreover, Derek Jacobi - Breaking the code *Mathematics* Bronowski on Pythagoras' Theorem.