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Many decorating techniques used today do not require elaborate cookie cutters. The simplest of shapes can be quite versatile in serving various themes. For example, a star-shaped cutter can be used for Christmas, 4th of July, and messages of congratulations. A circle can be decorated as a sun, ball, flower, spider web, or smiley face. This cutter is in the shape of a four leaf clover.

Cookie Mold Cutter

Many decorating techniques used today do not require elaborate cookie cutters. The simplest of shapes…

Many decorating techniques used today do not require elaborate cookie cutters. The simplest of shapes can be quite versatile in serving various themes. For example, a star-shaped cutter can be used for Christmas, 4th of July, and messages of congratulations. A circle can be decorated as a sun, ball, flower, spider web, or smiley face. This cutter is in the shape of a star.

Star Shaped Cookie Cutter

Many decorating techniques used today do not require elaborate cookie cutters. The simplest of shapes…

A circle in a aerodynamic chamber where the airflow hitting the object. The area at point DD is large creating a resistance.

Circle Aerodynamic

A circle in a aerodynamic chamber where the airflow hitting the object. The area at point DD is large…

Aerodynamic of the ellipse where the area at point DD is small. The small area creates less resistance for the plane while in flight.

Ellipse Aerodynamic

Aerodynamic of the ellipse where the area at point DD is small. The small area creates less resistance…

A wooden hollow sphere created by using a lathe and wooden templet at a desired diameter.

Wooden Sphere

A wooden hollow sphere created by using a lathe and wooden templet at a desired diameter.

A wheel is a circular device that is capable of rotating on its axis, facilitating movement or transportation while supporting a load, or performing labor in machines. Common examples are found in transport applications.

Eight Spoke Wheel

A wheel is a circular device that is capable of rotating on its axis, facilitating movement or transportation…

The illustration of constructing a circle or ellipse using isometric drawing. The inscribed circle is transferred to the top part of the cube by creating diagonal lines through the center and series of squares.

Isometric Drawing of Circle using Square

The illustration of constructing a circle or ellipse using isometric drawing. The inscribed circle is…

A development, or rolled out image, of two cylinders intersecting each other. The large rectangular diagram is the main cylindrical body with a circle inside it for the other cylinder. The smaller development is the intersected cylinder. This is commonly used to illustrate pipes.

Development of Two Intersecting Cylinder

A development, or rolled out image, of two cylinders intersecting each other. The large rectangular…

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…

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…

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 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 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…

Mechanical drawing exercise of shading squares and circle in ink. The squares are first drawn with the right angles, then rounded off with a compass. Using a pen, the sides of the shapes are darkened to show points where no light is hitting the image.

Mechanical Drawing Exercise Shading Sides of Inscribed Squares and Circle with Ink

Mechanical drawing exercise of shading squares and circle in ink. The squares are first drawn with the…

This is a tool used to measure circular bodies, very similar to how current calipers work. This tool features a perpendicular ruler to the circular opening.

Circular Body Measure Tool

This is a tool used to measure circular bodies, very similar to how current calipers work. This tool…

A spindle governor where both balls are connected to the base. The governor is used to regulate the amount of fuel of the steam engine. As the governor spins, the diameter of the circle increases.

Governor with the Balls Connected to the Base for Steam Engine

A spindle governor where both balls are connected to the base. The governor is used to regulate the…

"As the eccentric turns in the strap, the point O moves in the dotted circle around O', and the point A also moves in a circle. When half a revolution is accomplished the point O will be at O", the Point A will be at A", and the eccentric strap and valve rod will be in the position indicated by the dotted lines." —Derr, 1911

Shaft in an Eccentric Motion from Steam Engine

"As the eccentric turns in the strap, the point O moves in the dotted circle around O', and the point…

"Hydra viridis, the freshwater polyp. The animal is attached to the stem of a plant, and is represented with the base of attachment uppermost; the mouth, not actually seen in the drawing, is at the lower extremity of the body, surrounded by the circle tentacles." — Encyclopaedia Britannica Company, 1910

Freshwater Polyp

"Hydra viridis, the freshwater polyp. The animal is attached to the stem of a plant, and is represented…

"One standing at O will only see the half of the Sky which is above the circle NESW. The whole sky will seem to be turning about the line POP'; the Stars will seem to be moving along the paths EQW, BAB', etc. Stars so near the North Pole that they are inside the dark area KPN will never set."—The Foundation Library, 1911

The Sphere of the Sky

"One standing at O will only see the half of the Sky which is above the circle NESW. The whole sky will…

"A tablet of dark brown clay, much injured, dating from the 8th or 7th century B.C. The two large concentric circles indicate the ocean, or, as it is called in the cuneiform writing between the circles, the 'Briny Flood.' Beyond the ocean are seven successive projections of land, represented by triangles. Perhaps they refer to the countries existing beyond the Black Sea and the Red Sea. The two parallel lines within the inner circle represent the Euphrates. The little rings stand for the Babylonian cities in this region."—Webster, 1913

A Babylonian Map of the World

"A tablet of dark brown clay, much injured, dating from the 8th or 7th century B.C. The two large concentric…

"The Flanch is formed of a segment of a circle placed on the side of the shield. It is always borne double or in pairs, the one on the dexter and the other on the sinister side."—Aveling, 1891

Flanch Shield

"The Flanch is formed of a segment of a circle placed on the side of the shield. It is always borne…

"The Rustre differs from the mascle in that the perforation of the device is circular and not throughout."—Aveling, 1891

Rustre Shield

"The Rustre differs from the mascle in that the perforation of the device is circular and not throughout."—Aveling,…

An example of a heraldic shield with roundels.

Shield with Roundels

An example of a heraldic shield with roundels.

"From annulus, a ring. A mark of difference of the fifth son."—Aveling, 1891

Annulet

"From annulus, a ring. A mark of difference of the fifth son."—Aveling, 1891

"The mural crown is a circle of fold embattled, and it is associated with military success in sieges."—Aveling, 1891

Mural Crown

"The mural crown is a circle of fold embattled, and it is associated with military success in sieges."—Aveling,…

"The naval crown is a golden circle surmounted with sterns and square sails of ships, placed alternately."—Aveling, 1891

Naval Crown

"The naval crown is a golden circle surmounted with sterns and square sails of ships, placed alternately."—Aveling,…

The leaves of the livistona hoogendorpii tree are a rich dark green and form a complete circle.

Livistona Hoogendorpii

The leaves of the livistona hoogendorpii tree are a rich dark green and form a complete circle.

Pictured is a double perianth as seen in the flower of abutilon insigne. A double perianth has an outer circle of green sepals and an inner circle of colored petals.

Double Perianth

Pictured is a double perianth as seen in the flower of abutilon insigne. A double perianth has an outer…

Finding the center of gravity of an irregular plane figure. Divide one of the parallel surfaces into a triangle, parallelogram, circle, etc., based on the shape of the figure. Find the area of each part and combine the centers of gravity found for each.

Center of Gravity

Finding the center of gravity of an irregular plane figure. Divide one of the parallel surfaces into…

Sometimes it is not necessary for an entire wheel to be used. A projection of any kind that can cause an object to move in a circle may be considered a wheel, like in the image given.

Bucket and Crank

Sometimes it is not necessary for an entire wheel to be used. A projection of any kind that can cause…

A medal containing two circles of heads, each having seven, male and female alike. The heads of the inner circle are divided by spokes. The upper head has on either side of it a Victory offering a crown and palm branch.

Medal with Heads

A medal containing two circles of heads, each having seven, male and female alike. The heads of the…

Young and old sitting in a circle listening to stories. A younger woman holds a distaff. there is a spinning wheel in the foreground.

Story Time

Young and old sitting in a circle listening to stories. A younger woman holds a distaff. there is a…

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.

A circle in its common, or central form. This is used to assist students in finding the equation of any circle.

Common Form of Circle

A circle in its common, or central form. This is used to assist students in finding the equation of…

A circle with many tangent and secant lines passing through it.

Lines

A circle with many tangent and secant lines passing through it.

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.

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…

The chord of a circle.

Circle Chord

The chord of a circle.

Example of an equation with a given external point.

Equation Example

Example of an equation with a given external point.

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…

Polar property example.

Example

Polar property example.

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.

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.

Finding the equation of a line with polar coordinates.

Polar Coordinates

Finding the equation of a line with polar coordinates.

An inscribed triangle in a circle.

Particular Cases

An inscribed triangle in a 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.

A circle and triangle situated on coordinate planes.

Circle

A circle and triangle situated on coordinate planes.

"The constellation which is prominent in early summer in the skies of the southern United States (where the whole of the magnificent tail clears the horizon), contains the first magnitude red star Antares and several of the second magnitude. With the Chaldeans and Greeks is extended over one sixth of the planetary circle, the scorpion being represented with exaggerated claw embracing a circular space where Libra is now placed." —Whitney, 1889

The Scorpio Constellation, with Libra

"The constellation which is prominent in early summer in the skies of the southern United States (where…

"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 instrument for throwing stones or bullets, consisting of a strap and two strings attached to it. The stone or bullet is lodged to the strap, and, the ends of the strings being held in the hand, the sling is whirled rapidly round in a circle, and the missile thrown by letting go one of the strings. The velocity with which the projectile is discharged is the same as that with which it is whirled round in a circle having the string for its radius. The sling was a very general instrument of war among ancients." &mdash;Whitney, 1889

Sling

"An instrument for throwing stones or bullets, consisting of a strap and two strings attached to it.…