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"Orthorhombic. Crystals commonly tabular parallel to basal plane, showing also short prisms and low brachydomes." — Ford, 1912

Marcasite

"Orthorhombic. Crystals commonly tabular parallel to basal plane, showing also short prisms and low…

A desk with math books and a protractor.

Math Books

A desk with math books and a protractor.

Labeled shapes showing various measures of form.

Measures of Form

Labeled shapes showing various measures of form.

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 medium house.

Medium House

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 medium house.

Medium House

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 medium house.

Medium House

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 medium house.

Medium House

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

"The Metacenter is the point of intersection of the vertical line passing through the center of gravity of a floating body in equilibrio, and a vertical line through the center of gravity of the fluid displaced, if the body be turned through a small angle, so that the axis takes a position inclined to the vertical. If the metacenter is above the center of gravity, the position of the body is stable; if below it, it is unstable."—(Charles Leonard-Stuart, 1911)

Metacenter

"The Metacenter is the point of intersection of the vertical line passing through the center of gravity…

Another method for using perpendicular form.

Alternate Method

Another method for using perpendicular form.

Illustration used to prove "The line joining the mid-points of two sides of a triangle is parallel to the third side and equal to one half the third side."

Line Joining Midpoints on a Triangle

Illustration used to prove "The line joining the mid-points of two sides of a triangle is parallel to…

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 mocking bird.

Mocking Bird

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 mocking bird.

Mocking Bird

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 mocking bird.

Mocking Bird

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 mocking bird.

Mocking Bird

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

"A crystal form does not necessarily make a solid figure. One such an example is this, of the Monoclinic System.

Crystal of the monoclinic system

"A crystal form does not necessarily make a solid figure. One such an example is this, of the Monoclinic…

"The symmetry of the Monoclinic System is as follows: The crystallographic axis b is an axis of binary symmetry and the plane of the a and c axes is a plane of symmetry." — Ford, 1912

Symmetry of monoclinic system

"The symmetry of the Monoclinic System is as follows: The crystallographic axis b is an axis of binary…

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 mountain.

Mountain

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 mountain.

Mountain

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 mountain.

Mountain

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 mountain.

Mountain

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

"The symmetry of the Normal Class of the Hexagonal System is as follows: The vertical crystallographic axis is an axis of hexagonal symmetry. There are six horizontal axes of binary symmetry, three of them being coincident with the crystallographic axes and the other three lying midway between them." — Ford, 1912

Symmetry of normal class

"The symmetry of the Normal Class of the Hexagonal System is as follows: The vertical crystallographic…

Showing different types of oblique prisms: rectangular, right triangular, acute triangular, and obtuse triangular.

Oblique Prisms

Showing different types of oblique prisms: rectangular, right triangular, acute triangular, and obtuse…

Types of oblique prisms: right triangular prism, isosceles triangular prism, rectangular prism, cylinder.

Oblique Prisms

Types of oblique prisms: right triangular prism, isosceles triangular prism, rectangular prism, cylinder.

"A polygon of...eight sides [is] an octagon." —Hallock 1905

Octagon

"A polygon of...eight sides [is] an octagon." —Hallock 1905

An illustration showing how to construct a regular octagon from a square by cutting off the corners of the square. "With the corners as centers, draw circle arcs through the center of the square to the side, which determine the cut-off."

Construction Of An Octagon From a Square

An illustration showing how to construct a regular octagon from a square by cutting off the corners…

An illustration showing how to construct an octagon on a given line. "Prolong AB to C. With B as center and AB as radius, draw the circle AFDEC; from B, draw BI at right angles to AB; divide the angles ABC and DBC each into two equal parts; then BD is one side of the octagon. With A and E as centers, draw the arcs HKE and AKI, which determine the points H and I, and thus complete the octagon as shown in the illustration."

Construction Of An Octagon

An illustration showing how to construct an octagon on a given line. "Prolong AB to C. With B as center…

Illustration of a figure that is made up of 4 octagons with 5 squares (diamonds).

Design Consisting of Octagons and Squares

Illustration of a figure that is made up of 4 octagons with 5 squares (diamonds).

An octohedron.

Octahedron

An octohedron.

An octahedron, or double four-sided pyramid. It has 8 sides.

Octahedron

An octahedron, or double four-sided pyramid. It has 8 sides.

An octohedron.

Octahedron

An octohedron.

A combination of octahedron and dodecahedron.

Octahedron and dodecahedron

A combination of octahedron and dodecahedron.

"Combiantion of pyritohedron and octahedron." — Ford, 1912

Octahedron and pyritohedron

"Combiantion of pyritohedron and octahedron." — Ford, 1912

"A combination of pyritohedron and octahedron." — Ford, 1912

Octahedron and pyritohedron

"A combination of pyritohedron and octahedron." — Ford, 1912

"A combination of a trisoctahedron and an octahedron. It will be noted that the faces of the trisoctahedron bevel the edges of the ocrahedron." — Ford, 1912

Octahedron and trisoctahedron

"A combination of a trisoctahedron and an octahedron. It will be noted that the faces of the trisoctahedron…

"When a corner or an edge of one form is replaced by a face of another form, the first is said to be trunctuated by the second." — Ford, 1912

Cube trunctuated by octahedron

"When a corner or an edge of one form is replaced by a face of another form, the first is said to be…

A distorted octahedron.

Distorted octahedron

A distorted octahedron.

"A contact twin, since the two individuals lie simply in contact with each other upon a certain plane." — Ford, 1912

Twinned octahedron

"A contact twin, since the two individuals lie simply in contact with each other upon a certain plane."…

A straight line through the origin of a coordinate plane.

The Origin

A straight line through the origin of a coordinate plane.

Orthoclase

Orthoclase

Orthoclase

Orthoclase.

Orthoclase

Orthoclase.

"Monoclinic. Crystals are usually prismatic in habit and have as prominent forms, clinopinacoid, base, prism, with often smaller orthodomes." — Ford, 1912

Orthoclase

"Monoclinic. Crystals are usually prismatic in habit and have as prominent forms, clinopinacoid, base,…

"Monoclinic. Crystals are usually prismatic in habit and have as prominent forms, clinopinacoid, base, prism, with often smaller orthodomes." — Ford, 1912

Orthoclase

"Monoclinic. Crystals are usually prismatic in habit and have as prominent forms, clinopinacoid, base,…

"Monoclinic. Crystals are usually prismatic in habit and have as prominent forms, clinopinacoid, base, prism, with often smaller orthodomes." — Ford, 1912

Orthoclase

"Monoclinic. Crystals are usually prismatic in habit and have as prominent forms, clinopinacoid, base,…

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 palm tree.

Palm Tree

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 palm tree.

Palm Tree

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 palm tree.

Palm Tree

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 palm tree.

Palm Tree

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

An illustration showing how to construct a parabola by plotting. "Having given the axis, vertex, and focus of the parabola. Divide the transverse axis into any desired number of parts 1, 2, 3, etc., and draw ordinates through the divisions; take the distance A1, and set it off on the 1st ordinate from the focus f to a, so that A1 = fa. Repeat the same operation with the other ordinates - that is, set off the distance A5 from f to e, so that A5 = fe; and so the parabola is constructed."

Construction Of A Parabola

An illustration showing how to construct a parabola by plotting. "Having given the axis, vertex, and…

An illustration showing how to construct a parabola using a pencil and a string. "Having given the two axes, vertex, and focus of the parabola. Take a square cde, and fix to it a string at c; fix the other end of the string at the focus f. The length of the sting should be such that when the square is in the position of the axis Af, the string should reach to the vertex A. Move the square along BB, and the pencil P will describe the parabola."

Construction Of A Parabola

An illustration showing how to construct a parabola using a pencil and a string. "Having given the two…

An illustration showing how to construct a parabola. "Given the vertex A, axis x, and a point P. Draw AB at right angle to x, and BP parallel to x, divide AB and BP into an equal number of equal parts. From the vertex A draw lines to the divisions on BP, from the divisions on AB draw the ordinates parallel to x, the corresponding intersections are points in the parabola."

Construction Of A Parabola

An illustration showing how to construct a parabola. "Given the vertex A, axis x, and a point P. Draw…

An illustration showing how to construct a parabola. "Given the axis of ordinate B, and vertex A. Take A as a center and describe a semicircle from B which gives the focus of the parabola at f. Draw any ordinate y at right angle to the abscissa Ax, take a as radius and the focus f as a center, then intersect the ordinate y, by a circle-arc in P which will be a point in the parabola. In the same manner the whole Parabola is constructed."

Construction Of A Parabola

An illustration showing how to construct a parabola. "Given the axis of ordinate B, and vertex A. Take…

Illustration of the construction used to create a line parallel to a given line.

Construction Of A Parallel Line

Illustration of the construction used to create a line parallel to a given line.

Showing different types of parallel prisms: rectangular, right triangular, acute triangular, and obtuse triangular.

Parallel Prisms

Showing different types of parallel prisms: rectangular, right triangular, acute triangular, and obtuse…

Types of parallel prisms: right triangular prism, isosceles triangular prism, rectangular prism, cylinder.

Parallel Prisms

Types of parallel prisms: right triangular prism, isosceles triangular prism, rectangular prism, cylinder.

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…

"In the diagram, let AB and AC represent two forces acting upon the point, A. Draw the two dotted lines to complete the parallelogram." — Avery, 1895

Parallelogram

"In the diagram, let AB and AC represent two forces acting upon the point, A. Draw the two dotted lines…

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 parallelogram.

Parallelogram

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 parallelogram.

Parallelogram

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 parallelogram.

Parallelogram

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 parallelogram.

Parallelogram

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