Math and Programs you might be interested in.
Math and Programs you might be interested in. ^That I found to be really intriguing. It's like not only did Turing invent the concept of the modern computer, but he also created math on paper that is remarkably similar to programmed shaders. ^^Context free. ^Structure Synth is like a 3d version of this. Here's a piece of code for that program to start off with and or remix... #define HA 1.2262415695892090741876149601471 #define HB 0.12262415695892090741876149601471 #define TILESIZE 0.9 #define YOFFSET 3.4641012081519749420331123133873 set maxdepth 1000 r3 shape2astart rule hexO { { x 1.0 s HB HA HB } box { rz 60 x 1.0 s HB HA HB } box { rz 120 x 1.0 s HB HA HB } box { rz 180 x 1.0 s HB HA HB } box { rz 240 x 1.0 s HB HA HB } box { rz 300 x 1.0 s HB HA HB } box } rule start md 20{ {hue 560}hexO {rx 120 ry 120 rz 120 h -0.2}start } Anyway.
Science After Sunclipse » Blog Archive » “Is Algebra Necessary?” Are You High?
“This room smells of mathematics! Go out and fetch a disinfectant spray!” —A.H. Trelawney Ross, Alan Turing’s form master It’s been a while since I’ve felt riled enough to blog. But now, the spirit moves within me once more. First, I encourage you to read Andrew Hacker’s op-ed in The New York Times, “Is Algebra Necessary?” I will try to gather a few observations here which I haven’t seen made elsewhere, for the most part. Towards the end, Hacker’s reasoning gets just bizarre. Quantitative literacy clearly is useful in weighing all manner of public policies, from the Affordable Care Act, to the costs and benefits of environmental regulation, to the impact of climate change. OK, so how are we supposed to teach where “numbers come from” and “what they actually convey” when the students can’t manipulate algebraic formulas? It’s also nice how he skips past the serious problems we have with infrastructure. Philosophers don’t need to know mathematics? (by Oliver Byrne) Oh, poor Euclid. (by Eugene)
Steiner Surfaces - IPFW
Definition Let p0, p1, p2, p3 be quadratic polynomials in two variables u, v. This means they're of the form pi(u,v)=Au2+Buv+Cv2+Du+Ev+F for constant coefficients A, B, C, D, E, F. If you plot the parametric graph (x,y,z)=(p1/p0 , p2/p0 , p3/p0) for some range of input values u, v, the image should be a two-dimensional surface in (x,y,z)-space. Background The "real projective plane" is the set of lines through the origin in real 3-dimensional space; when each of these lines is represented by one point, the resulting set is, in an abstract way, a smooth, two-dimensional surface. A convenient way to assign coordinates to the real projective plane is to pick a basis of 3-space, and denote by [u0 : u1 : u2] the line equal to the set of all scalar multiples of the non-zero ordered triple (u0,u1,u2). [u0 : u1 : u2] --> [u02 : u12 : u22 : u1u2 : u0u2 : u0u1]. This surface can be projected into 4-space smoothly, but any projection into three dimensional space must have singularities. A. Animation
Tupper's self-referential formula
Tupper's self-referential formula is a self-referential formula defined by Jeff Tupper that, when graphed in two dimensions, can visually reproduce the formula itself. It is used in various math and computer science courses as an exercise in graphing formulae. The formula was first published in his 2001 SIGGRAPH paper that discusses methods related to the GrafEq formula-graphing program he developed. where denotes the floor function and mod is the modulo operation. Let k equal the following 543-digit integer: If one graphs the set of points (x, y) in and satisfying the inequality given above, the resulting graph looks like this (note that the axes in this plot have been reversed, otherwise the picture comes out upside-down): The formula itself is a general purpose method of decoding a bitmap stored in the constant k, so it could actually be used to draw any other image. , the formula tiles a vertical swath of the plane with a pattern that contains all possible 17-pixel-tall bitmaps.
A Programmer's Apology: The Library of Babel function
MathWorld calls this Tupper's Self-Referential Formula because a graph of that inequality in the domain 0<x<105, N<y<N+16 for a particular 541-digit number N shows an image of the function itself. Closer investigation reveals that MathWorld does not even begin to do justice to the function, for higher up on the graph of this function one can find the complete works of Shakespeare, the contents of the lost library of Alexandria, and perhaps even the solution to unifying quantum mechanic with general relativity! At y values nearer the origin, you can find tomorrow's winning lottery number! If that sounds unbelievable, read on.... Consider rearranging the function slightly, as above, with k=17. What is the value of the bit at position index in the binary representation of B? The graph of the formula contains every possible black and white bitmap of height k, in order, as you move up along the y-axis from the origin! setenv BC_LINE_LENGTH 19 bc obase=2
Some Cryptography Theory
This is our Mathematics page with links to various topics we've written up. We'll keep adding to this. Number theory: The multiplicative group modulo p Looks at the multiplicative group modulo p for a prime p which is used in public key cryptography using discrete logarithms. We consider some of the properties relevant to its use in cryptography and recap on some basic group theory. Number theory: Solving the discrete logarithm problem with bdcalc Looks at the discrete logarithm problem and how it can be solved (:-) using bdcalc available from the bdcalc page. Computing a cube root in hexadecimal Shows how to compute the cube root of a number in hexadecimal format and describes the algorithm to find the exact digits. Statistics: An on-line calculator for the binomial distribution Calculates a table of the binomial distribution for given parameters and displays graphs of the probability distribution function and cumulative distribution function. Using the CRT with RSA Elementary Number Theory
George Cain - Complex Analysis
by George Cain (c)Copyright 1999, 2001 by George Cain. This is a textbook for an introductory course in complex analysis. I owe a special debt of gratitude to Professor Matthias Beck who used the book in his class at SUNY Binghamton and found many errors and made many good suggestions for changes and additions to the book. Many thanks also to Professor Serban Raianu of California State University Dominguez Hills whose many helpful suggestions have considerably improved the book. I am also grateful to Professor Pawel Hitczenko of Drexel University, who prepared the nice supplement to Chapter 10 on applications of the Residue Theorem to real integration. The notes are available as Adobe Acrobat documents. Title page and Table of Contents Table of Contents Chapter One - Complex Numbers 1.1 Introduction 1.2 Geometry 1.3 Polar coordinates Chapter Two - Complex Functions 2.1 Functions of a real variable 2.2 Functions of a complex variable 2.3 Derivatives
Peter J. Olver - Applied Mathematics
Peter J. Olver Last Updated: January 4, 2014 Note: The first 11 chapters, including the exercises, are now published as a self-contained textbook, Applied Linear Algebra, coauthored with Chehrzad Shakiban. Chapters Linear Algebraic Systems. Appendices A. Click here to return to Peter Olver's home page.
