Illustration of 2 concentric squares.

2 Concentric Squares

Illustration of 2 concentric squares.

Illustration of 3 concentric squares that are equally spaced.

3 Concentric Squares

Illustration of 3 concentric squares that are equally spaced.

Illustration of 4 concentric squares that are equally spaced.

4 Concentric Squares

Illustration of 4 concentric squares that are equally spaced.

Illustration of 2 congruent squares that have the same center. One square has been rotated 45° in relation to the other.

2 Congruent Rotated Squares

Illustration of 2 congruent squares that have the same center. One square has been rotated 45° in…

Illustration of 4 congruent squares that have the same center. Each square has been rotated 22.5° in relation to the one next to it.

4 Congruent Rotated Squares

Illustration of 4 congruent squares that have the same center. Each square has been rotated 22.5°…

Illustration of 8 congruent squares that have the same center. Each square has been rotated 11.25° in relation to the one next to it.

8 Congruent Rotated Squares

Illustration of 8 congruent squares that have the same center. Each square has been rotated 11.25°…

Illustration of 16 congruent squares that have the same center. Each square has been rotated 5.625° in relation to the one next to it.

16 Congruent Rotated Squares

Illustration of 16 congruent squares that have the same center. Each square has been rotated 5.625°…

Illustration of 3 congruent squares that have the same center. Each square has been rotated 30° in relation to the one next to it.

3 Congruent Rotated Squares

Illustration of 3 congruent squares that have the same center. Each square has been rotated 30°…

Illustration of 6 congruent squares that have the same center. Each square has been rotated 15° in relation to the one next to it.

6 Congruent Rotated Squares

Illustration of 6 congruent squares that have the same center. Each square has been rotated 15°…

Illustration of 12 congruent squares that have the same center. Each square has been rotated 7.5° in relation to the one next to it.

12 Congruent Rotated Squares

Illustration of 12 congruent squares that have the same center. Each square has been rotated 7.5°…

Illustration showing the construction of a golden rectangle. Beginning with a unit square, a line is then drawn from the midpoint of one side of the square to its opposite corner. Using that line, an arc is drawn that defines the length of the rectangle. Two quantities are considered to be in the golden ratio if (a+ b)/a = a/b which is represented by the Greek letter phi.

Construction Of A Golden Rectangle

Illustration showing the construction of a golden rectangle. Beginning with a unit square, a line is…

Illustration showing the golden rectangle. Two quantities are considered to be in the golden ratio if (a+ b)/a = a/b which is represented by the Greek letter phi.

Golden Rectangle

Illustration showing the golden rectangle. Two quantities are considered to be in the golden ratio if…

Illustration showing a nesting of 2 golden rectangles. Two quantities are considered to be in the golden ratio if (a+ b)/a = a/b which is represented by the Greek letter phi. The large rectangle shown is divided to show the a golden rectangle. The smaller portion is then divided into the golden ratio again.

Golden Rectangles

Illustration showing a nesting of 2 golden rectangles. Two quantities are considered to be in the golden…

Illustration showing a nesting of 3 golden rectangles. Two quantities are considered to be in the golden ratio if (a+ b)/a = a/b which is represented by the Greek letter phi. The large rectangle shown is divided to show the a golden rectangle. The smaller portion is then divided into the golden ratio again, and so on.

Golden Rectangles

Illustration showing a nesting of 3 golden rectangles. Two quantities are considered to be in the golden…

Illustration showing a nesting of 4 golden rectangles. Two quantities are considered to be in the golden ratio if (a+ b)/a = a/b which is represented by the Greek letter phi. The large rectangle shown is divided to show the a golden rectangle. The smaller portion is then divided into the golden ratio again, and so on.

Golden Rectangles

Illustration showing a nesting of 4 golden rectangles. Two quantities are considered to be in the golden…

Illustration showing a nesting of 5 golden rectangles. Two quantities are considered to be in the golden ratio if (a+ b)/a = a/b which is represented by the Greek letter phi. The large rectangle shown is divided to show the a golden rectangle. The smaller portion is then divided into the golden ratio again, and so on.

Golden Rectangles

Illustration showing a nesting of 5 golden rectangles. Two quantities are considered to be in the golden…

Illustration showing a nesting of 6 golden rectangles. Two quantities are considered to be in the golden ratio if (a+ b)/a = a/b which is represented by the Greek letter phi. The large rectangle shown is divided to show the a golden rectangle. The smaller portion is then divided into the golden ratio again, and so on.

Golden Rectangles

Illustration showing a nesting of 6 golden rectangles. Two quantities are considered to be in the golden…

Illustration showing a nesting of 7 golden rectangles. Two quantities are considered to be in the golden ratio if (a+ b)/a = a/b which is represented by the Greek letter phi. The large rectangle shown is divided to show the a golden rectangle. The smaller portion is then divided into the golden ratio again, and so on.

Golden Rectangles

Illustration showing a nesting of 7 golden rectangles. Two quantities are considered to be in the golden…

Illustration showing succession of golden rectangles that are used to construct the golden spiral. Two quantities are considered to be in the golden ratio if (a+ b)/a = a/b which is represented by the Greek letter phi. Each rectangle shown is subdivided into smaller golden rectangles. The golden spiral is a special type of logarithmic spiral. Each part is similar to smaller and larger parts.

Golden Rectangles

Illustration showing succession of golden rectangles that are used to construct the golden spiral. Two…

Illustration showing succession of golden rectangles that are used to construct the golden spiral. Two quantities are considered to be in the golden ratio if (a+ b)/a = a/b which is represented by the Greek letter phi. Each rectangle shown is subdivided into smaller golden rectangles. The golden spiral is a special type of logarithmic spiral. Each part is similar to smaller and larger parts.

Golden Rectangles

Illustration showing succession of golden rectangles that are used to construct the golden spiral. Two…

Illustration of a decagonal prism with regular decagons for bases and rectangular faces. The hidden edges are shown.

Decagonal Prism

Illustration of a decagonal prism with regular decagons for bases and rectangular faces. The hidden…

Illustration of a swimming pool and water hose that is in the shape of a hollow regular decagonal prism with regular decagons on the ends/bases and square faces.

Swimming Pool Shaped Like A Decagonal Prism

Illustration of a swimming pool and water hose that is in the shape of a hollow regular decagonal prism…

Illustration of a non-regular decagonal prism in the shape of a star. Then ends/bases are made of star-shaped decagons and the faces are rectangular.

Star-Shaped Decagonal Prism

Illustration of a non-regular decagonal prism in the shape of a star. Then ends/bases are made of star-shaped…

Illustration of a non-regular decagonal prism in the shape of a star. Then ends/bases are made of star-shaped decagons and the faces are squares.

Star-Shaped Decagonal Prism

Illustration of a non-regular decagonal prism in the shape of a star. Then ends/bases are made of star-shaped…

Side view of a non-regular decagonal prism in the shape of a star. Then ends/bases are made of star-shaped decagons and the faces are squares.

Star-Shaped Decagonal Prism

Side view of a non-regular decagonal prism in the shape of a star. Then ends/bases are made of star-shaped…

Illustration of a right decagonal prism with regular decagons for bases and rectangular faces.

Decagonal Prism

Illustration of a right decagonal prism with regular decagons for bases and rectangular faces.

Illustration of 2 similar right decagonal prisms. Both have regular decagons for bases and rectangular faces. The height of the prism and length of the side of the decagon on the smaller decagonal prism are one half that of the larger.

Similar Decagonal Prisms

Illustration of 2 similar right decagonal prisms. Both have regular decagons for bases and rectangular…

Illustration of a right decagonal prism with regular decagons for bases and rectangular faces. The prism is resting on its side, one of the faces.

Decagonal Prism Resting On Its Side

Illustration of a right decagonal prism with regular decagons for bases and rectangular faces. The prism…

Illustration of a hollow right heptagonal/septagonal prism with regular heptagons/septagons for bases and rectangular faces.

Heptagonal/Septagonal Prism

Illustration of a hollow right heptagonal/septagonal prism with regular heptagons/septagons for bases…

Illustration of a regular right heptagonal/septagonal prism with regular heptagons/septagons for bases and square faces. The hidden edges are shown.

Heptagonal/Septagonal Prism

Illustration of a regular right heptagonal/septagonal prism with regular heptagons/septagons for bases…

Illustration of a right heptagonal/septagonal prism with regular heptagons/septagons for bases and rectangular faces. The hidden edges are shown.

Heptagonal/Septagonal Prism

Illustration of a right heptagonal/septagonal prism with regular heptagons/septagons for bases and rectangular…

Illustration of 2 similar right heptagonal/septagonal prisms. Both have regular heptagons/septagons for bases and rectangular faces. The height of the prism and length of the side of the heptagon on the smaller heptagonal prism are one half that of the larger.

Similar Heptagonal/Septagonal Prisms

Illustration of 2 similar right heptagonal/septagonal prisms. Both have regular heptagons/septagons…

Illustration of a right heptagonal/septagonal prism with regular heptagons/septagons for bases and rectangular faces.

Heptagonal/Septagonal Prism

Illustration of a right heptagonal/septagonal prism with regular heptagons/septagons for bases and rectangular…

Illustration of a right hexagonal prism.

Hexagonal Prism

Illustration of a right hexagonal prism.

Illustration of a right hexagonal prism with hidden edges shown.

Hexagonal Prism

Illustration of a right hexagonal prism with hidden edges shown.

Illustration of a right hexagonal prism with a height less than the length of the edge of the hexagon.

Hexagonal Prism

Illustration of a right hexagonal prism with a height less than the length of the edge of the hexagon.

Illustration of a right hexagonal prism with a height greater than the length of the edge of the hexagon.

Hexagonal Prism

Illustration of a right hexagonal prism with a height greater than the length of the edge of the hexagon.

Illustration of 2 similar right hexagonal prisms. The height of the prism and length of the side of the hexagon on the smaller hexagonal prism are one half that of the larger.

Similar Hexagonal Prisms

Illustration of 2 similar right hexagonal prisms. The height of the prism and length of the side of…

Illustration of 2 similar right hexagonal prisms. The height of the prism and length of the side of the hexagon on the smaller hexagonal prism are one half that of the larger.

Similar Hexagonal Prisms

Illustration of 2 similar right hexagonal prisms. The height of the prism and length of the side of…

A cluster of 4 right hexagonal prisms with congruent bases, but varying heights.

4 Hexagonal Prisms

A cluster of 4 right hexagonal prisms with congruent bases, but varying heights.

Illustration of a right hexagonal prism with hexagons for bases and square faces.

Hexagonal Prism

Illustration of a right hexagonal prism with hexagons for bases and square faces.

Illustration of a right hexagonal prism with hexagons for bases and square faces. The hidden edges are shown.

Hexagonal Prism

Illustration of a right hexagonal prism with hexagons for bases and square faces. The hidden edges are…

Illustration of a right hexagonal prism with hexagons for bases and rectangular faces. The height of the prism is greater than the length of a side of the hexagon. The hidden edges are shown.

Hexagonal Prism

Illustration of a right hexagonal prism with hexagons for bases and rectangular faces. The height of…

Illustration of a right nonagonal prism with regular nonagons for bases and rectangular faces. The hidden edges are shown.

Nonagonal Prism

Illustration of a right nonagonal prism with regular nonagons for bases and rectangular faces. The hidden…

Illustration of a right nonagonal prism with regular nonagons for bases and rectangular faces. The height of the prism is greater than the length of a side of the nonagon. The hidden edges are shown.

Nonagonal Prism

Illustration of a right nonagonal prism with regular nonagons for bases and rectangular faces. The height…

Illustration of a right octagonal prism with regular octagons for bases and rectangular faces. The hidden edges are shown.

Octagonal Prism

Illustration of a right octagonal prism with regular octagons for bases and rectangular faces. The hidden…

Illustration of 2 right octagonal prisms with congruent bases, but different heights. The height of the smaller prism is one half that of the larger.

2 Octagonal Prisms

Illustration of 2 right octagonal prisms with congruent bases, but different heights. The height of…

Illustration of 2 Similar right octagonal prisms. The height and length of the edges of the smaller prism are one half that of the larger.

2 Similar Octagonal Prisms

Illustration of 2 Similar right octagonal prisms. The height and length of the edges of the smaller…

Illustration of a right octagonal prism with regular octagons for bases and rectangular faces. The height of the prism is greater than the length of a side of the octagon. The hidden edges are shown.

Octagonal Prism

Illustration of a right octagonal prism with regular octagons for bases and rectangular faces. The height…

Illustration of a right octagonal prism with octagons for bases and rectangular faces. The height of the prism is greater than the length of a side of the octagon.

Octagonal Prism

Illustration of a right octagonal prism with octagons for bases and rectangular faces. The height of…

Illustration of a right octagonal prism, with octagons for bases and rectangular faces, that is resting on its side (an edge). The height of the prism is greater than the length of a side of the octagon.

Octagonal Prism Resting On Side

Illustration of a right octagonal prism, with octagons for bases and rectangular faces, that is resting…

Illustration of a right pentagonal prism with regular pentagons for bases and rectangular faces. The height of the prism is greater than the length of a side of the pentagon. The hidden edges are shown.

Pentagonal Prism

Illustration of a right pentagonal prism with regular pentagons for bases and rectangular faces. The…

Illustration of a right pentagonal prism with regular pentagons for bases and rectangular faces. The height of the prism is slightly greater than the length of a side of the pentagon. The hidden edges are shown.

Pentagonal Prism

Illustration of a right pentagonal prism with regular pentagons for bases and rectangular faces. The…

Illustration of a right pentagonal prism with regular pentagons for bases and rectangular faces. The height of the prism is slightly greater than the length of a side of the pentagon.

Pentagonal Prism

Illustration of a right pentagonal prism with regular pentagons for bases and rectangular faces. The…

Illustration of a right pentagonal prism with regular pentagons for bases and rectangular faces. The height of the prism is greater than the length of a side of the pentagon.

Pentagonal Prism

Illustration of a right pentagonal prism with regular pentagons for bases and rectangular faces. The…

Illustration of a right rectangular pyramid with hidden edges shown. The base is a rectangle and the faces are isosceles triangles.

Rectangular Pyramid

Illustration of a right rectangular pyramid with hidden edges shown. The base is a rectangle and the…

Illustration of a right rectangular pyramid with hidden edges shown. The base is a rectangle and the faces are isosceles triangles. The height of the pyramid is much larger then the length and width of the base.

Rectangular Pyramid

Illustration of a right rectangular pyramid with hidden edges shown. The base is a rectangle and the…

Illustration of 2 right rectangular pyramids with hidden edges shown. The rectangular bases are congruent, but the height of the smaller pyramid is one half that of the larger.

2 Right Rectangular Pyramids

Illustration of 2 right rectangular pyramids with hidden edges shown. The rectangular bases are congruent,…

Illustration of a non-right, or skewed, rectangular pyramid with hidden edges shown. The base is a rectangle and the faces are isosceles triangles.

Skewed Rectangular Pyramid

Illustration of a non-right, or skewed, rectangular pyramid with hidden edges shown. The base is a rectangle…

Illustration of a right rectangular pyramid with hidden edges shown. The base is a rectangle and the faces are isosceles triangles.

Rectangular Pyramid

Illustration of a right rectangular pyramid with hidden edges shown. The base is a rectangle and the…