• IPA: /ˈkɒŋkeɪv/

concave

1. curved like the inner surface of a sphere or bowl
2. (geometry, not comparable, of a polygon) not convex; having at least one internal angle greater than 180 degrees..
3. (functional analysis, not comparable, of a real-valued function on the reals) satisfying the property that all segments connecting two points on the function's graph lie below the function.
4. hollow; empty

   • c. 1598–1600, William Shakespeare, “As You Like It”, in Mr. William Shakespeares Comedies, Histories, & Tragedies: Published According to the True Originall Copies (First Folio), London: Printed by Isaac Iaggard, and Ed[ward] Blount, published 1623, OCLC 606515358 ↗, [Act III, scene iv]:

     as concave […] as a worm-eaten nut

• convex

• French: concave
• German: konkav
• Italian: concavo
• Portuguese: côncavo
• Russian: во́гнутый
• Spanish: cóncavo

concave (plural concaves)

1. A concave surface or curve.
2. The vault of the sky.
3. One of the celestial spheres of the Ptolemaic or geocentric model of the world.

   Aristotle makes [Fire] to move to the concave of the Moon. - Thomas Salusbury (1661).

4. (manufacturing) An element of a curved grid used to separate desirable material from tailings or chaff in mining and harvesting.
5. (surfing) An indentation running along the base of a surfboard, intended to increase lift.
6. (skateboarding) An indented area on the top of a skateboard, providing a position for foot placement and increasing board strength.

• Russian: невы́пуклый

concave (concaves, present participle concaving; past and past participle concaved)

1. To render concave, or increase the degree of concavity.