This did not find a place in libHX, but is always useful.

ARBITRARY ROOT
    The k'th root of n to the p'th power is the same as
    n to the (p/k)'th power.

GEOMETRY MATH
    sin(a)  = y / r;
    cos(a)  = x / r;
    tan(a)  = y / x; [also: sin(a) / cos(a)]
    sec(a)  = 1 / cos(a);
    csc(a)  = 1 / sin(a);
    cot(a)  = x / y; [also: cos(a) / sin(a)]

    asin(z) = -i * ln(iz + sqrt(1 - z**2));
    acos(z) = -i * ln(z + sqrt(z**2 - 1));
    atan(z) = i / 2 * ln((i + z) / (i - z));
    asec(z) = acos(1 / z);
    acsc(z) = asin(1 / z);
    acot(z) = atan(1 / z);

TEMPERATURES
    K = 273.16 + C;
    F = C * (9 / 5) + 32;
    R = 0.8 * C;

IMPERIAL MEASURES
    Linear measures
        Inch       2.54 cm
        Foot      12    inches                  <  30.48  cm>
        Yard       3    feet                    <  91.44  cm>
        Furlong  220    yards                   < 201.168 m>
        Mile    1760    yards (8 furlong)       <1690.344 m>

    Surveyor's measures
        Link    7.92 inches                     <20.1168 cm>
        Rod    25    links                      < 5.0292 m>
        Chain  22    yards                      <20.1168 m>

    Square measures
        Square inch    6.4516 Square cm
        Square foot  144      Square inch
        Square yard    9      Square foot
        Square rod    30.25   Square yard
        Square acre 4840      Square yard
        Square mile  640      Square acre

    Cubic measures
        Cubic inch     16.387064 cubic cm
        Cubic foot   1728        cubic inch
        Cubic yard     27        cubic foot
        Register ton  100        cubic foot

    Measures of capacity, Liquid
        Gill   0.142 liters
        Pint   4     gills                       <0.568 l>
        Quart  2     pints  <8 gills>            <1.136 l>
        Gallon 4     quarts <32 gills> <8 pints> <4.544 l>

    Measures of capacity, US Liquid
        Gill   0.118 liters
        Pint   4     gills                       <0.472 l>
        Quart  2     pints                       <0.944 l>
        Gallon 4     quarts                      <3.776 l>

    Measures of capacity, Dry
        Peck    2 gallons
        Bushel  4 pecks
        Quarter 8 bushels

    Measures of capacity, US Dry
        Pint   0.55 liters
        Quart  2    pints
        Peck   8    quarts
        Bushel 4    pecks

    Weights
        Grain            0.0648 grams
        Drachm          27.34   grains  <  1.77  g>
        Ounce           16      drachms < 28.34  g>
        Pound           16      ounces  <453.53  g>
        Stone           14      pounds  <  6.349 kg>
        Quarter         28      pounds  < 12.69  kg>
        Hundredweight  122      pounds  < 55.33  kg>
        Ton           2240      pounds (20 hundredweight) <1015 kg>

TRIANGLE
    Area = Width * Height;
    Area = sqrt(3) * a ** 2 / 4; (3x60 deg triangle)
    Height = sqrt(3) * a / 2; (3x60 deg triangle)

RECTANGLE
    Area = Width * Height;
    Circumference = 2 * (a + b);
    Diagonale = sqrt(a ** 2 + b ** 2);

SQUARE
    Area = SideLength ** 2;
    Circumference = 4 * a;
    Diagonale = sqrt(2) * a;

PARALLELOGRAM
    Area = Width * Height;

TRAPEZ
    Area = (NorthSideLength + SouthSideLength) * Height / 2;

CIRCLE
    Area = PI * Radius ** 2;
    Circumference = 2 * PI * Radius;
    Arch = 2 * PI * Radius * Alpha / 360;
    String = 2 * Radius * sin(Alpha); // DE: "Sehne"
    Height = 2 * Radius * sin(Alpha / 4) ** 2;
    Ring Area = PI * (OuterRadius ** 2 - InnerRadius ** 2);
    Segment = Arch * Radius - String * (Radius - Height) / 2;
    Sector = PI * Radius ** 2 * Alpha / 360;
    Ellipse = PI * a * b;

ARBITRARY SHAPED AREAS/POLYGONS
    Number of diagonales = (n * (n - 3)) / 2;

    Number of splits in a worst-case-shaped area (an area with as many concave
    angles as possible; no sides may overlap.):
      Sides 4, 5 => 1
      Sides 6, 7 => 2
      Sides 8+   => floor(Sides / 2)

REGULAR, N-SIDED POLYGONS
    Regular here means all angles are the same.
    Area = SideLength * ToSideHalfRadius * Sides / 2;

QUADER
    Volume = a * b * c;
    Surface = 2 * a * b + 2 * a * c + 2 * b * c;
    Cover = 2 * a * b + 2 * a * c;
    Mesh = 2 * (a + b + c)

CUBE
    Volume = a ** 3;
    Surface = 6 * a ** 2;
    Cover = 4 * a ** 2;
    Diagonale = sqrt(3) * a;
    Mesh = 6 * a

PRISM
    Volume = GroundShape * Height;

PYRAMID
    Volume = GroundShape * Height / 3;
    Blunted pyramid volume = (G1 + G2 + sqrt(G1 + G2)) * Height / 3;

CONE
    Volume = PI * Radius ** 2 * Height / 3;
    Blunted cone volume = PI * Height * (bigRadius ** 2 +
      bigRadius * smallRadius + smallRadius ** 2) / 3;
    Surface = PI * Radius * s + PI * Radius ** 2;
    Cover = PI * Radius * s;

SPHERE
    Volume = (4 / 3) * PI * r ** 3;
    Segment = (1 / 3) * PI * Height ** 2 * (3 * Radius - Height);
    Segment Cover = 2 * PI * Radius * Height;
    Sector = (2 / 3) * PI * Radius ** 2 * Height;
    Surface = 4 * PI * Radius ** 2;
    Zone = PI * (3 * bigRadius ** 2 + 3 * smallRadius ** 2 +
      3 * Height ** 2) * Height / 6;
    Hollow sphere volume = (4 / 3) * PI *
      (TotalRadius ** 3 - hollowRadius ** 3);
    Ellipsoid = (4 / 3) * PI * a * b * c;
    Mesh = x * 2 * PI * Radius; x e |N; x >= 2;

CYLINDER
    Volume = PI * Radius ** 2 * Height;
    Hollow cylinder volume = PI * Height * (bigRadius ** 2 - smallRadius ** 2);
    Cylindric ring = 2 * PI ** 2 * fullRadius * innerRadius;
    Mesh = 2 * PI * Radius + 2 * Height

TETRAEDER
    Volume = sqrt(2) * SideLength ** 3 / 12;
    Surface = 4 * sqrt(3 * SideLength ** 4 / 16);