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Illustration of a skewed (non-right) hexagonal antiprism. An antiprism is formed by having two parallel congruent bases connected by an alternating band of triangles. The bases in this illustration are hexagons.

Skewed Hexagonal Antiprism

Illustration of a skewed (non-right) hexagonal antiprism. An antiprism is formed by having two parallel…

Illustration of a hexagonal antiprism. An antiprism is formed by having two parallel congruent bases connected by an alternating band of triangles. The bases in this illustration are hexagons.

Hexagonal Antiprism

Illustration of a hexagonal antiprism. An antiprism is formed by having two parallel congruent bases…

Illustration of a nonagonal antiprism. An antiprism is formed by having two parallel congruent bases connected by an alternating band of triangles. The bases in this illustration are nonagons.

Nonagonal Antiprism

Illustration of a nonagonal antiprism. An antiprism is formed by having two parallel congruent bases…

Illustration of a skewed (non-right) nonagonal antiprism. An antiprism is formed by having two parallel congruent bases connected by an alternating band of triangles. The bases in this illustration are nonagons.

Skewed Nonagonal Antiprism

Illustration of a skewed (non-right) nonagonal antiprism. An antiprism is formed by having two parallel…

Illustration of a nonagonal antiprism. An antiprism is formed by having two parallel congruent bases connected by an alternating band of triangles. The bases in this illustration are nonagons.

Nonagonal Antiprism

Illustration of a nonagonal antiprism. An antiprism is formed by having two parallel congruent bases…

Illustration of an octagonal antiprism. An antiprism is formed by having two parallel congruent bases connected by an alternating band of triangles. The bases in this illustration are octagons.

Octagonal Antiprism

Illustration of an octagonal antiprism. An antiprism is formed by having two parallel congruent bases…

Illustration of an octagonal antiprism. An antiprism is formed by having two parallel congruent bases connected by an alternating band of triangles. The bases in this illustration are octagons.

Octagonal Antiprism

Illustration of an octagonal antiprism. An antiprism is formed by having two parallel congruent bases…

Illustration of a skewed (non-right) octagonal antiprism. An antiprism is formed by having two parallel congruent bases connected by an alternating band of triangles. The bases in this illustration are octagons.

Skewed Octagonal Antiprism

Illustration of a skewed (non-right) octagonal antiprism. An antiprism is formed by having two parallel…

Illustration of a pentagonal antiprism. An antiprism is formed by having two parallel congruent bases connected by an alternating band of triangles. The bases in this illustration are pentagons.

Pentagonal Antiprism

Illustration of a pentagonal antiprism. An antiprism is formed by having two parallel congruent bases…

Illustration of a pentagonal antiprism. An antiprism is formed by having two parallel congruent bases connected by an alternating band of triangles. The bases in this illustration are pentagons.

Pentagonal Antiprism

Illustration of a pentagonal antiprism. An antiprism is formed by having two parallel congruent bases…

Illustration of a skewed (non-right) pentagonal antiprism. An antiprism is formed by having two parallel congruent bases connected by an alternating band of triangles. The bases in this illustration are pentagons.

Skewed Pentagonal Antiprism

Illustration of a skewed (non-right) pentagonal antiprism. An antiprism is formed by having two parallel…

Illustration of a cyclic pentagon, a pentagon inscribed in a circle. This can also be described as a circle circumscribed about a pentagon. In this illustration, the pentagon is not regular (the lengths of the sides are not equal).

Cyclic Pentagon

Illustration of a cyclic pentagon, a pentagon inscribed in a circle. This can also be described as a…

Illustration of a cyclic quadrilateral, a quadrilateral inscribed in a circle. This can also be described as a circle circumscribed about a quadrilateral. In this illustration, the quadrilateral is not regular (the lengths of the sides are not equal).

Cyclic Quadrilateral

Illustration of a cyclic quadrilateral, a quadrilateral inscribed in a circle. This can also be described…

Illustration of a cyclic hexagon, a hexagon inscribed in a circle. This can also be described as a circle circumscribed about a hexagon. In this illustration, the hexagon is not regular (the lengths of the sides are not equal).

Cyclic Hexagon

Illustration of a cyclic hexagon, a hexagon inscribed in a circle. This can also be described as a circle…

Illustration of a cyclic hexagon, a hexagon inscribed in a circle. This can also be described as a circle circumscribed about a hexagon. In this illustration, the hexagon is not regular (the lengths of the sides are not equal).

Cyclic Hexagon

Illustration of a cyclic hexagon, a hexagon inscribed in a circle. This can also be described as a circle…

Illustration of a hexagon in a circle. Four of the six vertices of the hexagon are bound by the circle (are tangent to the circle). Because all six vertices are not on the circle, the hexagon is not cyclic; it is not inscribed in the circle.

Hexagon In A Circle

Illustration of a hexagon in a circle. Four of the six vertices of the hexagon are bound by the circle…

Illustration that can be used to prove the Pythagorean Theorem, the sum of the squares of the legs is equal to the square of the hypotenuse.

Geometric Pythagorean Theorem Proof

Illustration that can be used to prove the Pythagorean Theorem, the sum of the squares of the legs is…

Illustration that can be used to prove the Pythagorean Theorem, the sum of the squares of the legs is equal to the square of the hypotenuse. The geometrical illustration depicts a 3,4,5 right triangle with the square units drawn to prove that the sum of the squares of the legs (9 + 16) equals the square of the hypotenuse.

Geometric Pythagorean Theorem Proof

Illustration that can be used to prove the Pythagorean Theorem, the sum of the squares of the legs is…

A visual illustration used to prove the Pythagorean Theorem by rearrangement. When the 4 identical triangles are removed, the areas are equal. Thus, proving the sum of the squares of the legs is equal to the square of the hypotenuse.

Pythagorean Theorem Proof by Rearrangement

A visual illustration used to prove the Pythagorean Theorem by rearrangement. When the 4 identical triangles…

Illustration of a 5-point star inscribed in a circle. This can also be described as a circle circumscribed about a 5-point star.

Star Inscribed In A Circle

Illustration of a 5-point star inscribed in a circle. This can also be described as a circle circumscribed…

Illustration of a 6-point star created by two equilateral triangles (often described as the Star of David) inscribed in a circle. This can also be described as a circle circumscribed about a 6-point star, or two triangles.

Star Inscribed In A Circle

Illustration of a 6-point star created by two equilateral triangles (often described as the Star of…

Illustration of a 6-point star (convex dodecagon) inscribed in a circle. This can also be described as a circle circumscribed about a 6-point star, or convex dodecagon.

Star Inscribed In A Circle

Illustration of a 6-point star (convex dodecagon) inscribed in a circle. This can also be described…

Illustration of a 6-point star (convex dodecagon) inscribed in a large circle and circumscribed about a smaller circle.

Star Inscribed And Circumscribed About Circles

Illustration of a 6-point star (convex dodecagon) inscribed in a large circle and circumscribed about…

Illustration of a 6-point star (convex dodecagon) circumscribed about a circle. This can also be described as a circle inscribed in a 6-point star, or convex dodecagon.

Star Circumscribed About A Circle

Illustration of a 6-point star (convex dodecagon) circumscribed about a circle. This can also be described…

Illustration of an 8-point star, created by two squares at 45° rotations, inscribed in a circle. This can also be described as a circle circumscribed about an 8-point star, or two squares.

Star Inscribed In A Circle

Illustration of an 8-point star, created by two squares at 45° rotations, inscribed in a circle.…

Illustration of an 8-point star, or convex polygon, inscribed in a circle. This can also be described as a circle circumscribed about an 8-point star.

Star Inscribed In A Circle

Illustration of an 8-point star, or convex polygon, inscribed in a circle. This can also be described…

Illustration of an 8-point star (convex polygon) inscribed in a large circle and circumscribed about a smaller circle.

Star Inscribed And Circumscribed About Circles

Illustration of an 8-point star (convex polygon) inscribed in a large circle and circumscribed about…

Illustration of an 8-point star (convex polygon) circumscribed about a circle. This can also be described as a circle inscribed in an 8-point star, or convex polygon.

Star Circumscribed About A Circle

Illustration of an 8-point star (convex polygon) circumscribed about a circle. This can also be described…

A body is shown as projecting from its surface projection lines, and these lines are cut by a plane. By connecting the points on the plane made by the projection lines the projection of the body is formed, and it corresponds in shape with the body itself.

Projected Geometric View

A body is shown as projecting from its surface projection lines, and these lines are cut by a plane.…

These diagrams show that the bigger the circle or sphere, the more space in between.

Spheres

These diagrams show that the bigger the circle or sphere, the more space in between.

Illustration of pattern showing steps to make a box.

Pattern To Make A Box

Illustration of pattern showing steps to make a box.

Illustration of pattern showing steps to make a house. The house is a composite figure made up of a triangular prism and a rectangular solid.

Pattern To Make A House

Illustration of pattern showing steps to make a house. The house is a composite figure made up of a…

Illustration of pattern showing steps to make a barn. The barn is a composite figure made up of a triangular prism and a rectangular solid.

Pattern To Make A Barn

Illustration of pattern showing steps to make a barn. The barn is a composite figure made up of a triangular…

Illustration of an oblique cone.

Oblique Cone

Illustration of an oblique cone.

Illustration showing that can be used to prove that the base angles of an isosceles triangle are equal.

Base Angles In An Isosceles Triangle

Illustration showing that can be used to prove that the base angles of an isosceles triangle are equal.

Illustration showing that if equal segments measured from the end of the base are laid off on the base of an isosceles triangle, the lines joining the vertex of the triangle to the ends of the segments will be equal.

Equal Segments In An Isosceles Triangle

Illustration showing that if equal segments measured from the end of the base are laid off on the base…

Illustration showing that if equal segments measured from the end of the base prolonged are laid off on the base of an isosceles triangle, the lines joining the vertex of the triangle to the ends of the segments will be equal.

Equal Segments In An Isosceles Triangle

Illustration showing that if equal segments measured from the end of the base prolonged are laid off…

Illustration used to prove that triangle EFD is equilateral given that triangle ABC is equilateral and AE=BF=CD.

Equilateral Triangle Inscribed In An Equilateral Triangle

Illustration used to prove that triangle EFD is equilateral given that triangle ABC is equilateral and…

Illustration used to show that two triangles are equal if the three sides of one are equal respectively to the three sides of the other.

Equal Triangles

Illustration used to show that two triangles are equal if the three sides of one are equal respectively…

Illustration used to show how to construct an equilateral triangle, with a given line as a side.

Construction Of Equilateral Triangle

Illustration used to show how to construct an equilateral triangle, with a given line as a side.

Illustration used to show how to construct an angle equal to a given angle when given a vertex and a given side.

Construction Of An Equal Angle

Illustration used to show how to construct an angle equal to a given angle when given a vertex and a…

Illustration of model created by combining non regular geometric solids.

Combination of Geometric Solids

Illustration of model created by combining non regular geometric solids.

Illustration of an oblique view of a rectangular solid/prism at 30°.

Oblique View Of Rectangular Solid

Illustration of an oblique view of a rectangular solid/prism at 30°.

Illustration of an oblique view of a rectangular solid/prism at 45°.

Oblique View Of Rectangular Solid

Illustration of an oblique view of a rectangular solid/prism at 45°.

Illustration of an oblique view of a rectangular solid/prism at 60°.

Oblique View Of Rectangular Solid

Illustration of an oblique view of a rectangular solid/prism at 60°.

Illustration of an oblique view of a hollow cylinder.

Oblique View Of Hollow Cylinder

Illustration of an oblique view of a hollow cylinder.

Illustration of an oblique view of a hollow cylinder. The portion removed from the center of the cylinder is in the shape of a rectangular prism.

Oblique View Of Hollow Cylinder

Illustration of an oblique view of a hollow cylinder. The portion removed from the center of the cylinder…

Illustration of a shaded vertical cylinder, viewed from the side.

Vertical Cylinder

Illustration of a shaded vertical cylinder, viewed from the side.

Illustration of a shaded horizontal cylinder, viewed from the side.

Horizontal Cylinder

Illustration of a shaded horizontal cylinder, viewed from the side.

Illustration of a shaded section of a hollow cylinder viewed from the side.

Hollow Cylinder

Illustration of a shaded section of a hollow cylinder viewed from the side.

An illustration showing the construction used to divide a line AB into two equal parts; and to erect a perpendicular through the middle. "With the end A and B as centers, draw the dotted circle arcs with a radius greater than half the line. Through the crossings of the arcs draw the perpendicular CD, which divides the line into two equal parts."

Construction Of A Line Divided In Equal Parts

An illustration showing the construction used to divide a line AB into two equal parts; and to erect…

An illustration showing the construction used to erect a perpendicular. "With C as a center, draw the dotted circle arcs at A and B equal distances from C. With A and B as centers, draw the dotted circle arcs at D. From the crossing D draw the required perpendicular DC."

Construction Of A Perpendicular

An illustration showing the construction used to erect a perpendicular. "With C as a center, draw the…

An illustration showing the construction used to erect a perpendicular from a point to a line. "With C as a center, draw the dotted circle arc so that it cuts the line at A and B. With A and B as centers, draw the dotted cross arcs at D with equal radii. Draw the required perpendicular through C and crossing D."

Construction Of A Perpendicular

An illustration showing the construction used to erect a perpendicular from a point to a line. "With…

An illustration showing the construction used to erect a perpendicular at the end of a line. "With the point D as a center at a distance from the line, and with AD as radius, draw the dotted circle arc so that it cuts the line at E through E and D, draw the diameter EC: then join C and A, which will be the required perpendicular."

Construction Of A Perpendicular

An illustration showing the construction used to erect a perpendicular at the end of a line. "With the…

An illustration showing the construction used to erect a parallel line. "With C as a center, draw the dotted arc ED, with E as a center, draw through C the dotted arc F.C. With the radius FC and E as a center, draw the cross arc at D. Join C with the cross at D, which will be the required parallel line.

Construction Of A Parallel

An illustration showing the construction used to erect a parallel line. "With C as a center, draw the…

An illustration showing the construction used to erect an equal angle. "With D as a center, draw the dotted arc CE: and with the same radius and B as a center, draw the arc GF; then make GF equal to CE; then join BF, which will form the required angle, FBG=CDE."

Construction Of An Equal Angle

An illustration showing the construction used to erect an equal angle. "With D as a center, draw the…

An illustration showing the construction used to divide an angle into two equal parts. "With C as a center, draw the dotted arc DE; with D and E as centers, draw the cross arcs at F with equal radii. Join CF, which divides the angle into the required parts."

Construction Of A Divided Angle

An illustration showing the construction used to divide an angle into two equal parts. "With C as a…

An illustration showing the construction used to divide an angle into two equal parts when the lines do not extend to a meeting point. "Draw the lined CD and CE parallel, and at equal distances from the lines AB and FG. With C as a center, draw the dotted arc BG; and with B and G as centers, draw the cross arcs H. Join CD, which divides the angle into the required equal parts."

Construction Of A Divided Angle

An illustration showing the construction used to divide an angle into two equal parts when the lines…

An illustration showing the construction used to erect a parallelogram given two sides and an angle. "Draw the base line DE, and make the angle FDE = C; lines DE = B and DF = A; complete the parallelogram by cross arcs at G, and the problem is thus solved."

Construction Of A Parallelogram

An illustration showing the construction used to erect a parallelogram given two sides and an angle.…

An illustration showing the construction used to divide the line AB in the same proportion of parts as AC. "Join C and B, and through the given divisions 1, 2, and 3 draw lines parallel with CB, which solves the problem."

Divide A Line Proportionately

An illustration showing the construction used to divide the line AB in the same proportion of parts…