Surface of constant width
- Surface of constant width
In geometry, a surface of constant width is a convex form whose width, measured by the distance between two opposite parallelplanes touching its boundary, is the same regardless of the direction of those two parallel planes. One defines the width of the surface in a given direction to be the perpendicular distance between the parallels perpendicular to that direction.
More generally, any compact convex body D has one pair of parallel supporting planes in a given direction. A supporting plane is a plane that intersects the boundary of D but not the interior of D. One defines the width of the body as before. If the width of D is the same in all directions, then one says that the body is of constant width and calls its boundary a surface of constant width, and the body itself is referred to as a "spheroform".
A sphere is obviously a surface of constant width. A nontrivial example is Meissner's tetrahedron. Contrary to common belief the Reuleaux tetrahedron is "not" a surface of constant width.
References
* | year=2007
External links
* [http://www.lama.univ-savoie.fr/~lachand/Spheroforms.html Spheroforms]
* [http://www.lama.univ-savoie.fr/~lachand/pdfs/spheroforms.pdf T. Lachand-Robert & É. Oudet, "Bodies of constant width in arbitrary dimension"]
* [http://web.mat.bham.ac.uk/C.J.Sangwin/howroundcom/roundness/solids.html How Round is Your Circle? Solids of constant width]
Wikimedia Foundation.
2010.
Look at other dictionaries:
Curve of constant width — A Reuleaux triangle is a curve of constant width. The sides of the square are supporting lines: each touches the curve but does not intersect the interior. The Reuleaux triangle can be rotated whilst always touching each side of the square in a… … Wikipedia
Reuleaux triangle — A Reuleaux polygon is a curve of constant width that is, a curve in which all diameters are the same length. The best known version is the Reuleaux triangle. Both are named after Franz Reuleaux, a 19th century German engineer who did pioneering… … Wikipedia
Reuleaux tetrahedron — Animation of a Reuleaux tetrahedron, showing also the tetrahedron from which it is formed. Four spheres intersect to form a Reuleaux tetrahedron. The Reuleaux tetrahedron is the inter … Wikipedia
List of mathematics articles (S) — NOTOC S S duality S matrix S plane S transform S unit S.O.S. Mathematics SA subgroup Saccheri quadrilateral Sacks spiral Sacred geometry Saddle node bifurcation Saddle point Saddle surface Sadleirian Professor of Pure Mathematics Safe prime Safe… … Wikipedia
List of mathematics articles (C) — NOTOC C C closed subgroup C minimal theory C normal subgroup C number C semiring C space C symmetry C* algebra C0 semigroup CA group Cabal (set theory) Cabibbo Kobayashi Maskawa matrix Cabinet projection Cable knot Cabri Geometry Cabtaxi number… … Wikipedia
Field emission — (FE) is the emission of electrons from the surface of a condensed phase into another phase due to the presence of high electric fields. In this phenomenon, electrons with energies below the Fermi level tunnel through the potential barrier at the… … Wikipedia
locomotion — /loh keuh moh sheuhn/, n. the act or power of moving from place to place. [1640 50; see LOCOMOTIVE, MOTION] * * * Any of various animal movements that result in progression from one place to another. Locomotion is classified as either… … Universalium
Map projection — A medieval depiction of the Ecumene (1482, Johannes Schnitzer, engraver), constructed after the coordinates in Ptolemy s Geography and using his second map projection A map projection is any method of representing the surface of a sphere or other … Wikipedia
Gravity current — In fluid dynamics, a gravity current is a primarily horizontal flow in a gravitational field that is driven by a density difference, hence gravity currents also sometimes being referred to as density currents . Typically, the density difference… … Wikipedia
Technical pen — A technical pen is a specialized instrument used by an engineer, architect, or draftsperson (British: draughtsperson) to make lines of constant width for architectural, engineering, or technical drawings. It has been also generally called… … Wikipedia
