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.

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

+ 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