Calculate the number of fields or spaces, bars and knots of a two- and of a three-dimensional grid.
A two-dimensional grid contains fields, a three-dimensional grid contains spaces, each of them surrounded by bars. The number of fields easily calculates as m=a*b, the rooms as m=a*b*c.
Please enter at least a and b, c is optional.
A bar here is a straight line between two crossings. The calculation of the number of grid bars is more complicated. The formula is:
for 2D: n = (2a+1)*b+a
for 3D: n = [(2a+1)*b+a]*(c+1)+(a+1)*(b+1)*c
A knot is at the crossing of bars. The formula is:
for 2D: k = (a+1)*(b+1)
for 3D: k = (a+1)*(b+1)*(c+1)
Example: a three-dimensional grid with 6 spaces in length, 5 spaces in height and one space in depth has 30 spaces, 184 grid bars and 84 knots.
German: Dimension | Vielfacher Inhalt | Verhältnis | Diagonalen | Flächeninhalt | Rauminhalt | Schneiden | Stapel | Gitter | Anordnung | Rand | Innen-Außen | Lagerung | Ausbreitung | Stufenpyramide