In

geometryGeometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....

,

physicsPhysics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...

,

astronomyAstronomy is a natural science that deals with the study of celestial objects and phenomena that originate outside the atmosphere of Earth...

,

geographyGeography is the science that studies the lands, features, inhabitants, and phenomena of Earth. A literal translation would be "to describe or write about the Earth". The first person to use the word "geography" was Eratosthenes...

, and related sciences, a

**plane**In mathematics, a plane is a flat, two-dimensional surface. A plane is the two dimensional analogue of a point , a line and a space...

is said to be

**horizontal** at a given point if it is perpendicular to the

gradientIn vector calculus, the gradient of a scalar field is a vector field that points in the direction of the greatest rate of increase of the scalar field, and whose magnitude is the greatest rate of change....

of the

gravityGravitation, or gravity, is a natural phenomenon by which physical bodies attract with a force proportional to their mass. Gravitation is most familiar as the agent that gives weight to objects with mass and causes them to fall to the ground when dropped...

fieldIn physics, a field is a physical quantity associated with each point of spacetime. A field can be classified as a scalar field, a vector field, a spinor field, or a tensor field according to whether the value of the field at each point is a scalar, a vector, a spinor or, more generally, a tensor,...

at that point— in other words, if apparent gravity makes a plumb bob hang perpendicular to the plane at that point.

In

radioRadio is the transmission of signals through free space by modulation of electromagnetic waves with frequencies below those of visible light. Electromagnetic radiation travels by means of oscillating electromagnetic fields that pass through the air and the vacuum of space...

science,

**horizontal plane** is used to plot an antenna's relative

field strengthIn physics, the field strength of a field is the magnitude of its vector value.In theoretical physics, field strength is another name for the curvature form...

in relation to the ground (which directly affects a station's coverage area) on a

polar graphIn mathematics, the polar coordinate system is a two-dimensional coordinate system in which each point on a plane is determined by a distance from a fixed point and an angle from a fixed direction....

. Normally the maximum of 1.000 or 0

dBThe decibel is a logarithmic unit that indicates the ratio of a physical quantity relative to a specified or implied reference level. A ratio in decibels is ten times the logarithm to base 10 of the ratio of two power quantities...

is at the top, which is labeled 0

^{o}, running clockwise back around to the top at 360°. Other field strengths are expressed as a decimal less than 1.000, a percentage less than 100%, or decibels less than 0 dB. If the graph is of an actual or proposed installation,

rotationA rotation is a circular movement of an object around a center of rotation. A three-dimensional object rotates always around an imaginary line called a rotation axis. If the axis is within the body, and passes through its center of mass the body is said to rotate upon itself, or spin. A rotation...

is

applied so that the top is 0

^{o} true northTrue north is the direction along the earth's surface towards the geographic North Pole.True geodetic north usually differs from magnetic north , and from grid north...

. See also the perpendicular

vertical planeVertical plane is used in radio to plot an antenna's relative field strength perpendicular to the ground on a polar graph....

.

In general, something that is horizontal can be drawn from left to right (or right to left), such as the x-axis in the

Cartesian coordinate systemA Cartesian coordinate system specifies each point uniquely in a plane by a pair of numerical coordinates, which are the signed distances from the point to two fixed perpendicular directed lines, measured in the same unit of length...

.

## Discussion

Although the word

*horizontal* is common in daily life and language (see below), it is subject to many misconceptions.

- The concept of horizontality only makes sense in the context of a clearly measurable gravity field, i.e., in the 'neighborhood' of a planet, star, etc. When the gravity field becomes very weak (the masses are too small or too distant from the point of interest), the notion of being horizontal loses its meaning.

- A plane is horizontal only at the chosen point. Horizontal planes at two separate points are not parallel, they intersect.

- In general, a horizontal plane will only be perpendicular to a vertical direction
In astronomy, geography, geometry and related sciences and contexts, a direction passing by a given point is said to be vertical if it is locally aligned with the gradient of the gravity field, i.e., with the direction of the gravitational force at that point...

if both are specifically defined with respect to the same point: a direction is only vertical at the point of reference. Thus both horizontality and verticality are strictly speaking local concepts, and it is always necessary to state to which location the direction or the plane refers to. Note that (1) the same restriction applies to the straight lines contained within the plane: they are horizontal only at the point of reference, and (2) those straight lines contained in the plane but not passing by the reference point are not horizontal anywhere.

- In reality, the gravity field of a heterogeneous planet such as Earth
Earth is the third planet from the Sun, and the densest and fifth-largest of the eight planets in the Solar System. It is also the largest of the Solar System's four terrestrial planets...

is deformed due to the inhomogeneous spatial distribution of materials with different densitiesThe mass density or density of a material is defined as its mass per unit volume. The symbol most often used for density is ρ . In some cases , density is also defined as its weight per unit volume; although, this quantity is more properly called specific weight...

. Actual horizontal planes are thus not even parallel even if their reference points are along the same vertical line, since a vertical line is slightly curved.

- At any given location, the total gravitational force is not quite constant over time
Time is a part of the measuring system used to sequence events, to compare the durations of events and the intervals between them, and to quantify rates of change such as the motions of objects....

, because the objects that generate the gravity are moving. For instance, on Earth the horizontal plane at a given point (as determined by a pair of spirit levelA spirit level or bubble level is an instrument designed to indicate whether a surface ishorizontal or vertical . Different types of spirit levels may be used by carpenters, stonemasons, bricklayers, other building trades workers, surveyors, millwrights and other metalworkers, and in some...

s) changes with the position of the Moon (air, sea and land tideTides are the rise and fall of sea levels caused by the combined effects of the gravitational forces exerted by the moon and the sun and the rotation of the Earth....

s).

- On a rotating planet such as Earth, the strictly gravitational pull of the planet (and other celestial objects such as the Moon, the Sun
The Sun is the star at the center of the Solar System. It is almost perfectly spherical and consists of hot plasma interwoven with magnetic fields...

, etc.) is different from the apparent net force (e.g., on a free-falling object) that can be measured in the laboratory or in the field. This difference is the centrifugal force associated with the planet's rotation. This is a fictitious forceA fictitious force, also called a pseudo force, d'Alembert force or inertial force, is an apparent force that acts on all masses in a non-inertial frame of reference, such as a rotating reference frame....

: it only arises when calculations or experiments are conducted in non-inertial frames of referenceIn physics, an inertial frame of reference is a frame of reference that describes time homogeneously and space homogeneously, isotropically, and in a time-independent manner.All inertial frames are in a state of constant, rectilinear motion with respect to one another; they are not...

, such as the surface of the Earth.

## Practical use in daily life

The concept of a horizontal plane is thus anything but simple, although, in practice, most of these effects and variations are rather small: they are measurable and can be predicted with great accuracy, but they may not greatly affect our daily life.

This dichotomy between the apparent simplicity of a concept and an actual complexity of defining (and measuring) it in scientific terms arises from the fact that the typical linear scales and dimensions of relevance in daily life are 3 orders of magnitude (or more) smaller than the size of the Earth. Hence, the world appears to be flat locally, and horizontal planes in nearby locations appear to be parallel. Such statements are nevertheless approximations; whether they are acceptable in any particular context or application depends on the applicable requirements, in particular in terms of accuracy.

In graphical contexts, such as

drawing and draftingTechnical drawing, also known as drafting or draughting, is the act and discipline of composing plans that visually communicate how something functions or has to be constructed.Drafting is the language of industry....

on rectangular paper, it is very common to associate one of the dimensions of the paper with a horizontal, even though the entire sheet of paper is standing on a flat horizontal (or slanted) table. In this case, the horizontal direction is typically from the left side of the paper to the right side. This is purely conventional (although it is somehow 'natural' when drawing a natural scene as it is seen in reality), and may lead to misunderstandings or misconceptions, especially in an educational context.