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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 runner.

Runner

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 runner.

Runner

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

Rutile.

Rutile

Rutile.

"Tetragonal. Usually prismatic with pyramid terminations." — Ford, 1912

Rutile

"Tetragonal. Usually prismatic with pyramid terminations." — 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 sailboat.

Sailboat

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 sailboat.

Sailboat

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 sailboat.

Sailboat

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 sailboat.

Sailboat

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 saint.

Saint

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 saint.

Saint

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 saint.

Saint

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 saint.

Saint

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

"Nodal Cubic, with four primary lines and their satellite. In the diagram, ABC is the satellite line. From its intersections with the cubic curve tangents are drawn to the latter, AD, AE, BF, BG, CH, CI. The points of tangency lie three by three on four primary lines, FDH, DGI, EGH, FEI." -Whitney, 1911

Satellite

"Nodal Cubic, with four primary lines and their satellite. In the diagram, ABC is the satellite line.…

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 saw blade.

Saw Blade

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 saw blade.

Saw Blade

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 saw blade.

Saw Blade

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 saw blade.

Saw Blade

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

"This form consists of twelve scalene triangular faces. These faces correspond in their position to the alternate pairs of faces of a dihexagonal pyramid." — Ford, 1912

Scalenohedron

"This form consists of twelve scalene triangular faces. These faces correspond in their position to…

"A crystal of scapolite, upon which the faces of the third-order pyramid are shown." — Ford, 1912

Scapolite

"A crystal of scapolite, upon which the faces of the third-order pyramid are shown." — Ford, 1912

"Tetragonal; tri-pyramidal. Crystals usually simple pyramids of first order. Closely resemble isometric octahedrons in angles. Faces of the pyramid of third order are small and rare." — Ford, 1912

Scheelite

"Tetragonal; tri-pyramidal. Crystals usually simple pyramids of first order. Closely resemble isometric…

An illustration showing how to construct a screw helix.

Construction Of A Screw Helix

An illustration showing how to construct a screw helix.

"Grolier scroll, the flowing curved lines that surround and interlace the geometrical framework of a design for a book-cover in the style of Grolier." -Whitney, 1911

Grolier Scroll

"Grolier scroll, the flowing curved lines that surround and interlace the geometrical framework of a…

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 sea monster.

Sea Monster

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 Sea Monster.

Sea Monster

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 sea monster.

Sea Monster

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 sea monster.

Sea Monster

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 sea turtle.

Sea Turtle

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 sea turtle.

Sea Turtle

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 sea turtle.

Sea Turtle

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 sea turtle.

Sea Turtle

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 seagull.

Seagull

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 seagull.

Seagull

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 seagull.

Seagull

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 seagull.

Seagull

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

A secant is "a line which cuts a figure in any way. Specifically, in trigonometry, a line from the center of a circle through one extremity of an arc (whose secant it is said to be) to the tangent from the other extremity of the same arc; or the ratio of this line to the radius; the reciprocal of the cosine. The ratio of AB to AD is the secant of the angle A; and AB is the secant of the arc CD." —Whitney, 1889

Circle with Secant

A secant is "a line which cuts a figure in any way. Specifically, in trigonometry, a line from the center…

"This is a form consisting of six rectangular vertical faces, each of which intersects two of the horizontal axes equally and the immediate horizontal axis at one half this distance." — Ford, 1912

Prism of the second order

"This is a form consisting of six rectangular vertical faces, each of which intersects two of the horizontal…

"This is a form composed of twelve isoceles triangular faces, each of which intersects two of the horizontal axes equally, the third and immediate horizontal axis at one-half this distance, and also intersects the vertical axis." — Ford, 1912

Pyramid of the second order

"This is a form composed of twelve isoceles triangular faces, each of which intersects two of the horizontal…

"In geometry: (a) A plane figure inclosed between the arc of a circle, ellipse, or other central curve and two radii to its extremities from the center. Thus, in the figure, CDB is a sector of a circle." -Whitney, 1911

Sector

"In geometry: (a) A plane figure inclosed between the arc of a circle, ellipse, or other central curve…

An illustration showing a circle sector with radius r, center/central angle v, and length of circle arc b.

Circle Sector

An illustration showing a circle sector with radius r, center/central angle v, and length of circle…

An illustration showing a circle sector with center/central angle v and polygon angle w.

Circle Sector

An illustration showing a circle sector with center/central angle v and polygon angle w.

An illustration showing a circle sector with height of segment h and radius r.

Circle Sector

An illustration showing a circle sector with height of segment h and radius r.

Illustration of a circle used to prove "Any angle inscribed in a semicircle is a right angle."

Right Angles Inscribed in Semicircle Proof

Illustration of a circle used to prove "Any angle inscribed in a semicircle is a right angle."

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 shark.

Shark

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 shark.

Shark

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 shark.

Shark

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 shark.

Shark

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

"Shear is a particular form of strain produced by causing plane layers of a material to slide parallel to one another through spaces proportional to their distances from a fixed parallel plane"—Finley, 1917

Shear

"Shear is a particular form of strain produced by causing plane layers of a material to slide parallel…

An illustration showing how to construct Shield's anti-friction curve. "R represents the radius of the shaft, and C1, 2, 3, et., is the center line of the shaft. From o, set off the small distance oa; and set off a1 - R. Set off the same small distance from a to b, and make b2 = R. Continue in the same way with the other points, and the anti-friction curve is thus constructed.

Construction Of Shield's Anti-friction Curve

An illustration showing how to construct Shield's anti-friction curve. "R represents the radius of the…

Any system of coordinate axes to another set which is parallel to the former, but with different origins.

Axes Shift

Any system of coordinate axes to another set which is parallel to the former, but with different origins.

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 ship.

Ship

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 ship.

Ship

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 ship.

Ship

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 ship.

Ship

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

Illustration used to prove "The line bisecting one side of a triangle and parallel to another side bisects the third side."

Line Bisecting Side of a Triangle

Illustration used to prove "The line bisecting one side of a triangle and parallel to another side bisects…

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 sitting cat.

Sitting 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 sitting cat.

Sitting 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 sitting cat.

Sitting 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 sitting cat.

Sitting Cat

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

Illustration of a slanted line segment. A line segment is a section of a line with definite endpoints.

Segment, Slanted Line

Illustration of a slanted line segment. A line segment is a section of a line with definite endpoints.

Illustration of a slanted line segment. A line segment is a section of a line with definite endpoints.

Segment, Slanted Line

Illustration of a slanted line segment. A line segment is a section of a line with definite endpoints.