# curve

Pronunciation: say "KURV" US /kɚv/, UK/AUS /kɜːv/

## Noun

1. A gentle bend, such as in a road or river.
   - Simple: A gentle bend in a road, path, or river.
   - _The highway follows a long curve around the lake._
   - _Engineers banked the curve so trains could take it at speed._
2. A simple figure made of a line that bends throughout, with no straight portions and no angles.
   - Simple: A smooth line that bends and has no straight parts or corners.
   - _The designer sketched a flowing curve across the logo._
   - _Each letter in the font is built from delicate curves._
6. The pleasing, curving lines of a woman's figure. *(colloquial)*
   - Simple: The attractive, rounded shape of a woman's body.
   - _The gown was tailored to flatter her curves._
   - _He admired the gentle curve of her waist._
7. A grading method that adjusts a group's scores against each other, reshaping a cluster of low marks into a bell-shaped spread so more students receive higher grades.
   - Simple: A way of grading where scores are adjusted so more students get higher marks.
   - _The professor applied a curve after the exam proved unexpectedly hard._
   - _Students complained that the curve rewarded the class's weakest performances._
9. A one-dimensional figure with length but no width, formed as the graph of a continuous map from a one-dimensional space.
   - Simple: A line that bends smoothly through space and has length but no width.
   - _The students plotted the curve defined by the equation._
   - _Smooth curves can be described by parametric equations._
10. A continuous map that sends each point of a one-dimensional space to a point in a multidimensional space.
   - Simple: In math, a rule that matches each point on a line to a spot in a larger space.
   - _Topologists treat the curve as a map rather than as the set of points it covers._
   - _Two different curves can sweep out exactly the same set of points._
11. A figure in the plane defined by a polynomial relation between the coordinates; an algebraic curve.
   - Simple: A bending line in math that comes from an equation linking two coordinates.
   - _The cubic equation defines a curve with a single loop._
   - _Elliptic curves play a central role in modern number theory._
12. A one-dimensional continuum, that is, a connected compact space with a single dimension.
   - Simple: In math, a connected shape that has only one dimension, such as length.
   - _In point-set topology, an arc is a basic example of a curve._
   - _Certain curves studied in topology are nowhere smooth._

## Verb

3. To bend something, shaping it into a rounded or hooked form.
   - Simple: To bend something into a rounded shape.
   - _The blacksmith curved the iron rod over an anvil._
   - _Potters curve the clay walls outward as the wheel spins._
4. To follow a path or take a shape that gradually changes direction.
   - Simple: To slowly bend or turn away from a straight line.
   - _Mountain trails often curve toward the valley floor._
   - _The comet's path curved as it neared the sun._
5. To cause something to swerve away from a straight course.
   - Simple: To make something move off a straight path.
   - _Skilled players curve the ball to bend it past the wall._
   - _The striker curved the free kick into the top corner._
8. To adjust a set of grades according to a bell curve, raising or lowering scores relative to the group's overall performance.
   - Simple: To change students' grades so the scores fit a balanced pattern and more pass.
   - _The department chose to curve the results when the average fell too low._
   - _Professors who curve their exams reward relative rather than absolute performance._
13. To reject someone's romantic advances; to turn a person down.
   - Simple: To say no to someone who is flirting with you or asking you out.
   - _He kept flirting even after she curved him twice._
   - _They curve anyone who slides into their messages with a corny line._

## Adjective

14. Bent without angles; crooked or curved in form. *(obsolete)*
   - Simple: Bent into a smooth shape, with no sharp corners.
   - _The mapmaker traced a curve path along the coastline._
   - _His walking stick ended in a curve handle._

## Origin

Attested since the 1690s, it comes from Latin curvus ("bent, curved"), which traces back to the Proto-Indo-European root *(s)ker- ("to bend, curve, turn"). It is a doublet of curb, shrink, carcer, and cancer.

Source: DictionaryAI, https://dictionaryai.com/define/curve (written from Wiktionary data, CC BY-SA 4.0: https://creativecommons.org/licenses/by-sa/4.0/).