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Popcorn box that is in the shape of a frustum of a rectangular pyramid.

Popcorn Box Frustum Of A Rectangular Pyramid

Popcorn box that is in the shape of a frustum of a rectangular pyramid.

Illustration of a right hollow rectangular pyramid that has been cut by a plane parallel to the base. The top section has been removed and the remaining section has been turned upside down. It is known as the frustum of the pyramid. Hidden edges are shown in this drawing.

Frustum Of A Rectangular Pyramid

Illustration of a right hollow rectangular pyramid that has been cut by a plane parallel to the base.…

Illustration of a square circumscribed about a regular dodecagon. This could also be described as a dodecagon inscribed in a square.

Square Circumscribed About A Dodecagon

Illustration of a square circumscribed about a regular dodecagon. This could also be described as a…

Illustration of 2 squares; one inscribed in a regular dodecagon and the other circumscribed about the same dodecagon.

Squares Inscribed and Circumscribed About a Regular Dodecagon

Illustration of 2 squares; one inscribed in a regular dodecagon and the other circumscribed about the…

Illustration of a square inscribed in an regular dodecagon. This could also be described as a regular dodecagon circumscribed about a square.

Square Inscribed In A Dodecagon

Illustration of a square inscribed in an regular dodecagon. This could also be described as a regular…

Illustration of 3 squares inscribed in an regular dodecagon. Each vertex of the dodecagon is also a vertex of one of the squares.

3 Square Inscribed In A Dodecagon

Illustration of 3 squares inscribed in an regular dodecagon. Each vertex of the dodecagon is also a…

Illustration of a square inscribed in a square. The interior square is rotated 45° in relation to the exterior square.

Square Inscribed In A Square

Illustration of a square inscribed in a square. The interior square is rotated 45° in relation to…

Illustration of a square inscribed in a square that is inscribed in another square. Each successive square is rotated 45° in relation to the previous square.

Squares Inscribed In Squares

Illustration of a square inscribed in a square that is inscribed in another square. Each successive…

Illustration of a square inscribed in a square that is inscribed in another square. Each successive square is rotated 45° in relation to the previous square. Diagonals of the largest square are shown.

Squares Inscribed In Squares

Illustration of a square inscribed in a square that is inscribed in another square. Each successive…

Illustration of a square inscribed in a square that is inscribed in another square. Each successive square is rotated 45° in relation to the previous square. Line segments are drawn connecting the vertices of the smallest to the vertices of the largest square.

Squares Inscribed In Squares

Illustration of a square inscribed in a square that is inscribed in another square. Each successive…

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.

Illustration of 2 concentric squares.

2 Concentric Squares

Illustration of 2 concentric squares.

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…