puolilevy

Puolilevy is Finnish for semicircular disk, a planar region formed by taking a disk of radius R and cutting it along a diameter, taking one half. Its boundary consists of the straight diameter of length 2R and the curved semicircular arc of radius R.

If the semicircle has uniform density (a semicircular lamina), its area is A = (1/2)πR^2. The center of mass (centroid) lies on the axis of symmetry, a distance 4R/(3π) from the center toward the curved edge; equivalently, the centroid is at y = 4R/(3π) when the diameter lies on the x-axis and the semicircle is above it. The shape is commonly used in elementary geometry and mechanics as a simple, integrable region.

Variants include a semicircular plate (lamina) of various thickness or mass distribution; the term can also be used more generally for any half-disk shaped piece used in construction or manufacturing.

Applications: Puolilevy arises in statics and hydrodynamics as a test region for potential problems, in bending and torsion problems of plates, and in computational geometry as a simple test shape for numerical methods.

In Finnish mathematical literature, puolilevy is the standard term for a semicircular region, and the word literally means half-disk. See also: semicircle, lamina.