ClipArt ETC
A circle subdivided into two thirds and two sixths.

Two Thirds and Two Sixths of a Pie Fraction

A circle subdivided into two thirds and two sixths.

Two twelfths of a circle.

Two Twelfths of a Fraction Pie

Two twelfths of a circle.

A whole circle.

Whole Fraction Pie

A whole circle.

A circle with part of a triangle inscribed in it. They are lying on a coordinate plane.

Coordinate Plane

A circle with part of a triangle inscribed in it. They are lying on a coordinate plane.

Diagram used to prove the theorem: "Every section of a sphere by a lane is a circle."

Sphere Cut By Plane

Diagram used to prove the theorem: "Every section of a sphere by a lane is a circle."

Constructing the polar of a given point P with respect to a circle.

Polar of Point

Constructing the polar of a given point P with respect to a circle.

An illustration of a prismatoid with 2 circular bases.

Prismatoid With 2 Circular Bases

An illustration of a prismatoid with 2 circular bases.

An illustration of a prismatoid with 2 circular bases.

Prismatoid With 2 Circular Bases

An illustration of a prismatoid with 2 circular bases.

An illustration of a prismatoid with circular base.

Prismatoid With Circular Base

An illustration of a prismatoid with circular base.

If the chords of a circle are drawn through a fixed point, then the points of intersection of the pairs of tangents at the extremities of the chords will all lie on a fixed straight line.

Polar Property

If the chords of a circle are drawn through a fixed point, then the points of intersection of the pairs…

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

Illustration of a cyclic quadrilateral, a quadrilateral inscribed in a circle. This can also be described as a circle circumscribed about a quadrilateral. In this illustration, the quadrilateral is not regular (the lengths of the sides are not equal).

Cyclic Quadrilateral

Illustration of a cyclic quadrilateral, a quadrilateral inscribed in a circle. This can also be described…

Radial design.

Radial design

Radial design.

Radial design.

Radial design

Radial design.

Radial design.

Radial design

Radial design.

Radial design.

Radial design

Radial design.

Radial design.

Radial design

Radial design.

Radial design.

Radial design

Radial design.

Radial design.

Radial design

Radial design.

Radial design.

Radial design

Radial design.

Radial design.

Radial design

Radial design.

Radial design from a ceiling.

Radial design

Radial design from a ceiling.

Illustration showing that the radian is an angle that when placed at the center of a circle its sides intercept an arc equal to the radius.

Radians in Complete Circle

Illustration showing that the radian is an angle that when placed at the center of a circle its sides…

Given any three circles, the common chords meet at one point.

Radical Center of 3 Circles

Given any three circles, the common chords meet at one point.

Illustration used to draw lines which are radii of a circle where the center is inaccessible.

Construction of Radii of a Circle

Illustration used to draw lines which are radii of a circle where the center is inaccessible.

"In ordinary work the usual way of rectifying an arc is to step around it with the dividers, in spaces small enough as practically to coincide with the arc, and to step off the same number on the right line." —French, 1911

Rectifying Arc Using Dividers

"In ordinary work the usual way of rectifying an arc is to step around it with the dividers, in spaces…

"In a circle, sound is reflected from every plane surface placed around it, and hence, if the sound is emitted from the centre of a circle, this centre will be the point at which the echo will be most distinct." -Comstock 1850

Sound Reflection in a Circle

"In a circle, sound is reflected from every plane surface placed around it, and hence, if the sound…

Illustration of a regular heptagon/septagon circumscribed about a circle. This can also be described as a circle inscribed in a regular heptagon/septagon.

Regular Heptagon/Septagon Circumscribed about a Circle

Illustration of a regular heptagon/septagon circumscribed about a circle. This can also be described…

Illustration of ring (small circle in larger concentric circle).

Ring Made of Concentric Circles

Illustration of ring (small circle in larger concentric circle).

Illustration of ring (small circle in larger concentric circle) with piece cut out.

Ring With Piece Cut Out

Illustration of ring (small circle in larger concentric circle) with piece cut out.

Illustration of ring (small circle in larger concentric circle) sprung into place.

Ring Sprung Into Place

Illustration of ring (small circle in larger concentric circle) sprung into place.

Roman mosaic pattern of interlocking circles.

Roman Mosaic Circle Pattern

Roman mosaic pattern of interlocking circles.

"Use the entire blossom mingled with buds and green leaves, all short stemmed, not longer than three or four inches. Bind the stems with string on a circle made of a piece of willow or some other pliable material, and be sure to removed the thorns from all them stems before weaving the wreath." -Beard, 1906

Wreath of roses

"Use the entire blossom mingled with buds and green leaves, all short stemmed, not longer than three…

Circular rosette with 12 petals in a circle. It is made by rotating circles about a fixed point. The radii of the smaller circles are less than the distance between the point of rotation and the center of the circle. Thus, there is a hole in the center.

Circular Rosette With 12 Petals

Circular rosette with 12 petals in a circle. It is made by rotating circles about a fixed point. The…

Circular rosette with 12 petals. It is made by rotating circles about a fixed point. The radii of the smaller circles is equal to the distance between the point of rotation and the center of the circle. Thus, the circles meet in the center.

Circular Rosette With 12 Petals

Circular rosette with 12 petals. It is made by rotating circles about a fixed point. The radii of the…

Circular rosette with 16 petals in a circle. It is made by rotating circles about a fixed point. The radii of the smaller circles is equal to the distance between the point of rotation and the center of the circle. Thus, the circles meet in the center of the larger circle.

Circular Rosette With 16 Petals

Circular rosette with 16 petals in a circle. It is made by rotating circles about a fixed point. The…

Circular rosette with 16 petals in a circle. It is made by rotating circles about a fixed point. The radii of the smaller circles are less than the distance between the point of rotation and the center of the circle. Thus, there is a hole in the center.

Circular Rosette With 16 Petals

Circular rosette with 16 petals in a circle. It is made by rotating circles about a fixed point. The…

Circular rosette with 24 petals in a circle. It is made by rotating circles about a fixed point. The radii of the smaller circles are less than the distance between the point of rotation and the center of the circle. Thus, there is a hole in the center.

Circular Rosette With 24 Petals

Circular rosette with 24 petals in a circle. It is made by rotating circles about a fixed point. The…

Circular rosette with 24 petals. It is made by rotating circles about a fixed point. The radii of the smaller circles is equal to the distance between the point of rotation and the center of the circle. Thus, the circles meet in the center.

Circular Rosette With 24 Petals

Circular rosette with 24 petals. It is made by rotating circles about a fixed point. The radii of the…

Circular rosette with 3 petals. It is made by rotating circles about a fixed point. The radii of the smaller circles is equal to the distance between the point of rotation and the center of the circle. Thus, the circles meet in the center.

Circular Rosette With 3 Petals

Circular rosette with 3 petals. It is made by rotating circles about a fixed point. The radii of the…

Circular rosette with 32 petals in a circle. It is made by rotating circles about a fixed point. The radii of the smaller circles is equal to the distance between the point of rotation and the center of the circle. Thus, the circles meet in the center of the larger circle.

Circular Rosette With 32 Petals

Circular rosette with 32 petals in a circle. It is made by rotating circles about a fixed point. The…

Circular rosette with 32 petals in a circle. It is made by rotating circles about a fixed point. The radii of the smaller circles are less than the distance between the point of rotation and the center of the circle. Thus, there is a hole in the center.

Circular Rosette With 32 Petals

Circular rosette with 32 petals in a circle. It is made by rotating circles about a fixed point. The…

Circular rosette with 6 petals in a circle. It is made by rotating circles about a fixed point. The radii of the smaller circles is equal to the distance between the point of rotation and the center of the circle. Thus, the circles meet in the center of the larger circle.

Circular Rosette With 4 Petals

Circular rosette with 6 petals in a circle. It is made by rotating circles about a fixed point. The…

Circular rosette with 48 petals in a circle. It is made by rotating circles about a fixed point. The radii of the smaller circles are less than the distance between the point of rotation and the center of the circle. Thus, there is a hole in the center.

Circular Rosette With 48 Petals

Circular rosette with 48 petals in a circle. It is made by rotating circles about a fixed point. The…

Circular rosette with 6 petals in a circle. It is made by rotating circles about a fixed point. The radii of the smaller circles are less than the distance between the point of rotation and the center of the circle. Thus, there is a hole in the center.

Circular Rosette With 6 Petals

Circular rosette with 6 petals in a circle. It is made by rotating circles about a fixed point. The…

Circular rosette with 6 petals. It is made by rotating circles about a fixed point. The radii of the smaller circles is equal to the distance between the point of rotation and the center of the circle. Thus, the circles meet in the center.

Circular Rosette With 6 Petals

Circular rosette with 6 petals. It is made by rotating circles about a fixed point. The radii of the…

Circular rosette with 8 petals in a circle. It is made by rotating circles about a fixed point. The radii of the smaller circles is equal to the distance between the point of rotation and the center of the circle. Thus, the circles meet in the center of the larger circle.

Circular Rosette With 8 Petals

Circular rosette with 8 petals in a circle. It is made by rotating circles about a fixed point. The…

Circular rosette with 8 petals in a circle. It is made by rotating circles about a fixed point. The radii of the smaller circles are less than the distance between the point of rotation and the center of the circle. Thus, there is a hole in the center.

Circular Rosette With 8 Petals

Circular rosette with 8 petals in a circle. It is made by rotating circles about a fixed point. The…

Projection of a round bar.

Projection of Round Bar

Projection of a round bar.

Illustration of a wall with a rounded corner.

Corner of Rounded Wall

Illustration of a wall with a rounded corner.

"The power is generally applied by a wheel or a lever, and moves through the circumfrence of a circle. The distance between the two consecutive turns of any on continuous thread, measured in the direction of the axis of the screw, is called the pitch of the screw." -Avery 1895

Screw with Lever Arm

"The power is generally applied by a wheel or a lever, and moves through the circumfrence of a circle.…

"A screw cut on a solid, of such form that if any plane be taken through its longitudinal axis, the intersections of the plane by the perimeter are arcs of the pitch-circle of a wheel into which the screw is intended to work. It is so named from having been first employed by Mr. Hindley of York in England." —Whitney, 1889 <p>The hourglass shape of the screw increases the bearing area and therefore reduces wear.

Hindley's Screw

"A screw cut on a solid, of such form that if any plane be taken through its longitudinal axis, the…

A secant is "a line which cuts a figure in any way. Specifically, in trigonometry, a line from the center of a circle through one extremity of an arc (whose secant it is said to be) to the tangent from the other extremity of the same arc; or the ratio of this line to the radius; the reciprocal of the cosine. The ratio of AB to AD is the secant of the angle A; and AB is the secant of the arc CD." &mdash;Whitney, 1889

Circle with Secant

A secant is "a line which cuts a figure in any way. Specifically, in trigonometry, a line from the center…

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.

Illustration of a semicircle.

Semicircle

Illustration of a semicircle.

Illustration of a circle used to prove "Any angle inscribed in a semicircle is a right angle."

Right Angles Inscribed in Semicircle Proof

Illustration of a circle used to prove "Any angle inscribed in a semicircle is a right angle."

Illustration of a semicircle with chords and radii.

Semicircle With Chords and Radii

Illustration of a semicircle with chords and radii.

"Until hard rock is reached the sides of the excavation are supported temporarily by a lining"&mdash;Finley, 1917

Shaft lining

"Until hard rock is reached the sides of the excavation are supported temporarily by a lining"—Finley,…