circle

Table of Contents

Introduction References & Edit History Related Topics

Images & Videos

Understand how to calculate a circle's area with the help of chain and ruler

Eccentricity of conic sectionsThe eccentricity of a conic section completely characterizes its shape. For example, all circles have zero eccentricity, and all parabolas have unit eccentricity; hence, all circles (and all parabolas) have the same shape, only varying in size. (Under appropriate magnification they are indistinguishable.) In contrast, ellipses and hyperbolas vary greatly in shape.

transformation of a circular region into an approximately rectangular region

Figure 11: Beltrami's circle model.

concentric circles and infinity

Projective conic sectionsThe conic sections (ellipse, parabola, and hyperbola) can be generated by projecting the circle formed by the intersection of a cone with a plane (the reality plane, or RP) perpendicular to the cone's central axis. The image of the circle is projected onto a plane (the projective plane, or PP) that is oriented at the same angle as the cutting plane (Ω) passing through the apex (“eye”) of the double cone. In this example, the orientation of Ω produces an ellipse in PP.

Figure 5: Intersecting circles. If a circle with centre A has a point X inside, as well as a point Y outside, a second circle with centre B, and if X and Y lie on AB, then the circles have at least one common point on each side of AB.

Chord in a circle

Pascal's projective theoremThe 17th-century French mathematician Blaise Pascal proved that the three points (x, y, z) formed by intersecting the six lines that connect any six distinct points (A, B, C, D, E, F) on a circle are collinear.

Discover

airplane in flight (plane, aircraft, flying)

7 Puzzling Plane Disappearances

An ancient egyptian hieroglyphic painted carving showing the falcon headed god Horus seated on a throne and holding a golden fly whisk. Before him are the Pharoah Seti and the goddess Isis. Interior wall of the temple to Osiris at Abydos, Egypt.

11 Egyptian Gods and Goddesses

Paul Revere. "The bloody massacre perpetrated in King Street Boston on March 5th 1770 by a party of the 29th Regt.," engraved by Paul Revere. Boston Massacre.

There’s a Riot Goin’ On: Riots in U.S. History (Part One)

New York NY/ USA- November 23, 2018 Hordes of shoppers throng the Macy's Herald Square flagship store in New York looking for bargains on the day after Thanksgiving, Black Friday.

Why Is It Called Black Friday?

Statue of Nostradamus

Nostradamus and His Prophecies

Close up of praying mantis walking on stone ground against a blurred background in Japan

6 Animals That Eat Their Mates

Dancers at a Cinco de Mayo festival at the Mission District, San Francisco, California. (Photo dated 2019.) holidays

Is Cinco de Mayo Mexico's Independence Day?

circle: Related Content

Written and fact-checked by The Information Architects of Encyclopaedia Britannica

Last Updated: Jun 10, 2025

News •

Circle IPO leaves $1.72 billion on the table, seventh biggest underpricing in decades • June 7, 2025, 5:37 AM ET (Fortune)

Circle's blockbuster IPO paves way for other crypto public listings • June 5, 2025, 11:04 PM ET (Reuters)

Stablecoin issuer Circle kicks off its IPO, targeting a nearly $6 billion valuation • May 27, 2025, 7:42 AM ET (CNBC)

Photos and Videos

Eccentricity of conic sectionsThe eccentricity of a conic section completely characterizes its shape. For example, all circles have zero eccentricity, and all parabolas have unit eccentricity; hence, all circles (and all parabolas) have the same shape, only varying in size. (Under appropriate magnification they are indistinguishable.) In contrast, ellipses and hyperbolas vary greatly in shape.

transformation of a circular region into an approximately rectangular region

Figure 11: Beltrami's circle model.

concentric circles and infinity

Projective conic sectionsThe conic sections (ellipse, parabola, and hyperbola) can be generated by projecting the circle formed by the intersection of a cone with a plane (the reality plane, or RP) perpendicular to the cone's central axis. The image of the circle is projected onto a plane (the projective plane, or PP) that is oriented at the same angle as the cutting plane (Ω) passing through the apex (“eye”) of the double cone. In this example, the orientation of Ω produces an ellipse in PP.

Figure 5: Intersecting circles. If a circle with centre A has a point X inside, as well as a point Y outside, a second circle with centre B, and if X and Y lie on AB, then the circles have at least one common point on each side of AB.

Chord in a circle

Pascal's projective theoremThe 17th-century French mathematician Blaise Pascal proved that the three points (x, y, z) formed by intersecting the six lines that connect any six distinct points (A, B, C, D, E, F) on a circle are collinear.

Figure 10: Poincaré's circle model.

Understand how to calculate a circle's area with the help of chain and ruler

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Topics

arc great circle circumference diameter radius pi conic section parabola ellipse hyperbola

Key People

John Machin

English mathematician

Quiz

Italian-born physicist Dr. Enrico Fermi draws a diagram at a blackboard with mathematical equations. circa 1950.

Define It: Math Terms

Equations written on blackboard

Numbers and Mathematics