Meissner Bodies
Meissner and Schilling showed how to modify the Reuleaux tetrahedron to form a surface of constant width, by replacing three of its edge arcs by curved patches formed as the surfaces of rotation of a circular arc. According to which three edge arcs are replaced (three that have a common vertex or three that form a triangle) there result two noncongruent shapes that are sometimes called Meissner bodies or Meissner tetrahedra (for interactive pictures and films see Weber). Bonnesen and Fenchel conjectured that Meissner tetrahedra are the minimum-volume three-dimensional shapes of constant width, a conjecture which is still open. In connection with this problem, Campi, Colesanti and Gronchi showed that the minimum volume surface of revolution with constant width is the surface of revolution of a Reuleaux triangle through one of its symmetry axes.
Read more about this topic: Reuleaux Tetrahedron
Famous quotes containing the word bodies:
“When the landscape buckles and jerks around, when a dust column of debris rises from the collapse of a block of buildings on bodies that could have been your own, when the staves of history fall awry and the barrel of time bursts apart, some turn to prayer, some to poetry: words in the memory, a stained book carried close to the body, the notebook scribbled by hand—a center of gravity.”
—Adrienne Rich (b. 1929)