# Category:Mathematics

From Christoph's Personal Wiki

I took seven courses in calculus and linear algebra while attending university. This subject was, by far, my strongest. This category will contain articles pertaining to the subject of **mathematics**. I will use this category mainly for my easy reference.

## Contents

## Sub-Categories

## CAS and numerical analysis

- wikipedia:GNU Octave — a free computer program for performing numerical computations which is mostly compatible with MATLAB
- Mathomatic — a free, portable, general purpose computer algebra system (CAS)

## Misc

Note: Sandbox entry

Al-Khwārizmī's method of solving linear and quadratic equations worked by first reducing the equation to one of six standard forms (where *b* and *c* are positive integers)

- squares equal roots (
*x*^{2}=*bx*) - squares equal number (
*x*^{2}=*c*) - roots equal number (
*bx*=*c*) - squares and roots equal number (
*x*^{2}+*bx*=*c*) - squares and number equal roots (
*x*^{2}+*c*=*bx*) - roots and number equal squares (
*bx*+*c*=*x*^{2})

### Cool equations and numbers

- Euler's identity: e
^{iπ}+ 1 = 0 - 163
- Khinchin's constant, K ~2.685252...
- The Euler-Mascheroni Constant, γ ~0.577215...
- The Monster, |M|=808017424794512875886459904961710757005754368000000000
- The Oddest Prime: 2
- Feigenbaum's constant, δ ~4.669201...
- (pi)^2/6
- 78,557
- 691
- The Golden Ratio, φ 1.618...

### pi

- pi ~ 8.88/sqrt(8)
- pi ~ (2.22+2.22)/sqrt(2)
- pi ~ 355/113 ~ 22/7
- pi ~ actual length of rivers from source to mouth and their direct length as the crow flies.
- Barbier's Theorem (see: [1])
- The Pi-Search Page — search for sequences of digits in pi
- Pi-Search — search the first four billion binary digits of Pi for a string

### Proof that 0.999... is the same as 1

a = 0.999... 10a = 9.999... 10a - a = 9.999... - 0.999... 9a = 9 a = 1

### German tank equation

see: Gavyn Davies does the maths: How a statistical formula won the war

(M-1)(S+1)/S

*M* = maximum serial number, *S* = sample size

### Latitude/longitude into x,y

x=(longitude+127)*16 y=(50-latitude)*20

### Arithmetic

- Addition:

addend + augend ---------- = sum

- Subtraction:

minuend - subtrahend -------------- = difference

- Multiplication:

multicand * multiplier -------------- = product

- Division:

dividend / divisor ------------- = quotient

### Mental calculation

see: Mental calculation, Vedic_mathematics, Trachtenberg system

- Vertically and crosswise: 46x72

4 6 | x | 7 2 4x7 4x2+6x7 6x2 15 1 # <- carry 28 50 12 =3312

- Vertically and crosswise: 24x13

2 4 | x | 1 3 2x1 2x3+4x1 4x3 1 1 # <- carry 2 10 12 =312

## External links

Wikipedia and its sister project, WikiBooks, have many really good articles on just about everything related to mathematics. I will list some of the best articles (and categories) here:

- WikiBooks - Wikiversity - School of Mathematics
- wikipedia:Category:Mathematics
- wikipedia:Mathematics
- wikipedia:Table of mathematical symbols
- wikipedia:Octal (see: Online Converter for Decimal/Octal Numerals)
- wikipedia:Lotka-Volterra equation

### Other

- MathWorld — by Wolfram Research
- The Wolfram Integrator — by Wolfram Research
- PlanetMath.org — a collaboratively created, virtual community which aims to help make mathematical knowledge more accessible.
- PlanetPhysics.org — a collaboratively created, virtual community which aims to help make physics knowledge more accessible.
- The On-Line Encyclopedia of Integer Sequences (wikipedia)
- Scilab — a scientific software package for numerical computations providing a powerful open computing environment for engineering and scientific applications.
- The Octomatics Project — about a new number system which has a lot of advantages over our old decimal system.
- Pi is Wrong
- MathsChallenge.net
- Unbiased estimates (stdev)
- Project Euler
- Surfaces and Curves — by Paul Bourke
- why
*g*~ π^{2}— about the acceleration due to gravity. *Number Theory for Programmers*, Part 1- Who needs matrices?

## Pages in category "Mathematics"

The following 2 pages are in this category, out of 2 total.