Difference between revisions of "Category:Mathematics"

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* [[Linear Algebra]]
 
* [[Linear Algebra]]
  
−
== Misc ==
+
==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
 
Note: Sandbox entry
Line 19: Line 23:
 
* roots and number equal squares (''bx'' + ''c'' = ''x''<sup>2</sup>)
 
* roots and number equal squares (''bx'' + ''c'' = ''x''<sup>2</sup>)
  
−
== External links ==
+
===Cool equations and numbers===
 +
*[[wikipedia:Euler's identity|Euler's identity]]: e<sup>''i''&pi;</sup> + 1 = 0
 +
*163
 +
*Khinchin's constant, K ~2.685252...
 +
*The Euler-Mascheroni Constant, &gamma; ~0.577215...
 +
*The Monster, |M|=808017424794512875886459904961710757005754368000000000
 +
*The Oddest Prime: 2
 +
*Feigenbaum's constant, &delta; ~4.669201...
 +
*(pi)^2/6
 +
*78,557
 +
*691
 +
*The Golden Ratio, &phi; 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 [[wikipedia:as the crow flies|as the crow flies]].
 +
*[[wikipedia:Barbier's Theorem|Barbier's Theorem]] (see: [http://www.joyofpi.com/pifacts3.html])
 +
*[http://www.angio.net/pi/ The Pi-Search Page] &mdash; search for sequences of digits in pi
 +
*[http://pi.nersc.gov/ Pi-Search] &mdash; 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: [http://www.guardian.co.uk/g2/story/0,,1824525,00.html 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: [[wikipedia:Mental calculation|Mental calculation]], [[wikipedia:Vedic_mathematics|Vedic_mathematics]], [[wikipedia:Trachtenberg system|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 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:
 
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:
−
* [http://en.wikibooks.org/wiki/Wikiversity:School_of_Mathematics WikiBooks - Wikiversity - School of Mathematics]
+
*[http://en.wikibooks.org/wiki/Wikiversity:School_of_Mathematics WikiBooks - Wikiversity - School of Mathematics]
−
* [http://en.wikipedia.org/wiki/Category:Mathematics Wikipedia category on '''mathematics''']
+
*[[wikipedia:Category:Mathematics]]
−
* [http://en.wikipedia.org/wiki/Mathematics Wikipedia article on '''mathematics''']
+
*[[wikipedia:Mathematics]]
 +
*[[wikipedia:Table of mathematical symbols]]
 +
*[[wikipedia:Octal]] (see: [http://netzreport.googlepages.com/online_converter_for_dec_octal.html Online Converter for Decimal/Octal Numerals])
 +
*[[wikipedia:Lotka-Volterra equation]]
  
−
=== Other ===
+
===Other===
−
* [http://mathworld.wolfram.com/ MathWorld] &mdash; by Wolfram Research
+
*[http://mathworld.wolfram.com/ MathWorld] &mdash; by Wolfram Research
−
* [http://integrals.wolfram.com/index.jsp The Wolfram Integrator] &mdash; by Wolfram Research
+
*[http://integrals.wolfram.com/index.jsp The Wolfram Integrator] &mdash; by Wolfram Research
−
* [http://planetmath.org/ PlanetMath.org] &mdash; a collaboratively created, virtual community which aims to help make mathematical knowledge more accessible.
+
*[http://planetmath.org/ PlanetMath.org] &mdash; a collaboratively created, virtual community which aims to help make mathematical knowledge more accessible.
−
* [http://planetphysics.org/ PlanetPhysics.org] &mdash; a collaboratively created, virtual community which aims to help make physics knowledge more accessible.
+
*[http://planetphysics.org/ PlanetPhysics.org] &mdash; a collaboratively created, virtual community which aims to help make physics knowledge more accessible.
 +
*[http://www.research.att.com/~njas/sequences/ The On-Line Encyclopedia of Integer Sequences] ([http://en.wikipedia.org/wiki/Online_Encyclopedia_of_Integer_Sequences wikipedia])
 +
*[http://www.scilab.org/ Scilab] &mdash; a scientific software package for numerical computations providing a powerful open computing environment for engineering and scientific applications.
 +
*[http://www.infoverse.org/octomatics/octomatics.htm The Octomatics Project] &mdash; about a new number system which has a lot of advantages over our old decimal system.
 +
*[http://www.math.utah.edu/~palais/pi.html Pi is Wrong]
 +
*[http://mathschallenge.net/ MathsChallenge.net]
 +
*[http://www.statistics-help-online.com/node55.html Unbiased estimates] (stdev)
 +
*[http://projecteuler.net/ Project Euler]
 +
*[http://local.wasp.uwa.edu.au/~pbourke/surfaces_curves/ Surfaces and Curves] &mdash; by Paul Bourke
 +
*[http://godplaysdice.blogspot.com/2007/09/why-g-2.html why ''g'' ~ &pi;<sup>2</sup>] &mdash; about the acceleration due to gravity.
 +
*''Number Theory for Programmers'', Part 1
 +
*[http://www.embedded.com/columns/programmerstoolbox/204300487 Who needs matrices?]
  
 
[[Category:Science]]
 
[[Category:Science]]

Latest revision as of 16:08, 24 October 2014

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.

L

S

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