Illustration showing the golden angle. The golden angle is the smaller of two angles created by dividing the circumference of a circle according to the golden section. The ratio of the length of the larger arc to the smaller arc is equal to the ratio of the entire circumference to the larger arc. The golden angle is approximately 137.51°.

Golden Angle

Illustration showing the golden angle. The golden angle is the smaller of two angles created by dividing…

Illustration used to show how to bisect a given arc.

Bisecting an Arc

Illustration used to show how to bisect a given arc.

Illustration used to show how to "find an arc of a circle having a known radius, which shall be equal in length to a given straight line."

Construction Of Arc

Illustration used to show how to "find an arc of a circle having a known radius, which shall be equal…

Illustration showing arcs measured in positive and negative angles.

Positive and Negative Arcs in Circles

Illustration showing arcs measured in positive and negative angles.

Illustration used to show how to find the center when given an arc and its radius.

Construction Of Center

Illustration used to show how to find the center when given an arc and its radius.

Illustration of a circle with the arc aeb drawn and labeled.

Arc of Circle

Illustration of a circle with the arc aeb drawn and labeled.

An illustration of an arc of a circle. An arc is any part of the circumference of a circle.

Arc of Circle

An illustration of an arc of a circle. An arc is any part of the circumference of a circle.

Illustrations of a circle with arc, chord, inscribed angle, and circumscribed about a polygon.

Circle with Arc, Chord, Inscribed Angle, Circumscribed Polygon

Illustrations of a circle with arc, chord, inscribed angle, and circumscribed about a polygon.

Illustration of circle with arc and chord.

Arc and Chord in Circle

Illustration of circle with arc and chord.

A design created by inscribing 4 congruent tangent arcs in a circle.

Arcs Inscribed In A Circle

A design created by inscribing 4 congruent tangent arcs in a circle.

Illustration of a circle showing an angle included by a tangent and a chord drawn from the point of contact. The angle is measured by half the intercepted arc.

Circle With Chord and Tangent

Illustration of a circle showing an angle included by a tangent and a chord drawn from the point of…

Illustration of circle with arc, chord, diameter  and radius.

Parts of Circle

Illustration of circle with arc, chord, diameter and radius.

Illustration of circle with quadrant and 60 degree arc.

Quadrant of Circle With 60 degree Arc

Illustration of circle with quadrant and 60 degree arc.

An illustration showing a circle with radius r, diameter d, and chord c.

Radius, Diameter, and Chord In A Circle

An illustration showing a circle with radius r, diameter d, and chord c.

Illustration of a sector of a circle. A sector is the space between an arc and two radii drawn to the extremities of the arc.

Sector Of Circle

Illustration of a sector of a circle. A sector is the space between an arc and two radii drawn to the…

Illustration of a sector of a hollow circle. A sector is the space between an arc and two radii drawn to the extremities of the arc.

Sector Of A Hollow Circle

Illustration of a sector of a hollow circle. A sector is the space between an arc and two radii drawn…

Illustration of a circle with two intersecting chords within the circumference. The angle formed is measured by half the sum of the intercepted arcs.

Circle With Two Intersecting Chords

Illustration of a circle with two intersecting chords within the circumference. The angle formed is…

Illustration showing that from any point in the circumference of a circle, a chord and a tangent are drawn, the perpendiculars dropped on them from the middle point of the subtended arc are equal.

Circle With a Tangent Line and Chord

Illustration showing that from any point in the circumference of a circle, a chord and a tangent are…

Illustration used to show that "In equal circles, or in the same circle, if two chords are unequal, the greater chord is at the less distance from the center."

Unequal Chords in Equal Circles Theorem

Illustration used to show that "In equal circles, or in the same circle, if two chords are unequal,…

Illustration used to show that "In equal circles, or in the same circle, if two chords are unequal, the greater chord is at the less distance from the center."

Unequal Chords in Equal Circles Theorem

Illustration used to show that "In equal circles, or in the same circle, if two chords are unequal,…

Illustration showing angles formed by two secants, two tangents, or a tangent and a secant, drawn to a circle form an external point. The angle is measured by half the difference of the intercepted arcs.

Circles With Angles Formed by Secants and Tangents

Illustration showing angles formed by two secants, two tangents, or a tangent and a secant, drawn to…

Illustration showing various circles and the angles formed by intersecting lines.

Intersecting Lines in Circles

Illustration showing various circles and the angles formed by intersecting lines.

"Join AB and BC, bisect AB and BC by perpendiculars. Their intersection will be the center of the required circle." —French, 1911

Draw Circular Arc Through Three Given Points

"Join AB and BC, bisect AB and BC by perpendiculars. Their intersection will be the center of the required…

Always draw a circle in one stroke, inclining the compass in the direction of the line and rolling the handle between the thumb and finger.

Inking a Circle

Always draw a circle in one stroke, inclining the compass in the direction of the line and rolling the…

Illustration of the construction used to bisect a given arc.

Construction of Bisecting a Given Arc

Illustration of the construction used to bisect a given arc.

Arc pattern exercise

Arc Exercise

Arc pattern exercise

An illustration showing a model that illustrates the following relationships: a:x = x:a - x, x = √(a&sup2 + (a/2)&sup2 - a/2).

Model Of Geometric Proportions

An illustration showing a model that illustrates the following relationships: a:x = x:a - x, x = √(a²…

The Byzantine interlacement band consists of wavy arcs and curves that have an angular bend. This design comes from the St. Sofia in Constantinople, Turkey.

Byzantine Interlacement Band

The Byzantine interlacement band consists of wavy arcs and curves that have an angular bend. This design…

The Romanesque interlacement band consists of wavy arcs and curves that have an angular bend. It is found in the archivolt (band curve) in Segovia, Spain.

Romanesque Interlacement Band

The Romanesque interlacement band consists of wavy arcs and curves that have an angular bend. It is…

The Romanesque interlacement band consists of wavy arcs and curves that have an angular bend.

Romanesque Interlacement Band

The Romanesque interlacement band consists of wavy arcs and curves that have an angular bend.

Illustration used to show how to find a straight line of the same length as a given arc of a circle.

Construction Of Line Equal To Arc

Illustration used to show how to find a straight line of the same length as a given arc of a circle.

Pair of circular pulleys connected b a cord, showing the range of motion as arcs

Pulley

Pair of circular pulleys connected b a cord, showing the range of motion as arcs

An illustration showing a circle sector with radius r, center/central angle v, and length of circle arc b.

Circle Sector

An illustration showing a circle sector with radius r, center/central angle v, and length of circle…

An illustration showing a circle sector with center/central angle v and polygon angle w.

Circle Sector

An illustration showing a circle sector with center/central angle v and polygon angle w.

An illustration showing a circle sector with height of segment h and radius r.

Circle Sector

An illustration showing a circle sector with height of segment h and radius r.

Diagram of a sphere with sectors and arcs drawn.

Sphere With Sectors and Arcs

Diagram of a sphere with sectors and arcs drawn.

A sphere with arcs and poles. "The distance of all points in the circumference of a circle of a sphere from its poles are equal."

Sphere With Arcs and Poles

A sphere with arcs and poles. "The distance of all points in the circumference of a circle of a sphere…

A sphere with arcs drawn.

Sphere With Arcs

A sphere with arcs drawn.

Illustration of a sphere with arcs drawn.

Arcs Drawn on Sphere

Illustration of a sphere with arcs drawn.

Diagram showing 2 superimposed symmetrical spherical triangles.

Superimposed Symmetrical Spherical Triangles

Diagram showing 2 superimposed symmetrical spherical triangles.

Diagram showing 2 symmetrical spherical triangles.

Symmetrical Spherical Triangles

Diagram showing 2 symmetrical spherical triangles.

Diagram showing a spherical triangle.

Spherical Triangle

Diagram showing a spherical triangle.