# Circle vs. Hypocycloid — What's the Difference?

## Definitions

#### Circle➦

A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre; equivalently it is the curve traced out by a point that moves in a plane so that its distance from a given point is constant. The distance between any point of the circle and the centre is called the radius.

#### Hypocycloid➦

In geometry, a hypocycloid is a special plane curve generated by the trace of a fixed point on a small circle that rolls within a larger circle. As the radius of the larger circle is increased, the hypocycloid becomes more like the cycloid created by rolling a circle on a line.

#### Circle➦

A round plane figure whose boundary (the circumference) consists of points equidistant from a fixed point (the centre)
Draw a circle with a compass

#### Hypocycloid➦

The plane locus of a point fixed on a circle that rolls on the inside circumference of a fixed circle.

#### Circle➦

A group of people with a shared profession, interests, or acquaintances
She did not normally move in such exalted circles

#### Hypocycloid➦

(geometry) The locus of a point on the circumference of a circle that rolls without slipping inside the circumference of another circle. Category:en:Curves

#### Circle➦

Move all the way around (someone or something), especially more than once
They were circling Athens airport
We circled round the island

#### Hypocycloid➦

A curve traced by a point in the circumference of a circle which rolls on the concave side in the fixed circle. Cf. Epicycloid, and Trochoid.

#### Circle➦

A plane curve everywhere equidistant from a given fixed point, the center.

#### Hypocycloid➦

A line generated by a point on a circle that rolls around inside another circle

#### Circle➦

A planar region bounded by a circle.

#### Circle➦

Something, such as a ring, shaped like such a plane curve.

#### Circle➦

A circular or nearly circular course, circuit, or orbit:a satellite's circle around the earth.

#### Circle➦

A traffic circle.

#### Circle➦

A series or process that finishes at its starting point or continuously repeats itself; a cycle.

#### Circle➦

A group of people sharing an interest, activity, or achievement:well-known in artistic circles.

#### Circle➦

A territorial or administrative division, especially of a province, in some European countries.

#### Circle➦

A sphere of influence or interest; domain.

#### Circle➦

(Logic)A vicious circle.

#### Circle➦

To make or form a circle around:The hedge circles the fountain.

#### Circle➦

To move in a circle around:The ship circled the island.

#### Circle➦

To move in a circle.

#### Circle➦

(geometry) A two-dimensional geometric figure, a line, consisting of the set of all those points in a plane that are equally distant from a given point (center).
The set of all points (x, y) such that {{(x
R2}} is a circle of radius r around the point (1, 0).

#### Circle➦

A two-dimensional geometric figure, a disk, consisting of the set of all those points of a plane at a distance less than or equal to a fixed distance (radius) from a given point.

#### Circle➦

Any shape, curve or arrangement of objects that approximates to or resembles the geometric figures.
Children, please join hands and form a circle.

#### Circle➦

Any thin three-dimensional equivalent of the geometric figures.
Cut a circle out of that sheet of metal.

#### Circle➦

A curve that more or less forms part or all of a circle.
The crank moves in a circle.

#### Circle➦

A specific group of persons; especially one who shares a common interest.
Inner circle
Circle of friends
Literary circle

#### Circle➦

The orbit of an astronomical body.

#### Circle➦

(cricket) A line comprising two semicircles of 30 yards radius centred on the wickets joined by straight lines parallel to the pitch used to enforce field restrictions in a one-day match.

#### Circle➦

(Wicca) A ritual circle that is cast three times deosil and closes three times widdershins either in the air with a wand or literally with stones or other items used for worship.

#### Circle➦

A traffic circle or roundabout.

#### Circle➦

(obsolete) Compass; circuit; enclosure.

#### Circle➦

(astronomy) An instrument of observation, whose graduated limb consists of an entire circle. When fixed to a wall in an observatory, it is called a mural circle; when mounted with a telescope on an axis and in Y's, in the plane of the meridian, a meridian or transit circle; when involving the principle of reflection, like the sextant, a reflecting circle; and when that of repeating an angle several times continuously along the graduated limb, a repeating circle.

#### Circle➦

A series ending where it begins, and repeating itself.

#### Circle➦

(logic) A form of argument in which two or more unproved statements are used to prove each other; inconclusive reasoning.

#### Circle➦

Indirect form of words; circumlocution.

#### Circle➦

A territorial division or district.
The ten Circles of the Holy Roman Empire were those principalities or provinces which had seats in the German Diet.

#### Circle➦

(in the plural) A bagginess of the skin below the eyes from lack of sleep.
After working all night, she had circles under her eyes.

#### Circle➦

(transitive) To travel around along a curved path.
The wolves circled the herd of deer.

#### Circle➦

(transitive) To surround.
A high fence circles the enclosure.

#### Circle➦

(transitive) To place or mark a circle around.
Circle the jobs that you are interested in applying for.

#### Circle➦

(intransitive) To travel in circles.

#### Circle➦

A plane figure, bounded by a single curve line called its circumference, every part of which is equally distant from a point within it, called the center.

#### Circle➦

The line that bounds such a figure; a circumference; a ring.

#### Circle➦

An instrument of observation, the graduated limb of which consists of an entire circle.

#### Circle➦

A round body; a sphere; an orb.
It is he that sitteth upon the circle of the earth.

#### Circle➦

Compass; circuit; inclosure.
In the circle of this forest.

#### Circle➦

A company assembled, or conceived to assemble, about a central point of interest, or bound by a common tie; a class or division of society; a coterie; a set.
As his name gradually became known, the circle of his acquaintance widened.

#### Circle➦

A circular group of persons; a ring.

#### Circle➦

A series ending where it begins, and repeating itself.
Thus in a circle runs the peasant's pain.

#### Circle➦

A form of argument in which two or more unproved statements are used to prove each other; inconclusive reasoning.
That heavy bodies descend by gravity; and, again, that gravity is a quality whereby a heavy body descends, is an impertinent circle and teaches nothing.

#### Circle➦

Indirect form of words; circumlocution.
Has he given the lie,In circle, or oblique, or semicircle.

#### Circle➦

A territorial division or district.

#### Circle➦

To move around; to revolve around.
Other planets circle other suns.

#### Circle➦

To encompass, as by a circle; to surround; to inclose; to encircle.
Their heads are circled with a short turban.
So he lies, circled with evil.

#### Circle➦

To move circularly; to form a circle; to circulate.
Thy name shall circle round the gaping through.

#### Circle➦

Ellipse in which the two axes are of equal length; a plane curve generated by one point moving at a constant distance from a fixed point;
He calculated the circumference of the circle

#### Circle➦

An unofficial association of people or groups;
The smart set goes there
They were an angry lot

#### Circle➦

Something approximating the shape of a circle;
The chairs were arranged in a circle

#### Circle➦

Movement once around a course;
He drove an extra lap just for insurance

#### Circle➦

A road junction at which traffic streams circularly around a central island;
The accident blocked all traffic at the rotary

#### Circle➦

Street names for flunitrazepan

#### Circle➦

A curved section or tier of seats in a hall or theater or opera house; usually the first tier above the orchestra;
They had excellent seats in the dress circle

#### Circle➦

Any circular or rotating mechanism;
The machine punched out metal circles

#### Circle➦

Travel around something;
Circle the globe

Move in circles

#### Circle➦

Be around;
Developments surround the town
The river encircles the village

#### Circle➦

Form a circle around;
Encircle the errors