Overlapping Double Square Calculator

Name: Overlapping Double Square - Geometry Calculator
Author: Jürgen Kummer

Calculations for an overlapping double square. Such a shape is formed when two squares of equal size overlap symmetrically at their vertices.
Enter the side length of one square and the length of the short sides of this shape. Choose the number of decimal places, then click Calculate.

Formeln:

c = a - b

d_{1} = \sqrt{2} \cdot c

d_{2} = \sqrt{2} \cdot (a + b)

p = 4 \cdot (a + b)

A = 2 a^{2} - c^{2}

Lengths, diagonals and perimeter have the same unit (e.g. meter), the area has this unit squared (e.g. square meter).

The overlapping double square is a right octagon with two opposite concave corners. The other six corners are convex. The convex corners have right interior angles, while the concave corners have right exterior angles. Inside this shape lies another square with a side length equal to the overlap. This overlap indicates the extent to which the squares protrude into one another. The overlapping double square can also be viewed as a square with side length a+b from which a square with side length b has been removed at each of two opposite corners. Assembling it from simpler shapes without overlapping or subtraction can be done using a square with side length c and two identical L-shapes with inner side lengths c and width b. Another possibility is with two special axially symmetric pentagons, into which the double square can be subdivided along the short diagonal.
The short diagonal of this shape connects the two concave corners, while the long diagonal connects the two convex corners that are furthest apart. The relationship between the two diagonals is $\frac{d_{2}}{d_{1}} = \frac{a + b}{a - b}$

Such an overlapping double square has two axes of symmetry, which correspond to the two diagonals. It exhibits point symmetry with respect to the intersection of these diagonals, as well as rotational symmetry for a rotation angle of 180 degrees and multiples thereof.
Another rectangular shape, in addition to the rectangle itself, is the rectangular hexagon. See also there on such rectangular polygons in general.

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