Difference between revisions of "Category:Mathematics"
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==CAS and numerical analysis== | ==CAS and numerical analysis== | ||
| − | * [[wikipedia:GNU Octave]] — a free computer program for performing numerical computations which is mostly compatible with MATLAB | + | *[[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== | ==Misc== | ||
| Line 23: | Line 23: | ||
* roots and number equal squares (''bx'' + ''c'' = ''x''<sup>2</sup>) | * roots and number equal squares (''bx'' + ''c'' = ''x''<sup>2</sup>) | ||
| − | ===Cool numbers=== | + | ===Cool equations and numbers=== |
| + | *[[wikipedia:Euler's identity|Euler's identity]]: e<sup>''i''π</sup> + 1 = 0 | ||
*163 | *163 | ||
*Khinchin's constant, K ~2.685252... | *Khinchin's constant, K ~2.685252... | ||
| Line 34: | Line 35: | ||
*691 | *691 | ||
*The Golden Ratio, φ 1.618... | *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 [[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] — search for sequences of digits in pi | ||
| + | *[http://pi.nersc.gov/ 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: [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=== | ===Mental calculation=== | ||
| Line 61: | Line 110: | ||
*[[wikipedia:Category:Mathematics]] | *[[wikipedia:Category:Mathematics]] | ||
*[[wikipedia: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:Octal]] (see: [http://netzreport.googlepages.com/online_converter_for_dec_octal.html Online Converter for Decimal/Octal Numerals]) | ||
| + | *[[wikipedia:Lotka-Volterra equation]] | ||
===Other=== | ===Other=== | ||
| Line 68: | Line 119: | ||
*[http://planetmath.org/ PlanetMath.org] — a collaboratively created, virtual community which aims to help make mathematical knowledge more accessible. | *[http://planetmath.org/ PlanetMath.org] — a collaboratively created, virtual community which aims to help make mathematical knowledge more accessible. | ||
*[http://planetphysics.org/ PlanetPhysics.org] — a collaboratively created, virtual community which aims to help make physics knowledge more accessible. | *[http://planetphysics.org/ PlanetPhysics.org] — 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] — 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] — about a new number system which has a lot of advantages over our old decimal system. | *[http://www.infoverse.org/octomatics/octomatics.htm The Octomatics Project] — 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] — by Paul Bourke | ||
| + | *[http://godplaysdice.blogspot.com/2007/09/why-g-2.html why ''g'' ~ π<sup>2</sup>] — 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.
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 (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 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 ~ π2 — 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.
