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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 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 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 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…

An illustration used to show how the area of a circle is calculated. Area is equal to the product of pi and the radius squared.

Area Of A Circle

An illustration used to show how the area of a circle is calculated. Area is equal to the product of…

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 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 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…

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 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…

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 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…

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 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 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…

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…

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 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 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 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…

Illustration showing the golden angle. The golden angle is the smaller of two angles created by dividing the circumference of a circle according to the golden section. The ratio of the length of the larger arc to the smaller arc is equal to the ratio of the entire circumference to the larger arc. The golden angle is approximately 137.51°.

Golden Angle

Illustration showing the golden angle. The golden angle is the smaller of two angles created by dividing…

Illustration showing how the golden ratio in a regular pentagon (inscribed in a circle) can be found using Ptolemy's theorem. The lines that are bolded form a quadrilateral. Ptolemy's theorem says the square of b equals the sum of a squared and ab, which in turn gives the golden ratio.

Golden Ratio In A Pentagon

Illustration showing how the golden ratio in a regular pentagon (inscribed in a circle) can be found…

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…

Illustration of a polar graph/grid that is marked and labeled in 30° increments and units marked to 4.

Polar Grid In Degrees With Radius 4

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 4.

Polar Grid In Degrees With Radius 4

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 5.

Polar Grid In Degrees With Radius 5

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 5.

Polar Grid In Degrees With Radius 5

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 6.

Polar Grid In Degrees With Radius 6

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 6.

Polar Grid In Degrees With Radius 6

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 7.

Polar Grid In Degrees With Radius 7

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 7.

Polar Grid In Degrees With Radius 7

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 8.

Polar Grid In Degrees With Radius 8

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 8.

Polar Grid In Degrees With Radius 8

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 9.

Polar Grid In Degrees With Radius 9

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 9.

Polar Grid In Degrees With Radius 9

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 15° 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 15° increments and units marked…

Illustration of a polar graph/grid that is marked, but not labeled, in 15° 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 15° increments and units…

Illustration of a polar graph/grid that is marked and labeled in 15° increments and units marked to 1.

Polar Grid In Degrees With Radius 1

Illustration of a polar graph/grid that is marked and labeled in 15° increments and units marked…

Illustration of a polar graph/grid that is marked, but not labeled, in 15° increments and units marked to 1.

Polar Grid In Degrees With Radius 1

Illustration of a polar graph/grid that is marked, but not labeled, in 15° increments and units…

Illustration of a polar graph/grid that is marked and labeled in 15° 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 15° increments and units marked…

Illustration of a polar graph/grid that is marked, but not labeled, in 15° 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 15° increments and units…

Illustration of a polar graph/grid that is marked and labeled in 15° 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 15° increments and units marked…

Illustration of a polar graph/grid that is marked, but not labeled, in 15° 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 15° increments and units…

Illustration of a polar graph/grid that is marked and labeled in 15° increments and units marked to 4.

Polar Grid In Degrees With Radius 4

Illustration of a polar graph/grid that is marked and labeled in 15° increments and units marked…

Illustration of a polar graph/grid that is marked, but not labeled, in 15° increments and units marked to 4.

Polar Grid In Degrees With Radius 4

Illustration of a polar graph/grid that is marked, but not labeled, in 15° increments and units…

Illustration of a polar graph/grid that is marked and labeled in 15° increments and units marked to 5.

Polar Grid In Degrees With Radius 5

Illustration of a polar graph/grid that is marked and labeled in 15° increments and units marked…

Illustration of a polar graph/grid that is marked, but not labeled, in 15° increments and units marked to 5.

Polar Grid In Degrees With Radius 5

Illustration of a polar graph/grid that is marked, but not labeled, in 15° increments and units…