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In geometry, a convex curve is a plane curve that has a supporting line through each of its points. There are many other equivalent definitions of these curves, going back to Archimedes. Examples of convex curves include the convex polygons, the boundaries of convex sets, and the graphs of convex functions.
Convex geometry is a relatively young mathematical discipline. Although the first known contributions to convex geometry date back to antiquity and can be traced in the works of Euclid and Archimedes, it became an independent branch of mathematics at the turn of the 20th century, mainly due to the works of Hermann Brunn and Hermann Minkowski in dimensions two and three.
The Archimedean solids are a set of thirteen convex polyhedra whose faces are regular polygons, but not all alike, and whose vertices are all symmetric to each other. The solids were named after Archimedes , although he did not claim credit for them.
This is a list of Wikipedia articles about curves used in different fields: mathematics (including geometry, statistics, and applied mathematics), ...
A page from Archimedes' On Conoids and Spheroids. On Conoids and Spheroids (Ancient Greek: Περὶ κωνοειδέων καὶ σφαιροειδέων) is a surviving work by the Greek mathematician and engineer Archimedes (c. 287 BC – c. 212 BC).
Cicero Discovering the Tomb of Archimedes (1805) by Benjamin West. Archimedes was born c. 287 BC in the seaport city of Syracuse, Sicily, at that time a self-governing colony in Magna Graecia. The date of birth is based on a statement by the Byzantine Greek scholar John Tzetzes that Archimedes lived for 75 years before his death in 212 BC. [9]
A convex curve may be defined as the boundary of a convex set in the Euclidean plane. This means that a convex curve is always closed (i.e. has no endpoints). Sometimes, a looser definition is used, in which a convex curve is a curve that forms a subset of the boundary of a convex set. For this variation, a convex curve may have endpoints.
Similarly, although both Archimedes and Della Francesca found formulas for the volume of a cloister vault (see below), their work on this appears to be independent, as Archimedes' volume formula remained unknown until the early 20th century. [8] De quinque corporibus regularibus is one of three books known to have been written by della Francesca.