Calculations at a truncated square, a square with the corners equally cut off. This is an octagon with sides of two different lengths, whose opposite sides have the same length each and are parallel. The angles at the eight corners are all the same size; as with the regular octagon, they have 135 degrees.
Enter two lengths and choose the number of decimal places. Then click Calculate.
Formulas:
e = b / √2
l = √2 * ( a + e )
h = a + 2e
d = √ a² + ( a + 2e )²
p = 4 * ( a + b )
A = ( a + 2e )² - 2 * e²
Angle: 135°
Lengths, height, diagonal and perimeter have the same unit (e.g. meter), the area has this unit squared (e.g. square meter).
The truncated square is axially symmetrical to all of its four bisectors, but not to its four diagonals. It is point-symmetrical to its center, which is also the intersection of the bisectors and the diagonals. Its circumcircle has the diameter of the diagonal d, its incircle has the diameter of the smaller value of the height h and the length l.
This shape is found approximately in many solar cells, but with rounded short sides, like in the picture above. The reason for the rounding in the manufacturing process. Wafers are cut from a round block, but arranging circles next to each other leaves large gaps. Squares would be ideal for a gapless arrangement, but with these too much material would be cut off and thus wasted. A pseudo-square shape of the solar cells is a good compromise between the two shapes.
This picture shows a copper Heller from the Duchy of Saxony Hildburghausen, which was minted in 1788. It is slightly irregular, but has roughly the shape of a truncated square. Angular coins are called klippe, and such shapes are found primarily in low-value coins such as the Heller. Such a shape is probably chosen to make it easier to distinguish from other, especially higher-value coins.
