adj, noun ·Uncommon ·College level
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"The word weak is a simplex. Its derivative weaken is not."
"The question is: is 139. [“Priexal Vanja. ‘arrived Vanya’”] a simplex or is it a cleft structure in which all 'superfluous' constituents were deleted. […] The only indication that 139. is a simplex is the sentence intonation and the absence of a break between the verb and the subject."
"The word weak is a simplex. Its derivative weaken is not."
A generalization of a triangle or tetrahedron to an arbitrary dimension, the generalization being the simplest possible convex polytope for a given dimension; more accurately, the convex hull of n+1 affinely independent points in n-dimensional space.
Common synonyms include: basic polytope, easy, elementary simplex, geometric, geometric cell, geometric simplex.
The word weak is a simplex. Its derivative weaken is not.
Pronounced /ˈsɪmplɛks/.
The adjective is a learned borrowing from Latin simplex (“plain, simple; single”). The first part, sim-, comes from Proto-Indo-European *sem-, *sm̥- (“one; together”). The second part, -plex, may be from *pleḱ- (“to weave”). The noun is derived from the adjective. The plural forms simplices and simplicia are learned borrowings from Latin simplicēs (masculine or feminine) and simplicia (neuter), respectively plural forms of simplex. Noun noun sense 1 (“generalization of a triangle or tetrahedron to an arbitrary dimension”) was apparently coined by the Dutch mathematician Pieter Hendrik Schoute (1846–1913) as a short version of Simplicissimum in Mehrdimensionale Geometrie (in German, 1902). (In his pioneering works on algebraic topology, the French mathematician Henri Poincaré (1854–1912) had previously introduced the concept, but not the actual term simplex.)