Plane vs. Surface — What's the Difference?
By Maham Liaqat & Urooj Arif — Updated on April 22, 2024
Plane generally refers to a flat, two-dimensional surface extending infinitely in all directions, while a surface is any outer face or boundary of a solid object.
Difference Between Plane and Surface
Table of Contents
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Key Differences
A plane is a fundamental concept in geometry, representing an idealized flat surface with no thickness and extending infinitely in all directions. It's defined by three non-collinear points or a point and a normal vector. On the other hand, a surface includes a wider variety of forms, including both flat and curved dimensions, which can be limited or extend indefinitely.
Planes are strictly two-dimensional, meaning they have length and width but no depth, making them ideal for mathematical and theoretical studies in fields like geometry and algebra. Surfaces, however, vary in dimensionality and can include shapes like spheres, cylinders, and more complex topologies in three-dimensional space.
In terms of application, planes are often used in mathematical proofs, architectural designs, and computer graphics to simplify calculations and representations. Whereas surfaces are crucial in more physically grounded applications like aerodynamics, industrial design, and topographical modeling.
Visualization of a plane is typically represented by a flat grid or sheet, emphasizing its uniformity and simplicity. In contrast, surfaces are visualized according to their nature; for example, a globe represents a spherical surface, illustrating the diversity and complexity possible with surfaces.
The concept of a plane is more abstract and theoretical, often serving as a building block for more complex mathematical concepts and theories. Surface, however, is a more tangible concept, directly applicable to physical objects and real-world scenarios, reflecting its practical importance across various scientific and engineering disciplines.
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Comparison Chart
Dimensions
Two-dimensional
Can be two- or three-dimensional
Curvature
Always flat
Can be flat or curved
Boundaries
Infinite (no edges or boundaries)
Can be finite or infinite
Defining Characteristics
Defined by three non-collinear points or a point and a normal vector
Defined by its geometry (e.g., planes, curves)
Applications
Used in mathematical theories, architecture
Used in practical applications like design, engineering
Compare with Definitions
Plane
Used in physics to describe hypothetical surfaces.
The mirror's reflection can be modeled as light interacting with a plane.
Surface
In computer modeling, a representation of an object's exterior.
The 3D model's surface was textured to add realism.
Plane
A flat, two-dimensional surface extending infinitely.
The artist drew a perfect straight line on the infinite plane.
Surface
The outermost layer of an object, which can be flat or curved.
The surface of the water was disturbed by the falling stone.
Plane
In architecture, a representation to visualize structures.
The architect used several planes to delineate the new building's layout.
Surface
In art, the canvas or material on which an artist works.
The painter applied a thick layer of paint across the canvas's surface.
Plane
A concept in geometry used to define linear equations.
The equation x + y = 1 defines a plane in a Cartesian coordinate system.
Surface
In physics, the interface between two phases.
Oil and water form a distinct surface at their boundary.
Plane
In computer graphics, a tool to simulate environments.
Video game developers use planes to create flat terrains.
Surface
In mathematics, a two- or three-dimensional boundary of a volume.
The sphere's surface is perfectly smooth.
Plane
(Mathematics) A surface containing all the straight lines that connect any two points on it.
Surface
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.
Plane
A flat or level surface.
Surface
The outside part or uppermost layer of something
Poor road surfaces
The earth's surface
Plane
A level of development, existence, or achievement
Scholarship on a high plane.
Surface
A continuous set of points that has length and breadth but no thickness.
Plane
An airplane or hydroplane.
Surface
Relating to or found on the surface of something
Surface layers
Plane
A supporting surface of an airplane; an airfoil or wing.
Surface
Rise or come up to the surface of the water or the ground
He surfaced from his dive
Plane
A carpenter's tool with an adjustable blade for smoothing and leveling wood.
Surface
Provide (something, especially a road) with a particular surface
A small path surfaced with terracotta tiles
Plane
A trowel-shaped tool for smoothing the surface of clay, sand, or plaster in a mold.
Surface
The outer or the topmost boundary of an object.
Plane
The plane tree.
Surface
A material layer constituting such a boundary.
Plane
(Mathematics) Of or being a figure lying in a plane
A plane curve.
Surface
The boundary of a three-dimensional figure.
Plane
Flat; level.
Surface
The two-dimensional locus of points located in three-dimensional space.
Plane
To smooth or finish with a plane
Planed the door.
Surface
A portion of space having length and breadth but no thickness.
Plane
To remove with a plane
Plane off the rough edges on a board.
Surface
The superficial or external aspect
"a flamboyant, powerful confidence man who lives entirely on the surface of experience" (Frank Conroy).
Plane
To work with a plane.
Surface
An airfoil.
Plane
To rise partly out of the water, as a hydroplane does at high speeds.
Surface
Relating to, on, or at a surface
Surface algae in the water.
Plane
To soar or glide.
Surface
Relating to or occurring on or near the surface of the earth.
Plane
To travel by airplane.
Surface
Superficial.
Plane
Of a surface: flat or level.
Surface
Apparent as opposed to real.
Plane
A level or flat surface.
Surface
To provide with a surface or apply a surface to
Surface a table with walnut.
Surface a road with asphalt.
Plane
(geometry) A flat surface extending infinitely in all directions (e.g. horizontal or vertical plane). Category:en:Surfaces
Surface
To bring to the surface
Surface a submarine.
Plane
(anatomy) An imaginary plane which divides the body into two portions.
Surface
To make known; expose or reveal
The first news report that surfaced the allegations.
Plane
A level of existence or development.
Astral plane
Surface
To rise to the surface.
Plane
A roughly flat, thin, often moveable structure used to create lateral force by the flow of air or water over its surface, found on aircraft, submarines, etc. (Compare airfoil, hydrofoil.)}}
Surface
To emerge after concealment.
Plane
Any of 17 designated ranges of 216 (65,536) sequential code points each.
Surface
To work or dig a mine at or near the surface of the ground.
Plane
A tool for smoothing wood by removing thin layers from the surface.
Surface
The overside or up-side of a flat object such as a table, or of a liquid.
Plane
An airplane; an aeroplane.
Surface
The outside hull of a tangible object.
Plane
(entomology) Any of various nymphalid butterflies, of various genera, having a slow gliding flight.
Surface
(figurative) Outward or external appearance.
On the surface, the spy looked like a typical businessman.
Plane
(entomology) The butterfly Bindahara phocides, family Lycaenidae, of Asia and Australasia.
Surface
The locus of an equation (especially one with exactly two degrees of freedom) in a more-than-two-dimensional space. Category:en:Surfaces
Plane
(countable) A deciduous tree of the genus Platanus.
Surface
(transitive) To provide something with a surface.
Plane
(Northern UK) A sycamore.
Surface
(transitive) To apply a surface to something.
The crew surfaced the road with bitumen.
Plane
To smooth (wood) with a plane.
Surface
(intransitive) To rise to the surface.
There was great relief when the missing diver finally surfaced.
Plane
To move in a way that lifts the bow out of the water.
Surface
(transitive) To bring to the surface.
Plane
To glide or soar.
Surface
To come out of hiding.
Plane
Any tree of the genus Platanus.
Surface
To become known or apparent; to appear or be found.
Plane
A surface, real or imaginary, in which, if any two points are taken, the straight line which joins them lies wholly in that surface; or a surface, any section of which by a like surface is a straight line; a surface without curvature.
Surface
(transitive) To make (information or facts) known.
Plane
An ideal surface, conceived as coinciding with, or containing, some designated astronomical line, circle, or other curve; as, the plane of an orbit; the plane of the ecliptic, or of the equator.
Surface
(intransitive) To work a mine near the surface.
Plane
A block or plate having a perfectly flat surface, used as a standard of flatness; a surface plate.
Surface
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 bright surface of this ethereous mold.
Plane
A tool for smoothing boards or other surfaces of wood, for forming moldings, etc. It consists of a smooth-soled stock, usually of wood, from the under side or face of which projects slightly the steel cutting edge of a chisel, called the iron, which inclines backward, with an apperture in front for the escape of shavings; as, the jack plane; the smoothing plane; the molding plane, etc.
Surface
Hence, outward or external appearance.
Vain and weak understandings, which penetrate no deeper than the surface.
Plane
Without elevations or depressions; even; level; flat; lying in, or constituting, a plane; as, a plane surface.
Surface
A magnitude that has length and breadth without thickness; superficies; as, a plane surface; a spherical surface.
Plane
To make smooth; to level; to pare off the inequalities of the surface of, as of a board or other piece of wood, by the use of a plane; as, to plane a plank.
Surface
That part of the side which is terminated by the flank prolonged, and the angle of the nearest bastion.
Plane
To efface or remove.
He planed away the names . . . written on his tables.
Surface
To give a surface to; especially, to cause to have a smooth or plain surface; to make smooth or plain.
Plane
Figuratively, to make plain or smooth.
What student came but that you planed her path.
Surface
To work over the surface or soil of, as ground, in hunting for gold.
Plane
Of a boat, to lift more or less out of the water while in motion, after the manner of a hydroplane; to hydroplane.
Surface
To rise from the depths of a liquid to the surface; as, the submarine surfaced to recharge its batteries.
Plane
An aircraft that has a fixed wing and is powered by propellers or jets;
The flight was delayed due to trouble with the airplane
Surface
To become known or public; - said of information.
Plane
(mathematics) an unbounded two-dimensional shape;
We will refer to the plane of the graph as the X-Y plane
Any line joining two points on a plane lies wholly on that plane
Surface
To show up, as a person who was in hiding; as, he absconded with the payroll and surfaced in Argentina.
Plane
A level of existence or development;
He lived on a worldly plane
Surface
The outer boundary of an artifact or a material layer constituting or resembling such a boundary;
There is a special cleaner for these surfaces
The cloth had a pattern of red dots on a white surface
Plane
A power tool for smoothing or shaping wood
Surface
The extended two-dimensional outer boundary of a three-dimensional object;
They skimmed over the surface of the water
A brush small enough to clean every dental surface
The sun has no distinct surface
Plane
A carpenter's hand tool with an adjustable blade for smoothing or shaping wood;
The cabinetmaker used a plane for the finish work
Surface
The outermost level of the land or sea;
Earthquakes originate far below the surface
Three quarters of the Earth's surface is covered by water
Plane
Cut or remove with or as if with a plane;
The machine shaved off fine layers from the piece of wood
Surface
A superficial aspect as opposed to the real nature of something;
It was not what it appeared to be on the surface
Plane
Travel on the surface of water
Surface
Information that has become public;
All the reports were out in the open
The facts had been brought to the surface
Plane
Make even or smooth, with or as with a carpenter's plane;
Plane the top of the door
Surface
A device that provides reactive force when in motion relative to the surrounding air; can lift or control a plane in flight
Plane
Having a horizontal surface in which no part is higher or lower than another;
A flat desk
Acres of level farmland
A plane surface
Surface
Come to the surface
Surface
Put a coat on; cover the surface of; furnish with a surface;
Coat the cake with chocolate
Surface
Appear or become visible; make a showing;
She turned up at the funeral
I hope the list key is going to surface again
Surface
On the surface;
Surface materials of the moon
Subsurface materials of the moon
Surface
Involving a surface only;
Her beauty is only skin-deep
Superficial bruising
A surface wound
Common Curiosities
How do planes differ from flat surfaces?
While all planes are flat surfaces, not all flat surfaces are planes; for example, a flat surface could have finite boundaries.
What types of surfaces are there?
Surfaces can be planar (flat), curved (like spheres or cylinders), or irregular, and can be either two- or three-dimensional.
What defines a plane in geometry?
A plane is defined by three non-collinear points or a point and a normal vector, extending infinitely without curvature.
How are planes used in computer graphics?
Planes are used in computer graphics to create environments and simulate horizons or flat terrains.
Can a surface be a plane?
Yes, a surface can be a plane if it is perfectly flat and extends infinitely.
What role do surfaces play in physics?
In physics, surfaces define interactions at boundaries, such as between different phases of matter.
How do mathematicians use the concept of surfaces?
Mathematicians study surfaces to understand complex geometries and topologies, crucial in fields like topology and differential geometry.
Are planes considered three-dimensional?
Planes are not considered three-dimensional; they are two-dimensional since they only have length and width.
What is the practical application of studying surfaces?
Studying surfaces is crucial in fields like material science, engineering, and art, where understanding the properties of surfaces can impact design and functionality.
Is there a difference in how planes and surfaces are visualized?
Yes, planes are generally visualized as flat grids, whereas surfaces might be depicted as curved or irregular shapes depending on their nature.
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Written by
Maham LiaqatCo-written by
Urooj ArifUrooj is a skilled content writer at Ask Difference, known for her exceptional ability to simplify complex topics into engaging and informative content. With a passion for research and a flair for clear, concise writing, she consistently delivers articles that resonate with our diverse audience.