算盤

sound of Pi

2011-12-12T12:29:00.001-06:00

For more of Michael's music check out http://www.quebecantique.com or at itunes http://itunes.apple.com/us/album/the-abbey-tapes/id304380573 or if you like the old fashioned CD format: http://www.cdbaby.com/cd/quebecantique More of Michael's music: http://www.cdbaby.com/cd/michaelblake http://itunes.apple.com/us/album/the-forever-of-now/id64638999 http://itunes.apple.com/us/album/

What Tau Sounds Like

2011-12-11T23:18:00.000-06:00

Musician interprets the mathematical constant Tau to 126 decimal places. For an mp3 download of "What Tau Sounds Like" visit http://www.cdbaby.com/cd/michaelblake13

The Eternal Return of the Elite

2011-12-03T21:13:00.002-06:00

http://it.wikipedia.org/wiki/Vilfredo_Pareto This monograph first saw the light of day in 1901 and has been understood as a somewhat famous attempt at a non race-based understanding of 'elitism'. The failure of this attempt to be either genuinely explanatory or entirely successful seems, by almost all accounts, to have been historically verified by fascisms repeated descent into racism.

Ettore Majorana: Unpublished Research Notes on Theoretical Physics (Fundamental Theories of Physics)

2011-12-03T21:04:00.000-06:00

The editors of this volume bring to life a major part of Ettore Majorana’s work that up to now was not accessible to the general audience. These are the contents of the Quaderni (notebooks) of Ettore Majorana, edited and translated in English. Ettore Majorana had an astounding talent for Physics that made an impression on all the colleagues who had the opportunity to know him. Enrico Fermi, who

Animaciones

2011-04-05T13:48:00.010-05:00

1: Motor radial de un avión 2: Distribución oval 3: Principio de la máquina de coser 4: Movimiento de Cruz de Malta - de la mano del segundero, que controla al reloj 5: Mecanismo de cambio de velocidades (automóvil) 6: Junta universal para velocidad constante automática 7: Sistema de carga de proyectiles 8: Motor giratorio - motor de combustión interna, el

Origami Moving Cubes using Sonobe units

2011-03-23T17:41:00.002-05:00

http://www.youtube.com/jonakashima The Knotology of Heinz Strobl Japanese Origami Kit - Cube Unit Unfolding Mathematics with Unit Origami Origami Tessellations: Awe-Inspiring Geometric Designs Origami Design Secrets: Mathematical Methods for an Ancient Art Beginner's Book of Modular Origami Polyhedra: The Platonic Solids (Beginner's Book Of... (Dover Publications))

The 7.11 problem

2011-03-22T03:42:00.004-05:00

A man goes into a store and selects four items to purchase. He walks up to the counter to pay and the clerk says "Hold on, my cash register is broken, so I have to use a calculator to get your total... okay, that'll be $7.11" The man pays, and as he is walking out, the clerk yells "Wait a second! I multiplied the prices together instead of adding them. Let me get the total again... hey, what do

Symmetry

2011-03-05T11:26:00.000-06:00

1 x 8 + 1 = 9 12 x 8 + 2 = 98 123 x 8 + 3 = 987 1234 x 8 + 4 = 9876 12345 x 8 + 5 = 987 65 123456 x 8 + 6 = 987654 1234567 x 8 + 7 = 9876543 12345678 x 8 + 8 = 98765432 123456789 x 8 + 9 = 987654321 1 x 9 + 2 = 11 12 x 9 + 3 = 111 123 x 9 + 4 = 1111 1234 x 9 + 5 = 11111 12345 x 9 + 6 = 111111 123456 x 9 + 7 = 1111111 1234567 x 9 + 8 = 11111111 12345678 x 9 + 9 = 111111111 123456789 x 9 +10=

cofactor

2011-02-26T17:38:00.000-06:00

In linear algebra, the cofactor (sometimes called adjunct, see below) describes a particular construction that is useful for calculating both the determinant and inverse of square matrices. Specifically the cofactor of the (i, j) entry of a matrix, also known as the (i, j) cofactor of that matrix, is the signed minor of that entry. Finding the minors of a matrix A is a multi-step process:

Fields

2011-02-25T23:50:00.000-06:00

In abstract algebra, a field is an algebraic structure with notions of addition, subtraction, multiplication, and division, satisfying certain axioms. The most commonly used fields are the field of real numbers, the field of complex numbers, and the field of rational numbers, but there are also finite fields, fields of functions, various algebraic number fields, p-adic fields, and so forth.Any

magmas

2011-02-25T20:06:00.001-06:00

In abstract algebra, an algebraic structure consists of one or more sets, called underlying sets or carriers or sorts, closed under one or more operations, satisfying some axioms. Abstract algebra is primarily the study of algebraic structures and their properties. The notion of algebraic structure has been formalized in universal algebra. Types of magmasMagmas are not often studied as such;

2011-02-18T00:08:00.000-06:00

Linear algebraic groupFrom Wikipedia, the free encyclopediaIn mathematics, a linear algebraic group is a subgroup of the group of invertible n×n matrices (under matrix multiplication) that is defined by polynomial equations. An example is the orthogonal group, defined by the relation MTM = I where MT is the transpose of M. http://en.wikipedia.org/wiki/Linear_algebraic_group

flops in Matlab

2011-02-17T15:36:00.000-06:00

Somebody asked how one may count the number of floating point operations in a MATLAB program. Prior to version 6, one used to be able to do this with the command flops, but this command is no longer available with the newer versions of MATLAB. flops is a relic from the LINPACK days of MATLAB (LINPACK has since been replaced by LAPACK). With the use of LAPACK in MATLAB, it will be more

x = A \ b; in Matlab

2011-02-13T17:58:00.000-06:00

x = A \ b; Is A square? no => use QR to solve least squares problem. Is A triangular or permuted triangular? yes => sparse triangular solve Is A symmetric with positive diagonal elements? yes => attempt Cholesky after symmetric minimum degree. Otherwise => use LU on A (:, colamd(A))

Complexity of Matrix Inversion

2011-02-10T16:51:00.000-06:00

What is the computational complexity of inverting an nxn matrix? (In general, not special cases such as a triangular matrix.) Gaussian Elimination leads to O(n^3) complexity. The usual way to count operations is to count one for each "division" (by a pivot) and one for each "multiply-subtract" when you eliminate an entry. Here's one way of arriving at the O(n^3) result: At the beginning

Sparse Finite-Element Matrices in MATLAB

2011-02-09T18:46:00.000-06:00

March 1st, 2007Creating Sparse Finite-Element Matrices in MATLABI'm pleased to introduce Tim Davis as this week's guest blogger. Tim is a professor at the University of Florida, and is the author or co-author of many of our sparse matrix functions (lu, chol, much of sparse backslash, ordering methods such as amd and colamd, and other functions such as etree and symbfact). He is also the author

Nodal Discontinuos Galerkin methods

2011-02-09T18:38:00.000-06:00

http://www.caam.rice.edu/~timwar/Book/NodalDG.html http://www.caam.rice.edu/~timwar/TimWarburton/HomePage.html

dot product

2011-02-04T10:53:00.000-06:00

Vector formulationThe law of cosines is equivalent to the formulain the theory of vectors, which expresses the dot product of two vectors in terms of their respective lengths and the angle they enclose. Fig. 10 — Vector triangleProof of equivalence. Referring to Figure 10, note thatand so we may calculate:The law of cosines formulated in this notation states:which is equivalent to the above

Law of cosines

2011-02-04T09:29:00.000-06:00

Law of cosinesFrom Wikipedia, the free encyclopediaThis article is about the law of cosines in Euclidean geometry. For the cosine law of optics, see Lambert's cosine law.Figure 1 – A triangle. The angles α,β, and γ are respectively opposite the sides a, b, and c. Trigonometry History Usage Functions Generalized Inverse functions Further reading Reference Identities Exact constants

cross product

2011-02-04T00:35:00.001-06:00

http://www.physics.orst.edu/bridge/mathml/dot+cross.xhtml

Best approximation theorem

2011-02-01T10:02:00.000-06:00

Best approximation theoremTheoremLet X be an inner product space with induced norm, and a non-empty, complete convex subset. Then, for all , there exists a unique best approximation a0 to x in A.ProofSuppose x = 0 (if not the case, consider A − {x} instead) and let . There exists a sequence (an) in Asuch that. We now prove that (an) is a Cauchy sequence. By the parallelogram rule, we get. Since

Rotation matrix

2011-02-01T08:59:00.001-06:00

Rotation matrixFrom Wikipedia, the free encyclopediaIn linear algebra, a rotation matrix is a matrix that is used to perform a rotation in Euclidean space. For example the matrixrotates points in the xy-Cartesian plane counterclockwise through an angle θ about the origin of the Cartesian coordinate system. To perform the rotation, the position of each point must be represented by a column vector

Isometry

2011-02-01T08:40:00.000-06:00

IsometryFrom Wikipedia, the free encyclopediaFor the mechanical engineering and architecture usage, see isometric projection. For isometry in differential geometry, seeisometry (Riemannian geometry).In mathematics, an isometry is a distance-preserving map between metric spaces. Geometric figures which can be related by an isometry are called congruent.Isometries are often used in constructions

Unitary matrix

2011-02-01T08:32:00.000-06:00

Unitary matrixFrom Wikipedia, the free encyclopediaIn mathematics, a unitary matrix is an complex matrix U satisfying the conditionwhere In is the identity matrix in n dimensions and is the conjugate transpose (also called the Hermitian adjoint) of U. Note this condition says that a matrix U is unitary if and only if it has an inverse which is equal to its conjugate transpose A unitary matrix

Self-adjoint operator

2011-02-01T08:11:00.000-06:00

Self-adjoint operatorFrom Wikipedia, the free encyclopediaIn mathematics, on a finite-dimensional inner product space, a self-adjoint operator is one that is its own adjoint, or, equivalently, one whose matrix is Hermitian, where a Hermitian matrix is one which is equal to its own conjugate transpose. By the finite-dimensional spectral theorem such operators have an orthonormal basis in which