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出典:Wiktionary
出典:『Wiktionary』 (2025/10/08 19:09 UTC 版)
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 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.)
simplex (not comparable)
simplex (plural simplexes or (algebraic topology, geometry, linguistics) simplices or simplicia)
| Examples (algebraic topology, geometry) |
|---|
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| 10 | ||||
| I 1 |
2 → | 10 → | ||
|---|---|---|---|---|
| Cardinal: ūnus Ordinal: prīmus Adverbial: semel Proportional: simplus Multiplier: simplex Distributive: singulus Collective: ūniō Fractional: integer |
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From sem- (“one; single-”) + -plex (“-fold”). The first element (from Proto-Indo-European *sem-, *sm̥-) does not occur independently in Latin, but is also seen in semel (“once”) and semper (“always, forever”). De Vaan reconstructs Proto-Italic *sm̥-plak-s, but also reconstructs Proto-Italic *-plek-s.
simplex (genitive simplicis, comparative simplicior, superlative simplicissimus, adverb simpliciter); third-declension one-termination adjective
Third-declension one-termination adjective.
| singular | plural | ||||
|---|---|---|---|---|---|
| masc./fem. | neuter | masc./fem. | neuter | ||
| nominative | simplex | simplicēs | simplicia | ||
| genitive | simplicis | simplicium | |||
| dative | simplicī | simplicibus | |||
| accusative | simplicem | simplex | simplicēs | simplicia | |
| ablative | simplicī | simplicibus | |||
| vocative | simplex | simplicēs | simplicia | ||
出典:Wikipedia
出典:『Wikipedia』 (2011/05/13 01:50 UTC 版)
In geometry, a simplex (plural simplexes or simplices) is a generalization of the notion of a triangle or tetrahedron to arbitrary dimension. Specifically, an n-simplex is an n-dimensional polytope which is the convex hull of its n + 1 vertices. For example, a 2-simplex is a triangle, a 3-simplex is a tetrahedron, and a 4-simplex is a pentachoron. A single point may be considered a 0-simplex, and a line segment may be considered a 1-simplex. A simplex may be defined as the smallest convex set containing the given vertices.
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