Curve vs. Surface — What's the Difference?

In mathematics, a curve (also called a curved line in older texts) is an object similar to a line, but that does not have to be straight. Intuitively, a curve may be thought of as the trace left by a moving point.

A surface, as the term is most generally used, is the outermost or uppermost layer of a physical object or space. It is the portion or region of the object that can first be perceived by an observer using the senses of sight and touch, and is the portion with which other materials first interact.

A line that deviates from straightness in a smooth, continuous fashion.

The outside part or uppermost layer of something

A surface that deviates from planarity in a smooth, continuous fashion.

A continuous set of points that has length and breadth but no thickness.

Something characterized by such a line or surface, especially a rounded line or contour of the human body.

Relating to or found on the surface of something

A relatively smooth bend in a road or other course.

Rise or come up to the surface of the water or the ground

A line representing data on a graph.

Provide (something, especially a road) with a particular surface

A trend derived from or as if from such a graph

The outer or the topmost boundary of an object.

A graphic representation showing the relative performance of individuals as measured against each other, used especially as a method of grading students in which the assignment of grades is based on predetermined proportions of students.

A material layer constituting such a boundary.

The graph of a function on a coordinate plane.

The boundary of a three-dimensional figure.

The intersection of two surfaces in three dimensions.

The two-dimensional locus of points located in three-dimensional space.

The graph of the solutions to any equation of two variables.

A portion of space having length and breadth but no thickness.

(Baseball) A curve ball.

The superficial or external aspect

(Slang) Something that is unexpected or designed to trick or deceive.

An airfoil.

To move in or take the shape of a curve

Relating to, on, or at a surface

To cause to curve.

Relating to or occurring on or near the surface of the earth.

(Baseball) To pitch (a ball) with a curve.

Superficial.

To grade (students, for example) on a curve.

Apparent as opposed to real.

(obsolete) Bent without angles; crooked; curved. Category:en:Curves

To provide with a surface or apply a surface to

A gentle bend, such as in a road.

To bring to the surface

A simple figure containing no straight portions and no angles; a curved line.

To make known; expose or reveal

A grading system based on the scale of performance of a group used to normalize a right-skewed grade distribution (with more lower scores) into a bell curve, so that more can receive higher grades, regardless of their actual knowledge of the subject.

To rise to the surface.

(analytic geometry) A continuous map from a one-dimensional space to a multidimensional space.

To emerge after concealment.

(geometry) A one-dimensional figure of non-zero length; the graph of a continuous map from a one-dimensional space.

To work or dig a mine at or near the surface of the ground.

(algebraic geometry) An algebraic curve; a polynomial relation of the planar coordinates.

The overside or up-side of a flat object such as a table, or of a liquid.

(topology) A one-dimensional continuum.

The outside hull of a tangible object.

The attractive shape of a woman's body.

(figurative) Outward or external appearance.

(transitive) To bend; to crook.

The locus of an equation (especially one with exactly two degrees of freedom) in a more-than-two-dimensional space. Category:en:Surfaces

(transitive) To cause to swerve from a straight course.

(transitive) To provide something with a surface.

(intransitive) To bend or turn gradually from a given direction.

(transitive) To apply a surface to something.

(transitive) To grade on a curve (bell curve of a normal distribution).

(intransitive) To rise to the surface.

(transitive) (slang) To reject, to turn down romantic advances.

(transitive) To bring to the surface.

Bent without angles; crooked; curved; as, a curve line; a curve surface.

To come out of hiding.

A bending without angles; that which is bent; a flexure; as, a curve in a railway or canal.

To become known or apparent; to appear or be found.

A line described according to some low, and having no finite portion of it a straight line.

(transitive) To make (information or facts) known.

To bend; to crook; as, to curve a line; to curve a pipe; to cause to swerve from a straight course; as, to curve a ball in pitching it.

(intransitive) To work a mine near the surface.

To bend or turn gradually from a given direction; as, the road curves to the right.

The exterior part of anything that has length and breadth; one of the limits that bound a solid, esp. the upper face; superficies; the outside; as, the surface of the earth; the surface of a diamond; the surface of the body.

The trace of a point whose direction of motion changes

Hence, outward or external appearance.

A line on a graph representing data

A magnitude that has length and breadth without thickness; superficies; as, a plane surface; a spherical surface.

A baseball thrown with spin so that its path curves as it approach the batter

That part of the side which is terminated by the flank prolonged, and the angle of the nearest bastion.

The property possessed by the curving of a line or surface

To give a surface to; especially, to cause to have a smooth or plain surface; to make smooth or plain.

Curved segment (of a road or river or railroad track etc.)

To work over the surface or soil of, as ground, in hunting for gold.

Turn sharply; change direction abruptly;

To rise from the depths of a liquid to the surface; as, the submarine surfaced to recharge its batteries.

Extend in curves and turns;

To become known or public; - said of information.

Form an arch or curve;

To show up, as a person who was in hiding; as, he absconded with the payroll and surfaced in Argentina.

Bend or cause to bend;

The outer boundary of an artifact or a material layer constituting or resembling such a boundary;

Form a curl, curve, or kink;

The extended two-dimensional outer boundary of a three-dimensional object;

The outermost level of the land or sea;

A superficial aspect as opposed to the real nature of something;

Information that has become public;

A device that provides reactive force when in motion relative to the surrounding air; can lift or control a plane in flight

Come to the surface

Put a coat on; cover the surface of; furnish with a surface;

Appear or become visible; make a showing;

On the surface;

Involving a surface only;