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Right circular cylinder with diameter of 8 and height h.

Right Circular Cylinder

Right circular cylinder with diameter of 8 and height h.

Right circular cylinder with a radius of 1 foot and a height/altitude of 2 feet.

Right Circular Cylinder With 1 ft. Radius and 2 ft. height.

Right circular cylinder with a radius of 1 foot and a height/altitude of 2 feet.

A large cylinder containing 2 smaller congruent cylinders. The small cylinders are externally tangent to each other and internally tangent to the larger cylinder.

2 Smaller Cylinders In A Larger Cylinder

A large cylinder containing 2 smaller congruent cylinders. The small cylinders are externally tangent…

A large cylinder containing 3 smaller congruent cylinders. The small cylinders are externally tangent to each other and internally tangent to the larger cylinder.

3 Smaller Cylinders In A Larger Cylinder

A large cylinder containing 3 smaller congruent cylinders. The small cylinders are externally tangent…

A large cylinder containing 4 smaller congruent cylinders. The small cylinders are externally tangent to each other and internally tangent to the larger cylinder.

4 Smaller Cylinders In A Larger Cylinder

A large cylinder containing 4 smaller congruent cylinders. The small cylinders are externally tangent…

A large cylinder containing 7 smaller congruent cylinders. The small cylinders are externally tangent to each other and internally tangent to the larger cylinder.

7 Smaller Cylinders In A Larger Cylinder

A large cylinder containing 7 smaller congruent cylinders. The small cylinders are externally tangent…

An illustration showing how to construct a cyma, or two circle arcs that will tangent themselves, and two parallel lines at given points A and B. "Join A and B; divide AB into four equal parts and erect perpendiculars. Draw Am at right angles from A, and Bn at right angles from B; then m and n are the centers of the circle arcs of the required cyma."

Construction Of A Cyma

An illustration showing how to construct a cyma, or two circle arcs that will tangent themselves, and…

Design made by drawing one large circle and then two circles that are vertically placed and internally tangent to the original circle. Erase the left side of the top circle and the right side of the bottom circle to create the design. It resembles the yin and yang symbol.

Design Similar to Yin Yang Symbol

Design made by drawing one large circle and then two circles that are vertically placed and internally…

Circular design 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. The circles meet in the center of the larger circle. The design is achieved by removing consecutive halves of the circles (semi-circles).

Circular Design

Circular design made by rotating circles about a fixed point. The radii of the smaller circles is equal…

Circular design 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. The circles meet in the center of the larger circle. The design is achieved by removing consecutive halves of the circles (semi-circles).

Circular Design

Circular design made by rotating circles about a fixed point. The radii of the smaller circles is equal…

Using C as a center, draw two circles with different diameters. The intersection of the diameter lines will determine the points on the curve.

Determining Points on Ellipse Using Circles

Using C as a center, draw two circles with different diameters. The intersection of the diameter lines…

A development or rolled out image exercise problem of the dome and finding the true shape of the hip, or edge, of the dome by using projections or with dividers.

Development Exercise of Dome and True Shape of Hip

A development or rolled out image exercise problem of the dome and finding the true shape of the hip,…

When drawing the circle, the compass is turned by the handle with the thumb and forefinger in a clockwise motion.

Drawing a Circle Using Compass

When drawing the circle, the compass is turned by the handle with the thumb and forefinger in a clockwise…

Illustration used to draw a an ellipse using string and pins by describing a circles with diameters equal to the minor and major axes of the ellipse.

Construction of Ellipse by Describing Circles

Illustration used to draw a an ellipse using string and pins by describing a circles with diameters…

Illustration used to draw a an ellipse with major axis AB and minor axis CD.

Construction of Ellipse

Illustration used to draw a an ellipse with major axis AB and minor axis CD.

Illustration of an ellipse, whose major axis is vertical, inscribed in a circle whose diameter is equal to the length of the major axis of the ellipse. The ellipse is externally tangent to the circle.

Ellipse Inscribed In A Circle

Illustration of an ellipse, whose major axis is vertical, inscribed in a circle whose diameter is equal…

Illustration showing an ellipse (and circle) as a section from a cylinder.

Section of a Cylinder Showing an Ellipse

Illustration showing an ellipse (and circle) as a section from a cylinder.

Illustration of 16 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.

16 Rotated Concentric Ellipses

Illustration of 16 concentric congruent ellipses that are rotated about the center at equal intervals…

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…

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…

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…

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

An illustration showing a model of a circle with intersecting chords that illustrates the following relationship: a:c = b:d, ad = bc. Product of the means equals the product of the extremes.

Model Of Geometric Proportions In A Circle

An illustration showing a model of a circle with intersecting chords that illustrates the following…

An illustration showing a model of 2 circles with tangent lines, diameters, and radii that illustrates the following geometric relationship: "x = aR/(R - r), a = √(t&sup2 + (R - r)&sup2), t = √(a&sup2 - (R - r)&sup2, sin.v = t/a."

Model Of Geometric Relationships In 2 Circles

An illustration showing a model of 2 circles with tangent lines, diameters, and radii that illustrates…

An illustration showing a model of 2 circles with tangent lines, diameters, and radii that illustrates the following geometric relationship: " t = √(a&sup2 - (R + r)&sup2, a = √(t&sup2 - (R + r)&sup2 "

Model Of Geometric Relationships In 2 Circles

An illustration showing a model of 2 circles with tangent lines, diameters, and radii that illustrates…

An illustration showing a model of a circle with an exterior angle formed between a tangent and a secant that illustrates the following geometric relationship: a:t = t:b, t&sup2 = ab

Model Of Geometric Relationships In A Circle

An illustration showing a model of a circle with an exterior angle formed between a tangent and a secant…

An illustration showing a model of a circle with angles formed between tangents and secants that illustrates the following geometric relationship: t&sup2 = (a + b)(a - b).

Model Of Geometric Relationships In A Circle

An illustration showing a model of a circle with angles formed between tangents and secants that illustrates…

Illustration of a polar graph/grid that is marked and labeled in 30° increments and units marked to 10.

Polar Grid In Degrees With Radius 10

Illustration of a polar graph/grid that is marked and labeled in 30° increments and units marked…

Illustration of a polar graph/grid that is marked, but not labeled, in 30° increments and units marked to 10.

Polar Grid In Degrees With Radius 10

Illustration of a polar graph/grid that is marked, but not labeled, in 30° increments and units…

Illustration of a polar graph/grid that is a unit circle marked and labeled in 30° increments.

Polar Grid In Degrees With Radius 1

Illustration of a polar graph/grid that is a unit circle marked and labeled in 30° increments.

Illustration of a polar graph/grid that is a unit circle marked, but not labeled, in 30° increments.

Polar Grid In Degrees With Radius 1

Illustration of a polar graph/grid that is a unit circle marked, but not labeled, in 30° increments.

Illustration of a polar graph/grid that is marked and labeled in 30° increments and units marked to 2.

Polar Grid In Degrees With Radius 2

Illustration of a polar graph/grid that is marked and labeled in 30° increments and units marked…

Illustration of a polar graph/grid that is marked, but not labeled, in 30° increments and units marked to 2.

Polar Grid In Degrees With Radius 2

Illustration of a polar graph/grid that is marked, but not labeled, in 30° increments and units…

Illustration of a polar graph/grid that is marked and labeled in 30° increments and units marked to 3.

Polar Grid In Degrees With Radius 3

Illustration of a polar graph/grid that is marked and labeled in 30° increments and units marked…

Illustration of a polar graph/grid that is marked, but not labeled, in 30° increments and units marked to 3.

Polar Grid In Degrees With Radius 3

Illustration of a polar graph/grid that is marked, but not labeled, in 30° increments and units…