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Illustration of a square inscribed in a closed concave geometric figure with 24 sides in the shape of a 12-point star. The two figures are concentric.

Square Inscribed in a 12-Point Star

Illustration of a square inscribed in a closed concave geometric figure with 24 sides in the shape of…

Illustration of an equilateral triangle inscribed in a closed concave geometric figure with 24 sides in the shape of a 12-point star. The two figures are concentric.

Triangle Inscribed In A 12-Point Star

Illustration of an equilateral triangle inscribed in a closed concave geometric figure with 24 sides…

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 an angelfish.

Angelfish

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 an angelfish.

Angelfish

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 an angelfish.

Angelfish

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 an angelfish.

Angelfish

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 an arch.

Arch

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 an arch.

Arch

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 an arch.

Arch

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 an arch.

Arch

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 an arrow pointing left.

Arrow Pointing Left

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 an arrow pointing left.

Arrow Pointing Left

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 an arrow pointing left.

Arrow Pointing Left

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 an arrow pointing left.

Arrow Pointing Left

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

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…

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 bear.

Bear

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 bear.

Bear

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 bear.

Bear

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 bear.

Bear

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 bearded man in a tophat.

Bearded Man in a Tophat

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 bearded man in a tophat.

Bearded Man in a Tophat

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 bearded man in tophat.

Bearded Man in Tophat

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 bearded man in tophat.

Bearded Man in Tophat

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 beta fish.

Beta Fish

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 beta fish.

Beta Fish

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 beta fish.

Beta Fish

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 beta fish.

Beta Fish

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

Illustration showing that the bisector of a given angle is the locus of points equidistant from the sides of the angle.

Angle Bisector

Illustration showing that the bisector of a given angle is the locus of points equidistant from the…

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…

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…

Sheet metal blank for making a cylindrical box with a diameter of 1 inch and a height of 2 inches.

Cylindrical Box - Blank

Sheet metal blank for making a cylindrical box with a diameter of 1 inch and a height of 2 inches.

Illustration of pattern showing steps to make a box.

Pattern To Make A Box

Illustration of pattern showing steps to make a box.

"Leaf-shaped bronze sword." — The Encyclopedia Britannica, 1910

Bronze Sword

"Leaf-shaped bronze sword." — The Encyclopedia Britannica, 1910

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 illustration of a vertical cross section of the spherical zones of a casting with a diameter of 16 inches.

Vertical Cross Section of Spherical Zones of a Casting

An illustration of a vertical cross section of the spherical zones of a casting with a diameter of 16…

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…

"In a body of equal thickness, as a board, or a slab of marble, but otherwise of an irregular shape, the centre of gravity may be found by suspending it, first from one point, and then from another, and marking, by means of a plumb line, the perpendicular ranges from the point of suspension. the centre of gravity will be the point where these two lines cross each other." -Comstock 1850

Center of Gravity

"In a body of equal thickness, as a board, or a slab of marble, but otherwise of an irregular shape,…

"When such a surface is irregular in shape, suspend it at any point, so that it may move freely, and when it has come to rest, drop a plumb line from the point of suspension and mark its direction on the surface. Do the same at any other point, and the centre of gravity will lie where the two line intersect." —Quackenbos 1859

Center of Gravity

"When such a surface is irregular in shape, suspend it at any point, so that it may move freely, and…

A circle divided evenly by a dotted line.

Divided Circle

A circle divided evenly by a dotted line.

An illustration showing a circle with radius r, diameter d, and chord c.

Radius, Diameter, and Chord In A Circle

An illustration showing a circle with radius r, diameter d, and chord c.

An illustration of a composite figure made up of a quadrilateral frustum and half of a cylinder. Frustum edges range between 6 feet and 11 feet 5 inches and cylinder has a height of 12 feet.

Composite Figure of Quadrilateral Frustum With Half of a Cylinder Attached

An illustration of a composite figure made up of a quadrilateral frustum and half of a cylinder. Frustum…

"The contours of a concave (hollowed out) cone are close together at the center (top), and far apart at the outside (bottom)." — Moss, 1914

Contours of a concave cone

"The contours of a concave (hollowed out) cone are close together at the center (top), and far apart…

Cross section of concrete conduit. The diagram can be used to find volume.

Cross Section of Concrete Conduit

Cross section of concrete conduit. The diagram can be used to find volume.

An illustration of a circular cone.

Circular Cone

An illustration of a circular cone.

A rolled out image of a cone by dividing the base in equal parts and arcs to measure the true lengths.

Development of Cone

A rolled out image of a cone by dividing the base in equal parts and arcs to measure the true lengths.

An illustration of a circular cone with the top cut off by a plane parallel to the base. The remaining part is called a frustum of a pyramid or a cone.

Circular Cone Frustum

An illustration of a circular cone with the top cut off by a plane parallel to the base. The remaining…

An illustration of a right circular cone with labels on slant height and altitude.

Right Circular Cone

An illustration of a right circular cone with labels on slant height and altitude.

An illustration of a right circular cone with labels on slant height (12.422), radius (8), and altitude (12).

Right Circular Cone

An illustration of a right circular cone with labels on slant height (12.422), radius (8), and altitude…

An illustration of a right circular cone with altitude of 10 ft. and angle of 30 degrees.

Right Circular Cone 10 Feet High With 30 Degree Angle

An illustration of a right circular cone with altitude of 10 ft. and angle of 30 degrees.

An illustration of a right circular cone with la radius of 1 foot and a height of 2 feet. Illustration could be used to find volume.

Right Circular Cone With 2 ft. Height and 1 ft. Radius

An illustration of a right circular cone with la radius of 1 foot and a height of 2 feet. Illustration…

An illustration of a right circular cone with labels on dimensions, and hole cut out. Illustration could be used for finding volume where subtraction is used.

Right Circular Cone With Hole Cut Out

An illustration of a right circular cone with labels on dimensions, and hole cut out. Illustration could…