A circle and triangle situated on coordinate planes.

Circle

A circle and triangle situated on coordinate planes.

Circle modeling the earth. O is the center of the earth, r the radius of the earth, and h the height of the point P above the surface; it is required to find the distance from the point P to the horizon at A.

Circle With Center o and Radius r with point P

Circle modeling the earth. O is the center of the earth, r the radius of the earth, and h the height…

Illustrations of a circle with a chord and triangle inside.

Circle with Chord and Triangle

Illustrations of a circle with a chord and triangle inside.

Illustration showing a circle with a diameter, radius, lines, triangle, and segment drawn.

Circle With Diameter, Radius, Segment, Line

Illustration showing a circle with a diameter, radius, lines, triangle, and segment drawn.

Illustration of a circle with an angle inscribed in a segment greater than a semicircle, an acute angle.

Circle With Inscribed Angle Greater Than Semicircle

Illustration of a circle with an angle inscribed in a segment greater than a semicircle, an acute angle.

Illustration of a circle with an angle inscribed in a segment less than a semicircle, an obtuse angle.

Circle With Inscribed Angle Less Than Semicircle

Illustration of a circle with an angle inscribed in a segment less than a semicircle, an obtuse angle.

Illustration of a circle with a right angle inscribed in a semicircle.

Circle With Inscribed Right Angle in Semicircle

Illustration of a circle with a right angle inscribed in a semicircle.

Illustration showing a circle with equilateral triangles and another circle within.

Circle With Triangles and Circle Within

Illustration showing a circle with equilateral triangles and another circle within.

Illustration of circle with radius of 4000, and triangle with 45 degree angle enclosed.

Circles With Radius 4000 and Enclosed Triangle

Illustration of circle with radius of 4000, and triangle with 45 degree angle enclosed.

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…

Circle with triangle to show how to divide a line in extreme and mean ratio.

Circle and Triangle

Circle with triangle to show how to divide a line in extreme and mean ratio.

Circle with triangles.

Circle and Triangles

Circle with triangles.

Circle with triangle and chords.

Circle and Triangle

Circle with triangle and chords.

Circle with triangle and chords.

Circle and Triangle

Circle with triangle and chords.

Circle with triangle and chords.

Circle and Triangle

Circle with triangle and chords.

Circle with triangle inscribed.

Circle and Inscribed Triangle

Circle with triangle inscribed.

Illustration of triangle inscribed in circle. Or, circle circumscribed about triangle.

Triangle Inscribed in Circle

Illustration of triangle inscribed in circle. Or, circle circumscribed about triangle.

Illustration showing a circle with an inscribed triangle and radii.

Circle With Inscribed Triangle and Radii

Illustration showing a circle with an inscribed triangle and radii.

Circle with two triangles.

Circle and Triangles

Circle with two triangles.

Illustration showing that a circle may be considered as made up of triangles whose bases form the circumference.

Triangles Making Up A Circle

Illustration showing that a circle may be considered as made up of triangles whose bases form the circumference.

Illustration showing a circle with an inscribed quadrilateral and triangles formed by extended chords.

Circle With Inscribed Quadrilateral and Triangles Formed

Illustration showing a circle with an inscribed quadrilateral and triangles formed by extended chords.

Illustration showing that from any point in the circumference of a circle, a chord and a tangent are drawn, the perpendiculars dropped on them from the middle point of the subtended arc are equal.

Circle With a Tangent Line and Chord

Illustration showing that from any point in the circumference of a circle, a chord and a tangent are…

Illustration showing 2 intersecting circles with a lines drawn that form a triangle.

Two Intersecting Circles With Lines

Illustration showing 2 intersecting circles with a lines drawn that form a triangle.

"The compasses, next to the T square and triangles, are used more than any other instrument. A pencil and pen point are provided, either of which may be inserted into a socket in one leg of the instrument, for the drawing of circles in pencil or ink." — Hallock, 1905

Compasses

"The compasses, next to the T square and triangles, are used more than any other instrument. A pencil…

"The compasses, next to the T square and triangles, are used more than any other instrument. A pencil and pen point are provided, either of which may be inserted into a socket in one leg of the instrument, for the drawing of circles in pencil or ink." — Hallock, 1905

Compasses

"The compasses, next to the T square and triangles, are used more than any other instrument. A pencil…

"The compasses, next to the T square and triangles, are used more than any other instrument. A pencil and pen point are provided, either of which may be inserted into a socket in one leg of the instrument, for the drawing of circles in pencil or ink." — Hallock, 1905

Compasses

"The compasses, next to the T square and triangles, are used more than any other instrument. A pencil…

"The compasses, next to the T square and triangles, are used more than any other instrument. A pencil and pen point are provided, either of which may be inserted into a socket in one leg of the instrument, for the drawing of circles in pencil or ink." — Hallock, 1905

Compasses

"The compasses, next to the T square and triangles, are used more than any other instrument. A pencil…

"The compasses, next to the T square and triangles, are used more than any other instrument. A pencil and pen point are provided, either of which may be inserted into a socket in one leg of the instrument, for the drawing of circles in pencil or ink." — Hallock, 1905

Compasses

"The compasses, next to the T square and triangles, are used more than any other instrument. A pencil…

"The compasses, next to the T square and triangles, are used more than any other instrument. A pencil and pen point are provided, either of which may be inserted into a socket in one leg of the instrument, for the drawing of circles in pencil or ink." — Hallock, 1905

Compasses

"The compasses, next to the T square and triangles, are used more than any other instrument. A pencil…

Illustration of a figure made up of 4 smaller figures (triangles).

Composite Figure

Illustration of a figure made up of 4 smaller figures (triangles).

Illustration of a composite figure made up of rings, rectangles, triangles, etc..

Composite Figure

Illustration of a composite figure made up of rings, rectangles, triangles, etc..

"If a cone be cut by a plane, parallel to the base, so as to form two parts, the lower part is called the frustum of the cone." — Hallock, 1905

Cone

"If a cone be cut by a plane, parallel to the base, so as to form two parts, the lower part is called…

Illustration of a plane passing through the vertex of a cone (section made is a triangle).

Plane Passing Through the Vertex of a Cone

Illustration of a plane passing through the vertex of a cone (section made is a triangle).

Illustration of a plane passing through the vertex of a cone (section made is a triangle).

Plane Passing Through the Vertex of a Cone

Illustration of a plane passing through the vertex of a cone (section made is a triangle).

Two dimensional view of the cuts required to create the conic sections hyperbola, parabola, ellipse, and circle.

Conic Sections 2D

Two dimensional view of the cuts required to create the conic sections hyperbola, parabola, ellipse,…

This modern French console has a front view like a pendant triangle.

Modern French Console

This modern French console has a front view like a pendant triangle.

The Renaissance console is shaped in front-view like a pendant triangle. This console is found in a castle in Blois, France.

Renaissance Console

The Renaissance console is shaped in front-view like a pendant triangle. This console is found in a…

Illustration of a triangle with its incircle and three excircles constructed.

Triangle With Circle Constructions

Illustration of a triangle with its incircle and three excircles constructed.

Illustration of the construction used to make a triangle when given two sides and the angle opposite one of them. This is for case 1 of the ambiguous case, when a is less than b.

Construction of a Triangle When Given Two Sides and the Angle Opposite (Ambiguous Case)

Illustration of the construction used to make a triangle when given two sides and the angle opposite…

Illustration of the construction used to make a triangle when given two sides and the angle opposite one of them. This is for case 2 of the ambiguous case, when a is equal to b.

Construction of a Triangle When Given Two Sides and the Angle Opposite (Ambiguous Case)

Illustration of the construction used to make a triangle when given two sides and the angle opposite…

Illustration of the construction used to make a triangle when given two sides and the angle opposite one of them. This is for case 2 of the ambiguous case, when a is equal to b.

Construction of a Triangle When Given Two Sides and the Angle Opposite (Ambiguous Case)

Illustration of the construction used to make a triangle when given two sides and the angle opposite…

Illustration used to construct a triangle , given the perimeter, one angle, and the altitude from the vertex of the given angle.

Construction of a Triangle Given Perimeter, Angle, Altitude

Illustration used to construct a triangle , given the perimeter, one angle, and the altitude from the…

Illustration showing the correct and incorrect position of a right line pen against a T-square, triangle, or straight edge when doing geometric constructions.

Positioning Pen for Constructions

Illustration showing the correct and incorrect position of a right line pen against a T-square, triangle,…

"Draw three-inch square. Draw lines AB, BC, DE and EF at 30 degrees. Divide lower side into seven equal parts with the dividers. Draw the vertical lines, and mark divisions on AC with pencil as each line is drawn. Through the division points on top and bottom draw the converging lines using the triangle alone as a straight-edge." —French, 1911

Drawing Converging Lines

"Draw three-inch square. Draw lines AB, BC, DE and EF at 30 degrees. Divide lower side into seven equal…

"This triangular shape is a good one also for a movable poultry-house in its simplest form." — Harcourt, 1889

Triangular coop

"This triangular shape is a good one also for a movable poultry-house in its simplest 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 cormorant.

Cormorant

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 cormorant.

Cormorant

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 cormorant.

Cormorant

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 cormorant.

Cormorant

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 cup.

Cup

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 cup.

Cup

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 cup.

Cup

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 cup.

Cup

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

Illustration of blueprint used by highway engineers to widen the pavement on the inside of the curve of a road.

Curve in Pavement of Road

Illustration of blueprint used by highway engineers to widen the pavement on the inside of the curve…

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 dancer.

Dancer

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 dancer.

Dancer

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 dancer.

Dancer

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 dancer.

Dancer

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

A homemade section liner device made by slipping a wooden block to hold the triangle to make cross hatching lines.

Section Lining Device

A homemade section liner device made by slipping a wooden block to hold the triangle to make cross hatching…

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 diver.

Diver

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