**Normal Math-Formulas**

**Introduction**

Following you find a nomination of various mathematical formulas. They should be a reference and also be helpful, to close possibly knowledge gaps. Because without good math knowledge complex games and applications can't be realized.

Note: Instead of the used sign '^' please use the PureBasic function Pow() from the 'Math' library. 'PI' stands for the constant value "PI = 3.1415...". An example for realizing such a formula in PureBasic code: A = PI*r^2 will be A = PI*Pow(r,2)

**Square**

l = Side length

e = Corner measure (ment)

A = Surface

U = Extent

Surface:A = l^2

Extent:U = 4*l

Corner measure (ment):e = SQR(2)*l

**Rhombus/Lozenge**

l = Side length

b = Width

A = Surface

U = Extent

Surface:A = l*b

Extent:U = 4*l

**Rectangle**

l = Length

b = Width

e = Corner measure (ment)

A = Surface

U = Extent

Surface:A = l*b

Extent:U = 2*l+2*b

Corner measure (ment):e = SQR(l^2+b^2))

**Rhomboid/Parallelogramm**

l = Lengthens

h = Height

b = Width

A = Surface

U = Extent

Surface:A = l*h

Extent:U = 2*l+2*b

**Trapezoid**

a = Side 1

b = Side 2

c = Side 3

d = Side 4

lm = Middle length

h = Height

A = Surface

U = Extent

Surface:A = (a+c)/2*h

Extent:U = a+b+c+d

Middle Length:lm = (a+c)/2

**Triangle**

a = Side 1

b = Side 2

c = Side 3

l = Side length

h = Height

A = Surface

U = Extent

Surface:

A = (l*h)/2

A = 1/4*SQR(U*(U-2*a)*(U-2*b)*(U-2*c))

Extent:U = a+b+c

**Polygon**

l = Side length

d = Interior circle diameter

D = Periphery diameter

n = Number of corners

a = Central angle

ss = Corner angle

A = Surface

U = Extent

Interior circle diameter:d = SQR(D*D-l*l)

Periphery diameter:D = SQR(d*d+l*l)

Side length:l = D*SIN(180/n)

Central angle:a = 360/n

Corner angle:ss = 180-a

Surface:A = n*l*d/4

Extent:U = l*n

**Circle**

r = Radius

D = Diameter

A = Surface

U = Extent

Surface:

A = PI*r^2

A = PI/4*d^2

Extent:

U = 2*PI*r

U = PI*d

**Sector of a circle**

r = Radius

D = Diameter

l = Sinew length

lb = Length of curve

a = Central angle

A = Surface

U = Extent

Sinew length:l = 2*r*SIN(a/2)

Length of curve:lb = PI*r*a/180

Surface:

A = PI*D^2*a/1440

A = lb*r/2

Extent:U = lb+D

**Circle section**

r = Radius

D = Diameter

l = Sinew length

lb = Length of curve

a = Central angle

b = Width

A = Surface

U = Extent

Sinew Length:

l = 2*r*SIN(a/2)

l = 2*SQR(b*(2*r-b))

Length of curve:lb = PI*r*a/180

Width:

b = l/2*TAN(a/4)

b = r-SQR(r^2-l^2/4)

Radius:r = b/2+l^2/(8*b)

Surface:

A = PI*d^2*a/1440-(l*(r-b))/2

A = (lb*r-l*(r-b))/2

Extent:U = lb+l

**Annulus**

d = Inside diameter

D = Outside diameter

dm = Middle diameter

b = Width

A = Surface

Middle diameter:dm = (D+d)/2

Surface:

A = PI*dm*b

A = PI/4*(D^2-d^2)

**Memory consumption of a picture**

a = Width of picture (in Pixel)

b = Height of picture (in Pixel)

bits = Colordepth of the picture (in Bits)

size = a * b * (bits / 8)

**Distance between two points**

(x1|y1) = XY coordinates of point No. 1

(x2|y2) = XY coordinates of point No. 2

a = Distance between the points

a = SQR((x1-x2)^2 + (y1-y2)^2)

**"Mixing" of two values**

a = 1st Number

b = 2nd Number

v = Relationship (0% - 100%)

e = Result

e = ((a*v)/100) + ((b*(100-v)) / 100)