Category:Mathematics

From Christoph's Personal Wiki
Jump to: navigation, search

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

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: eiπ + 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 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:

Other

Pages in category "Mathematics"

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