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Illustration showing that the perpendicular bisector of a given line is the locus of points equidistant from the extremities of the line.

Perpendicular Bisector of a Line

Illustration showing that the perpendicular bisector of a given line is the locus of points equidistant…

Multiple lines showing many bisectors on the coordinate plane.

Line Bisectors

Multiple lines showing many bisectors on the coordinate plane.

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures consisting of triangles, squares, and parallelograms are used to construct the given shape. This tangram depicts a boat.

Boat

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures…

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures consisting of triangles, squares, and parallelograms are used to construct the given shape. This tangram depicts a boat.

Boat

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures…

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures consisting of triangles, squares, and parallelograms are used to construct the given shape. This tangram depicts a boat.

Boat

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures…

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures consisting of triangles, squares, and parallelograms are used to construct the given shape. This tangram depicts a boat.

Boat

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures…

A tetrahedron crystal of Boracite

Boracite Crystal

A tetrahedron crystal of Boracite

A cube crystal of Boracite

Boracite Crystal

A cube crystal of Boracite

A rhombic dodecahedron crystal of Boracite

Boracite Crystal

A rhombic dodecahedron crystal of Boracite

"Orthohombric. Crystals usually short prismatic to tabular. Sometimes quite complex with many prism, pyramid and dome faces. Frequently twinned, giving tabular crystals with recurring reentrant angles in the prism zone." — Ford, 1912

Bournonite

"Orthohombric. Crystals usually short prismatic to tabular. Sometimes quite complex with many prism,…

Brookite.

Brookite

Brookite.

"The only orthorhombic mineral of importance belonging to the hemimorphic class is calamine. When its crystals are doubly terminated they show different forms at either end of the vertical axis." — Ford, 1912

Calamine

"The only orthorhombic mineral of importance belonging to the hemimorphic class is calamine. When its…

"Orthohombic, hemimorphic. Crystals usually tabular parallel to the brachypinacoid. They show prism faces and are terminated above usually by a combination of macrodomes and brachydomes and base, and below by a pyramid." — Ford, 1912

Calamine

"Orthohombic, hemimorphic. Crystals usually tabular parallel to the brachypinacoid. They show prism…

Calcite

Calcite

Calcite

Calcite

Calcite

Calcite

Calcite.

Calcite

Calcite.

Calcite.

Calcite

Calcite.

Calcite.

Calcite

Calcite.

Calcite.

Calcite

Calcite.

Calcite.

Calcite

Calcite.

Calcite.

Calcite

Calcite.

Calcite.

Calcite

Calcite.

Calcite.

Calcite

Calcite.

"Hexagonal-rhombohedral. Crystals are very varied in habitat, often highly complex. Over 300 different forms have been described." — Ford, 1912

Calcite

"Hexagonal-rhombohedral. Crystals are very varied in habitat, often highly complex. Over 300 different…

"Hexagonal-rhombohedral. Crystals are very varied in habitat, often highly complex. Over 300 different forms have been described." — Ford, 1912

Calcite

"Hexagonal-rhombohedral. Crystals are very varied in habitat, often highly complex. Over 300 different…

"Hexagonal-rhombohedral. Crystals are very varied in habitat, often highly complex. Over 300 different forms have been described." — Ford, 1912

Calcite

"Hexagonal-rhombohedral. Crystals are very varied in habitat, often highly complex. Over 300 different…

"Hexagonal-rhombohedral. Crystals are very varied in habitat, often highly complex. Over 300 different forms have been described." — Ford, 1912

Calcite

"Hexagonal-rhombohedral. Crystals are very varied in habitat, often highly complex. Over 300 different…

"Hexagonal-rhombohedral. Crystals are very varied in habitat, often highly complex. Over 300 different forms have been described." — Ford, 1912

Calcite

"Hexagonal-rhombohedral. Crystals are very varied in habitat, often highly complex. Over 300 different…

Rhombohedron calcite crystal

Calcite

Rhombohedron calcite crystal

A flat rhombohedron calcite crystal

Calcite

A flat rhombohedron calcite crystal

An acute rhombohedron calcite crystal

Calcite

An acute rhombohedron calcite crystal

A prism and rhombohedron calcite crystal

Calcite

A prism and rhombohedron calcite crystal

A scalenohedron and rhombohedron calcite crystal

Calcite

A scalenohedron and rhombohedron calcite crystal

A basal pinacoid, prism, and rhoombohedron calcite crystal

Calcite

A basal pinacoid, prism, and rhoombohedron calcite crystal

A calcite crystal

Calcite

A calcite crystal

A calcite crystal

Calcite

A calcite crystal

A calcite crystal

Calcite

A calcite crystal

A calcite crystal

Calcite

A calcite crystal

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures consisting of triangles, squares, and parallelograms are used to construct the given shape. This tangram depicts a camel.

Camel

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures…

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures consisting of triangles, squares, and parallelograms are used to construct the given shape. This tangram depicts a camel.

Camel

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures…

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures consisting of triangles, squares, and parallelograms are used to construct the given shape. This tangram depicts a camel.

Camel

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures…

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures consisting of triangles, squares, and parallelograms are used to construct the given shape. This tangram depicts a camel.

Camel

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures…

An inscribed triangle in a circle.

Particular Cases

An inscribed triangle in a circle.

Cassiterite.

Cassiterite

Cassiterite.

"Tetragonal. Common forms are prisms and pyramids of first and second orders." — Ford, 1912

Cassiterite

"Tetragonal. Common forms are prisms and pyramids of first and second orders." — Ford, 1912

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures consisting of triangles, squares, and parallelograms are used to construct the given shape. This tangram depicts a cat.

Cat

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures…

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures consisting of triangles, squares, and parallelograms are used to construct the given shape. This tangram depicts a cat.

Cat

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures…

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures consisting of triangles, squares, and parallelograms are used to construct the given shape. This tangram depicts a cat.

Cat

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures…

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures consisting of triangles, squares, and parallelograms are used to construct the given shape. This tangram depicts a cat.

Cat

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures…

Celestite.

Celestite

Celestite.

"Orthorhombic. Crystals resemble closely those of barite. Commonly tabular parallel to the base or prismatic parallel to the brachy- or macro-axis with prominent development of the domes. Crystals which are elongated parallel to the brachy-axis are frequently terminated in front by four faces in nearly equal development, consisting of 2 prism faces and 2 of the macrodome." — Ford, 1912

Celestite

"Orthorhombic. Crystals resemble closely those of barite. Commonly tabular parallel to the base or prismatic…

An illustration showing how to construct the center and radius of a circle that will tangent a given circle and line. "Through the given point C, draw the line EF at right angles to AB; set off from C the radius r of the given circle. Join G and F. With G and F as centers draw the arc crosses m and n. Join mn, and where it crosses the line EF is the center of the required circle."

Construction Of A Center And Radius Of A Circle That Will Tangent A Given Circle And Line

An illustration showing how to construct the center and radius of a circle that will tangent a given…

An illustration showing how to construct the center and radius of a circle that will tangent a given circle and line. "From C, erect the perpendicular CG; set off the given radius r from C to H. With H as a center and r as radius, draw the cross arcs on the circle. Through the cross arcs draw the line IG; then G is the center of the circle arc FIC, which tangents the line at C and the circle at F."

Construction Of A Center And Radius Of A Circle That Will Tangent A Given Circle And Line

An illustration showing how to construct the center and radius of a circle that will tangent a given…

An illustration showing how to construct the center and radius of a circle that will tangent a given circle. "Through the given point C, draw the tangent GF; bisect the angle FGE; then o is the center of the required circle that will tangent AB at C, and the line DE."

Construction Of A Center And Radius Of A Circle That Will Tangent A Given Circle

An illustration showing how to construct the center and radius of a circle that will tangent a given…

An illustration showing how to construct a center and radius of a circle that will tangent the three sides of a triangle. "Bisect two of the angles in the triangle, and the crossing C is the center of the required circle."

Construction Of The Center And Radius Of A Circle Tangent To Triangle Sides

An illustration showing how to construct a center and radius of a circle that will tangent the three…

"A crystal has a center of symmetry if an imaginary line is passed from some point on its surface through its center, and a similar point is found on the line at an equal distance beyond the center." — Ford, 1912

Symmetry center

"A crystal has a center of symmetry if an imaginary line is passed from some point on its surface through…

"Habit varied and crystal show many forms. Crystals often tabular parallel to brachypinacoid." — Ford, 1912

Cerussite

"Habit varied and crystal show many forms. Crystals often tabular parallel to brachypinacoid." —…

Chabazite.

Chabazite

Chabazite.

"Hexagonal-rhombohedral. Common form is the simple rhombohedron, r, having nearly cubic angles. May show several different rhombohedrons." — Ford, 1912

Chabazite

"Hexagonal-rhombohedral. Common form is the simple rhombohedron, r, having nearly cubic angles. May…

Chalcanthite.

Chalcanthite

Chalcanthite.