Category:Mathematics

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.

Sub-Categories

• Algebra
• Trigonometry
• Calculus
• Linear Algebra

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 (x² = bx)
• squares equal number (x² = c)
• roots equal number (bx = c)
• squares and roots equal number (x² + bx = c)
• squares and number equal roots (x² + c = bx)
• roots and number equal squares (bx + c = x²)

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 ~ actual length of rivers from source to mouth and their direct length as the crow flies.
• Barbier's Theorem (see: [1])

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 related

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: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 ~ π² — about the acceleration due to gravity.
• Number Theory for Programmers, Part 1
• Who needs matrices?