ClipArt ETC
Illustration of 2 concentric ellipses, whose major axes are vertical, inscribed in a circle whose diameter is equal to the length of the major axes of the ellipses. The ellipses, which decrease in width in equal increments, are externally tangent to the circle. The illustration could be used as a 3-dimensional drawing of a sphere.

2 Ellipses Inscribed In A Circle

Illustration of 2 concentric ellipses, whose major axes are vertical, inscribed in a circle whose diameter…

Illustration of 2 concentric congruent ellipses that are rotated about the center at 90°. The ellipses are externally tangent to the circle in which they are inscribed.

2 Rotated Concentric Ellipses

Illustration of 2 concentric congruent ellipses that are rotated about the center at 90°. The ellipses…

An illustration of 2 ellipses that have the equal vertical axes, but different horizontal axes. The ellipse on the left has a larger horizontal axis than the ellipse on the right.

2 Ellipses With Equal Vertical Axes

An illustration of 2 ellipses that have the equal vertical axes, but different horizontal axes. The…

An illustration of 2 ellipses that have the equal vertical axes, but different horizontal axes. The ellipse on the left has a larger horizontal axis than the ellipse on the right. The ellipse on the left has equal horizontal and vertical axes, making it a circle.

2 Ellipses With Equal Vertical Axes

An illustration of 2 ellipses that have the equal vertical axes, but different horizontal axes. The…

An illustration of 3 concentric ellipses that are tangent at the end points of the vertical axes. The horizontal axes (the major axes of the ellipses) decreases in size in each successive ellipse. The major axis equals the minor axis in the smallest ellipse, thus forming a circle.

3 Concentric Ellipses

An illustration of 3 concentric ellipses that are tangent at the end points of the vertical axes. The…

An illustration of 3 concentric ellipses that are tangent at the end points of the vertical axes, which is drawn in the illustration. The horizontal axes decreases in size in each successive ellipse. The major axis is horizontal for the outmost ellipse and vertical for the innermost ellipse. When the major and minor axes are equal, the result is a circle (as in the second/middle ellipse).

3 Concentric Ellipses

An illustration of 3 concentric ellipses that are tangent at the end points of the vertical axes, which…

An illustration of 3 concentric ellipses that are tangent at the end points of the vertical axes. The horizontal axes decreases in size in each successive ellipse. The major axis is horizontal for the outmost ellipse and vertical for the innermost ellipse. When the major and minor axes are equal, the result is a circle (as in the second/middle ellipse).

3 Concentric Ellipses

An illustration of 3 concentric ellipses that are tangent at the end points of the vertical axes. The…

An illustration of 4 concentric ellipses that are tangent at the end points of the vertical axes. The horizontal axes (the major axes of the ellipses) decreases in size in each successive ellipse.

4 Concentric Ellipses

An illustration of 4 concentric ellipses that are tangent at the end points of the vertical axes. The…

An illustration of 4 concentric ellipses that are tangent at the end points of the vertical axes. The horizontal axes decreases in size in each successive ellipse. The major axis is horizontal for the outer two ellipses and vertical for the innermost ellipse. When the major and minor axes are equal, the result is a circle (as in the third ellipse).

4 Concentric Ellipses

An illustration of 4 concentric ellipses that are tangent at the end points of the vertical axes. The…

An illustration of 4 concentric ellipses that are tangent at the end points of the vertical axes, which is drawn in the illustration. The horizontal axes decreases in size in each successive ellipse. The major axis is horizontal for the outer two ellipses and vertical for the innermost ellipse. When the major and minor axes are equal, the result is a circle (as in the third ellipse).

4 Concentric Ellipses

An illustration of 4 concentric ellipses that are tangent at the end points of the vertical axes, which…

Illustration of 4 concentric congruent ellipses that are rotated about the center at equal intervals of 45°. The ellipses are externally tangent to the circle in which they are inscribed.

4 Rotated Concentric Ellipses

Illustration of 4 concentric congruent ellipses that are rotated about the center at equal intervals…

An illustration of 5 concentric ellipses that are tangent at the end points of the vertical axes. The horizontal axes decreases in size in each successive ellipse. The major axis is horizontal for the outer three ellipses and vertical for the innermost ellipse. When the major and minor axes are equal, the result is a circle (as in the fourth ellipse).

5 Concentric Ellipses

An illustration of 5 concentric ellipses that are tangent at the end points of the vertical axes. The…

An illustration of 5 concentric ellipses that are tangent at the end points of the vertical axes, which is drawn in the illustration. The horizontal axes decreases in size in each successive ellipse. The major axis is horizontal for the outer three ellipses and vertical for the innermost ellipse. When the major and minor axes are equal, the result is a circle (as in the fourth ellipse).

5 Concentric Ellipses

An illustration of 5 concentric ellipses that are tangent at the end points of the vertical axes, which…

An illustration of 6 concentric ellipses that are tangent at the end points of the vertical axes. The horizontal axes decreases in size in each successive ellipse. The major axis is horizontal for the outer four ellipses and vertical for the innermost ellipse. When the major and minor axes are equal, the result is a circle (as in the fifth ellipse).

6 Concentric Ellipses

An illustration of 6 concentric ellipses that are tangent at the end points of the vertical axes. The…

An illustration of 6 concentric ellipses that are tangent at the end points of the vertical axes, which is drawn in the illustration. The horizontal axes decreases in size in each successive ellipse. The major axis is horizontal for the outer four ellipses and vertical for the innermost ellipse. When the major and minor axes are equal, the result is a circle (as in the fifth ellipse).

6 Concentric Ellipses

An illustration of 6 concentric ellipses that are tangent at the end points of the vertical axes, which…

Illustration of 8 concentric congruent ellipses that are rotated about the center at equal intervals of 22.5°. The ellipses are externally tangent to the circle in which they are inscribed.

8 Rotated Concentric Ellipses

Illustration of 8 concentric congruent ellipses that are rotated about the center at equal intervals…

Illustration of concentric ellipses, whose major axes are vertical, inscribed in a circle whose diameter is equal to the length of the major axes of the ellipses. The ellipses, which decrease in width in equal increments until the smallest one is a line, are externally tangent to the circle. The illustration could be described as a circle rotated about the poles of the vertical axis. It could also be used as a 3-dimensional drawing of a sphere.

Ellipses Inscribed In A Circle

Illustration of concentric ellipses, whose major axes are vertical, inscribed in a circle whose diameter…

Illustration of concentric ellipses, whose major axes are vertical, inscribed in a circle whose diameter is equal to the length of the major axes of the ellipses. The ellipses, which decrease in width in equal increments until the smallest one is a line, are externally tangent to the circle. The illustration could be described as a circle rotated about the poles of the vertical axis. It could also be used as a 3-dimensional drawing of a sphere.

Ellipses Inscribed In A Circle

Illustration of concentric ellipses, whose major axes are vertical, inscribed in a circle whose diameter…

According to Norse mythology, in Elfland, elves and fairies would dance in a circle in the moonlight. "Whenever the fairies danced at night, the grass grew greener. Any one going through the forest the next day could tell where the elves had been by the rings of green grass." -Klugh, 1909

Elves and Fairies Dancing

According to Norse mythology, in Elfland, elves and fairies would dance in a circle in the moonlight.…

A large, circular Chinese encampment.

Chinese encampment

A large, circular Chinese encampment.

"In geometry, a curve generated by the motion of a point on the circumference of a circle which rolls upon the convex side of a fixed circle." -Whitney, 1911

Epicycloid

"In geometry, a curve generated by the motion of a point on the circumference of a circle which rolls…

Epicycloid is generated by a circle rolled outside of another circle, whereas a hypocycloid is circle rolled inside another circle.

Epicycloid and Hypocycloid

Epicycloid is generated by a circle rolled outside of another circle, whereas a hypocycloid is circle…

"Epicycloidal wheel, a wheel or ring fixed to a framework, toothed on its inner side, and having in gear with it another toothed wheel, of half the diameter of the first, fitted so as to revolve about the center of the latter. It is used for converting circular into alternate motion, or alternate into circular." -Whitney, 1911

Epicycloidal Wheel

"Epicycloidal wheel, a wheel or ring fixed to a framework, toothed on its inner side, and having in…

Tangent lines are drawn from a given external point to a circle. The equation is found by joining their points of contact

Chord Equation

Tangent lines are drawn from a given external point to a circle. The equation is found by joining their…

To find the equation of a circle whose center is the origin and whose radius is 3 units in length.

Circle Equation

To find the equation of a circle whose center is the origin and whose radius is 3 units in length.

Finding the equation of a circle with the origin as its center.

Circle Equation

Finding the equation of a circle with the origin as its center.

Finding the equation of the normal at any point on a circle.

Normal Equation

Finding the equation of the normal at any point on a circle.

An illustration showing how to construct an equilateral triangle inscribed in a circle. "With the radius of the circle and center C draw the arc DFE; with the same radius, and D and E as centers, set off the points A and B. Join A and B, B and C, C and A, which will be the required triangle."

Construction Of An Equilateral Triangle Inscribed In A Circle

An illustration showing how to construct an equilateral triangle inscribed in a circle. "With the radius…

Illustration of 10 congruent equilateral triangles that have the same center. Each triangle has been rotated 12° in relation to the one next to it. The outer vertices are connected with a smoother curve to form a circle. Hence, the circle is circumscribed about the triangles.

10 Congruent Rotated Equilateral Triangles

Illustration of 10 congruent equilateral triangles that have the same center. Each triangle has been…

An illustration showing how to construct an evolute of a circle. "Given the pitch p, the angle v, and radius r. Divide the angle v into a number of equal parts, draw the radii and tangents for each part, divide the pitch p into an equal number of equal parts, then the first tangent will be one part, second two parts, third three parts, etc., and so the Evolute is traced."

Construction Of An Evolute Of A Circle

An illustration showing how to construct an evolute of a circle. "Given the pitch p, the angle v, and…

Polar property example.

Example

Polar property example.

Example of an equation with a given external point.

Equation Example

Example of an equation with a given external point.

A mechanical drawing exercise of a circle with curved wavy lines. The image is drawn by dividing horizontal lines into half inches, and draw smaller half circles within the large circle.

Mechanical Drawing Exercise Circle with Wavy Curved Lines Inside

A mechanical drawing exercise of a circle with curved wavy lines. The image is drawn by dividing horizontal…

A mechanical drawing exercise of drawing a curved line with circle in the middle. The image is drawn by drawing a small circle in the middle. The curved lines around the circle is drawn by using the ticked line as the radius.

Curved Line with Circle Mechanical Drawing Exercise

A mechanical drawing exercise of drawing a curved line with circle in the middle. The image is drawn…

A drawing exercise for drawing eight concentric circles by dividing the paper in quarters as shown. When doing the exercise, the center cannot be enlarged as the circle gets smaller. The exercise is done in ink with fine lines.

Drawing Exercise Eight Concentric Circles using Ink

A drawing exercise for drawing eight concentric circles by dividing the paper in quarters as shown.…

Mechanical drawing exercise of drawing dotted lined concentric circles. The circles are first drawn by dividing the paper into quarters, then draw the circles in pencil. Ink dotted lines on the penciled circles.

Dotted Lined Eight Concentric Circles using Ink and Pencil Drawing Exercise

Mechanical drawing exercise of drawing dotted lined concentric circles. The circles are first drawn…

An inscribed circle pattern exercise for mechanical drawing. The pattern is drawn by dividing the horizontal line into half inches. Using a compass, draw the large circle then the smaller circle tangent to the bigger circle using a bow instrument.

Drawing Exercise of Inscribed Circle Pattern Tangent to Left Side

An inscribed circle pattern exercise for mechanical drawing. The pattern is drawn by dividing the horizontal…

Mechanical drawing exercise for circle with two tangent points on both sides of the circle. The paper is first divided into quarters, then the large circle is drawn. Smaller circles are then drawn within the circle tangent to the horizontal line.

Inscribed Circle with Smaller Circles at Tangent Points Both Sides of the Large Circle Mechanical Drawing Exercise

Mechanical drawing exercise for circle with two tangent points on both sides of the circle. The paper…

A mechanical drawing practice problem of shading the sides of the inscribed circles. The darker area shows where the light is not hitting the image making the 2D image look 3D. These shadings are done in pen.

Mechanical Drawing Exercise Shading Sides of Inscribed Circle with Ink

A mechanical drawing practice problem of shading the sides of the inscribed circles. The darker area…

An exercise to shade small circles with bow pen for mechanical drawing. The paper is first divided into 4" square. At each corners, draw a 3&fras;8" diameter. The shading is done by reducing and increasing the pressure of the bow while drawing the circle.

Mechanical Drawing Exercise Shading Sides of Small Circles with Bow Pen

An exercise to shade small circles with bow pen for mechanical drawing. The paper is first divided into…

2 circles that are similar figures

Similar Figures

2 circles that are similar figures

A flashcard featuring an illustration of a Circle

Flashcard of a Circle

A flashcard featuring an illustration of a Circle

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…

An illustration of a prismatoid with circular base.

Geometric Solid with Circular Base

An illustration of a prismatoid with circular base.

This geometrical circle pattern found in the St. Croce church in Florence, Italy.

Geometrical Pattern

This geometrical circle pattern found in the St. Croce church in Florence, Italy.

Two students drawing geometrical shapes on the chalkboard. A student is also using a scale while students sitting at desks take notes.

Geometry

Two students drawing geometrical shapes on the chalkboard. A student is also using a scale while students…

Three suspended concentric circles free to move independently of each other at right angles.

Gyroscope

Three suspended concentric circles free to move independently of each other at right angles.

Illustration of beginning of construction of a regular heptagon in a circle.

Construction of Regular Heptagon in a Circle

Illustration of beginning of construction of a regular heptagon in a circle.

An illustration showing how to construct a hexagon in a given circle. "The radius of the circle is equal to the side of the hexagon."

Construction Of A Hexagon In A Circle

An illustration showing how to construct a hexagon in a given circle. "The radius of the circle is equal…

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

Cyclic Hexagon

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

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

Cyclic Hexagon

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

Illustration of regular hexagon and triangle inscribed in circle.

Hexagon Inscribed in Circle by Construction

Illustration of regular hexagon and triangle inscribed in circle.

Generating a hyperbola from two equal and parallel circular disks.

Generate Hyperbola

Generating a hyperbola from two equal and parallel circular disks.

Optical Illusion

Illusion, Von Recklinghausen's Illusion

Optical Illusion

Inlaid pattern from Pisa cathedral.

Inlaid Pattern

Inlaid pattern from Pisa cathedral.

The lines joining any point on a conic to the two foci are equally inclined to the tangent and normal at that point. This is an ellipse.

Conic Foci Involution

The lines joining any point on a conic to the two foci are equally inclined to the tangent and normal…

"Curves other than arcs of circles are drawn with the pencil or ruling pen by means of curved or irregular-shaped rulers, called irregular curves. A series of points is first determined through which the curved line is to pass. The line is then drawn through these points by using such parts of the irregular curve as will pass through several of the points at once, the curve being shifted from time to time as required." — Hallock, 1905

Irregular Curves

"Curves other than arcs of circles are drawn with the pencil or ruling pen by means of curved or irregular-shaped…

From Kipling's The Jungle Book, Baloo singing the Law of the Jungle to a pack of wolves.

Baloo Singing to Wolves

From Kipling's The Jungle Book, Baloo singing the Law of the Jungle to a pack of wolves.

Finding the length of a tangent from a given point to a circle.

Tangent Length

Finding the length of a tangent from a given point to a circle.

Lengthening bar is used to draw circles bigger than 10 inches.

Use of Lengthening Bar

Lengthening bar is used to draw circles bigger than 10 inches.