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Illustration of a square inscribed in a closed concave geometric figure with 24 sides in the shape of a 12-point star. The two figures are concentric.

Square Inscribed in a 12-Point Star

Illustration of a square inscribed in a closed concave geometric figure with 24 sides in the shape of…

Illustration of an equilateral triangle inscribed in a closed concave geometric figure with 24 sides in the shape of a 12-point star. The two figures are concentric.

Triangle Inscribed In A 12-Point Star

Illustration of an equilateral triangle inscribed in a closed concave geometric figure with 24 sides…

Illustration of concentric circles.

Concentric Circles

Illustration of concentric circles.

Illustration of concentric circles used to find area between two circles (ring).

Concentric Circles (Ring) Area

Illustration of concentric circles used to find area between two circles (ring).

Conjugate diameters perpendicular to each other are called, axes, and the points where they cut the curve vertices of the conic.

Conic Axes

Conjugate diameters perpendicular to each other are called, axes, and the points where they cut the…

Dotted lines can indicate a relationship among figures, such as one inside another.

Drawing Lines 1

Dotted lines can indicate a relationship among figures, such as one inside another.

Shading of the right and lower sides gives dimension to drawings.

Drawing Lines 2

Shading of the right and lower sides gives dimension to drawings.

Circles should be unshaded or shaded evenly with thick and thin lines, changing at about 45 degrees.

Drawing Lines 4

Circles should be unshaded or shaded evenly with thick and thin lines, changing at about 45 degrees.

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 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…

Illustration of 2 regular congruent pentagons that have the same center. One pentagon has been rotated 36° in relation to the other.

2 Congruent Rotated Pentagons

Illustration of 2 regular congruent pentagons that have the same center. One pentagon has been rotated…

Illustration of 4 regular congruent pentagons that have the same center. Each pentagon has been rotated 18° in relation to the one next to it.

4 Congruent Rotated Pentagons

Illustration of 4 regular congruent pentagons that have the same center. Each pentagon has been rotated…

Illustration of 8 regular congruent pentagons that have the same center. Each pentagon has been rotated 9° in relation to the one next to it.

8 Congruent Rotated Pentagons

Illustration of 8 regular congruent pentagons that have the same center. Each pentagon has been rotated…

Cross section of pipe, 2 concentric circles

Cross Section of Pipe

Cross section of pipe, 2 concentric circles

Illustration of a circle inside of a rectangle. The two figures have the same center.

Circle Inside Rectangle

Illustration of a circle inside of a rectangle. The two figures have the same center.

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.

Illustration of 2 concentric squares whose vertices are connected by line segments.

2 Concentric Squares

Illustration of 2 concentric squares whose vertices are connected by line segments.