Three dimensional representation of the intersecting planes required to create the conic sections hyperbola, parabola, ellipse, and circle.

Conic Sections 3D

Three dimensional representation of the intersecting planes required to create the conic sections hyperbola,…

Diagram of a cone with spheres and cut by a plane to depict the conic sections.

Cone depicting Conic Sections

Diagram of a cone with spheres and cut by a plane to depict the conic sections.

Diagram of a cone with inscribed spheres and cut by various planes to depict the conic sections: circle, ellipse.

Cone depicting Conic Sections

Diagram of a cone with inscribed spheres and cut by various planes to depict the conic sections: circle,…

Diagram showing how to construct a conic when given the focus and the auxiliary circle. If the focus is outside the circle, we get a hyperbola. If it's inside the circle, we get an ellipse. If the auxiliary circle is a straight line (radius is infinite), we get a parabola.

Construction of a Conic

Diagram showing how to construct a conic when given the focus and the auxiliary circle. If the focus…

Diagram showing how to construct a conic when given the focus and the auxiliary circle. The focus is on the left of the auxiliary circle, thus producing a very obtuse hyperbola.

Focus In Auxiliary Circle of Conic

Diagram showing how to construct a conic when given the focus and the auxiliary circle. The focus is…

Diagram showing how to construct a conic when given the focus and the auxiliary circle. As the focus moves inside the circle the ellipse broadens out until the focus reaches the center and becomes a circle.

Focus In Auxiliary Circle of Conic

Diagram showing how to construct a conic when given the focus and the auxiliary circle. As the focus…

Also known as Pinus coulteri. The pine cone of a Coulter Pine tree.

Pine Cone of Coulter Pine

Also known as Pinus coulteri. The pine cone of a Coulter Pine tree.

An illustration of finding an intersection of a cone and cylinder by either cutting the vertex of the cone and parallel to the cylinder; or by cutting circles from the right cone perpendicular to the axes.

Intersection of Cylinder and Cone

An illustration of finding an intersection of a cone and cylinder by either cutting the vertex of the…

An illustration of finding an intersection of a cone and cylinder by either cutting the vertex of the cone and parallel to the cylinder; or by cutting circles from the right cone perpendicular to the axes.

Intersection of Cylinder and Cone

An illustration of finding an intersection of a cone and cylinder by either cutting the vertex of the…

An illustration of a Douglas fir cone, seed, and foliage.

Douglas Fir Cone, Seed, and Foliage

An illustration of a Douglas fir cone, seed, and foliage.

Also known as Pseudotsuga menziesii. An evergreen conifer species found in western North America.

Pine Cone of Douglas Spruce

Also known as Pseudotsuga menziesii. An evergreen conifer species found in western North America.

"An improved form of the lamp, in which a portion of the cone B is removed to show the two parallel flat wicks A, A, which have each a separate slit or opening in the cone. C is the coincident winder for raising or lowering the wicks in the tubes, by which the wicks can be moved separately or simultaneously as desired. D is a lever for raising the extinguishers E, whereby not onl is the light instantly extinguished, but the wicks are also covered and protected from dirt, while all evaporation by the wick-holder is prevented." —The Encyclopedia Britannica, 1910

Duplex Burner

"An improved form of the lamp, in which a portion of the cone B is removed to show the two parallel…

Illustration showing an ellipse formed by the intersection of the surface of a cone with a plane neither parallel nor perpendicular to a straight line of the surface of the cone nor the axis.

Ellipse

Illustration showing an ellipse formed by the intersection of the surface of a cone with a plane neither…

Illustration showing the definition of an ellipse as a conic section. "The section of a right circular cone made by a plane that cuts all the elements of the surface of the cone is an ellipse."

Conic Section Showing an Ellipse

Illustration showing the definition of an ellipse as a conic section. "The section of a right circular…

Illustration showing the definition of an ellipse as a conic section. "The section of a right circular cone made by a plane that cuts all the elements of the surface of the cone is an ellipse."

Conic Section Showing an Ellipse

Illustration showing the definition of an ellipse as a conic section. "The section of a right circular…

Illustration showing the definition of an ellipse as a conic section. The plane cuts the cone obliquely.

Conic Section Showing Ellipse

Illustration showing the definition of an ellipse as a conic section. The plane cuts the cone obliquely.

Illustration showing the definition of an ellipse as a conic section. The section of a right circular cone made by a plane that cuts all the elements of the surface of the cone is an ellipse. The plane is neither parallel nor perpendicular to the axis.

Conic Section Showing An Ellipse

Illustration showing the definition of an ellipse as a conic section. The section of a right circular…

An illustration showing the intersection of a plane and a cone. The cone is intersected by a plane neither parallel to nor perpendicular to the base, nor parallel to a side. Thus forming an ellipse.

Conic Section Showing An Ellipse

An illustration showing the intersection of a plane and a cone. The cone is intersected by a plane neither…

Diagram showing how to construct an ellipse when given the two foci and the length of the major axis (2a).

Construction of an Ellipse

Diagram showing how to construct an ellipse when given the two foci and the length of the major axis…

Diagram of an ellipse that can used to illustrate the definition. "The constant ration between the distances of a point on an ellipse from the focus and the directrix equals the linear eccentricity divided by the semi major axis."

Definition of Ellipse

Diagram of an ellipse that can used to illustrate the definition. "The constant ration between the distances…

Diagram that illustrates "The algebraic sum of the distances of any point from the foci of a conic is greater or less than 2a, according as the point is without or within the curve."

Foci Distances on an Ellipse

Diagram that illustrates "The algebraic sum of the distances of any point from the foci of a conic is…

Diagram of an ellipse that can used to illustrate the different parts. Segment MN is the major axis, segment CD is the conjugate (minor) axis, and point O is the center of the ellipse. Both foci are also labeled in the illustration.

Parts of Ellipse

Diagram of an ellipse that can used to illustrate the different parts. Segment MN is the major axis,…

Diagram an ellipse with a tangent line that illustrates "A line through a point on the ellipse and bisecting the external angle between the focal radii is a tangent."

Tangent to an Ellipse

Diagram an ellipse with a tangent line that illustrates "A line through a point on the ellipse and bisecting…

Also known as Picea engelmannii. A species of spruce tree native to western North America.

Engelmann Spruce Pine Cone

Also known as Picea engelmannii. A species of spruce tree native to western North America.

The most interesting monuments of Etruscan architecture which have been preserved are the tombs. They are for the most part chambers hewn in the rock, and supported by square piers. The tombs were either subterranean, and had an entrance façade hewn out of the rock, or they assume the shape of tumuli, which had one or more conical elevations resting on a superstructure. Sometimes these tombs are quadrangular with a pyramidal superstructure

Etruscan Tomb at Castel d'Asso

The most interesting monuments of Etruscan architecture which have been preserved are the tombs. They…

"A conical pin of hard wood, from 12 to 24 inches long, and from 1 to 3 inches in diameter at the butt, used to open the strands of rope in splicing." -Whitney, 1911

Setting Fid

"A conical pin of hard wood, from 12 to 24 inches long, and from 1 to 3 inches in diameter at the butt,…

A flashcard featuring an illustration of a Cone

Flashcard of a Cone

A flashcard featuring an illustration of a Cone

Also known as Pinus balfouriana. The pine cone of a Foxtail Pine tree.

Pine Cone of Foxtail Pine

Also known as Pinus balfouriana. The pine cone of a Foxtail Pine tree.

Also known as Abies fraseri. A species of fir native to the eastern United States mountains.

Pine Cone of Fraser Fir

Also known as Abies fraseri. A species of fir native to the eastern United States mountains.

"The part of any solid between two planes, which may be either parallel or inclined to each other: as, the frustum of a cone ... In the figure the dotted line, c, indicates the part of the cone cut off to form the frustum, f." -Whitney, 1911

Frustum of a Cone

"The part of any solid between two planes, which may be either parallel or inclined to each other: as,…

A kind of inverted hollow cone with a pipe.

Funnel

A kind of inverted hollow cone with a pipe.

A conically shaped utensil having a narrow tube at the small end; used to channel the flow of substances into a container with a small mouth.

Automatic Funnel

A conically shaped utensil having a narrow tube at the small end; used to channel the flow of substances…

Also known as Abies grandis. A fir native to the Pacific Northwest and Northern California.

Pine Cone of Grand Fir

Also known as Abies grandis. A fir native to the Pacific Northwest and Northern California.

An illustration of the hemlock spruce's seed, cone, and foliage.

Hemlock Spruce Cone, Seed and Foliage

An illustration of the hemlock spruce's seed, cone, and foliage.

Cone of horsetail.

Cone of horsetail

Cone of horsetail.

Illustration showing a hyperbola as a curve formed by the intersection of the surface of a cone with a plane parallel to the axis of the cone.

Hyperbola

Illustration showing a hyperbola as a curve formed by the intersection of the surface of a cone with…

Diagram depicting a cone with both nappes intersected by plane J to form a hyperbola.

Cone Intersected by a Plane to Form a Hyperbola

Diagram depicting a cone with both nappes intersected by plane J to form a hyperbola.

Illustration showing the definition of an hyperbola as a conic section. "The section of a right circular cone made by a plane that cuts both nappes of the cone is a hyperbola." A double right circular cone with a plane parallel to the axis cutting through the cones.

Conic Section Showing an Hyperbola

Illustration showing the definition of an hyperbola as a conic section. "The section of a right circular…

Illustration showing the definition of a hyperbola as a conic section.

Conic Section Showing Hyperbola

Illustration showing the definition of a hyperbola as a conic section.

Illustration showing the definition of an hyperbola as a conic section. A hyperbola is formed from a double right circular cone with a plane parallel to the axis cutting through the cones.

Conic Section Showing A Hyperbola

Illustration showing the definition of an hyperbola as a conic section. A hyperbola is formed from a…

An illustration showing the intersection of a plane and a double cone. The cone is intersected by a plane parallel to the axis. Thus forming a Hyperbola.

Conic Section Showing A Hyperbola

An illustration showing the intersection of a plane and a double cone. The cone is intersected by a…

Diagram showing how to construct a hyperbola when given the two foci and the length of the major axis (2a).

Construction of a Hyperbola

Diagram showing how to construct a hyperbola when given the two foci and the length of the major axis…

Diagram part of a hyperbola with a tangent line that illustrates "A line through a point on the hyperbola and bisecting the internal angle between the focal radii is a tangent."

Tangent to a Hyperbola

Diagram part of a hyperbola with a tangent line that illustrates "A line through a point on the hyperbola…

Also known as Libocedrus decurrens.

Branch of Incense Cedar

Also known as Libocedrus decurrens.

Also known as Pinus attenuata. The pine cone of a Knobcone Pine tree.

Pine Cone of Knobcone Pine

Also known as Pinus attenuata. The pine cone of a Knobcone Pine tree.

Also known as Pinus flexilis. A pine cone of the Limber Pine tree.

Pine Cone of Limber Pine

Also known as Pinus flexilis. A pine cone of the Limber Pine tree.

A piece of limestone.

Limestone

A piece of limestone.

Also known as Pinus taeda. The pine cone of a Southeastern United States pine tree.

Pine Cone of Loblolly Pine

Also known as Pinus taeda. The pine cone of a Southeastern United States pine tree.

Also known as Pinus contorta. The pine cone of a Lodgepole Pine tree, commonly found in western North America.

Pine Cone of Lodgepole Pine

Also known as Pinus contorta. The pine cone of a Lodgepole Pine tree, commonly found in western North…

Also known as Pinus palustris. The pine cone of a Longleaf Pine tree.

Pine Cone of Longleaf Pine

Also known as Pinus palustris. The pine cone of a Longleaf Pine tree.

An illustration of the magnolia flower's cone of ripe fruits.

Magnolia Cone of Ripe Fruits

An illustration of the magnolia flower's cone of ripe fruits.

Also known as Pinus serotina. The pine cone of a Marsh Pine tree.

Pine Cone of Marsh Pine

Also known as Pinus serotina. The pine cone of a Marsh Pine tree.

Also known as Pinus cembroides. A pine cone of a Mexican Pinyon tree.

Pine Cone of Mexican Pinyon

Also known as Pinus cembroides. A pine cone of a Mexican Pinyon tree.

Also known as Pinus radiata. The pine cone of a Monterey Pine tree.

Pine Cone of Monterey Pine

Also known as Pinus radiata. The pine cone of a Monterey Pine tree.

Also known as Tsuga mertensiana. A species of hemlock native to the west coast of North America, between Alaska and Caiifornia.

Pine Cone of Mountain Hemlock

Also known as Tsuga mertensiana. A species of hemlock native to the west coast of North America, between…

Also known as Abies nobilis. Native to the Cascade Range and Coast Range mountains.

Pine Cone of Noble Fir

Also known as Abies nobilis. Native to the Cascade Range and Coast Range mountains.

"1. Norfolk Island Pine (Araucaria excelsa). 2. Cone of Araucaria Cookii."-Whitney, 1902

Norfolk Island Pine

"1. Norfolk Island Pine (Araucaria excelsa). 2. Cone of Araucaria Cookii."-Whitney, 1902

"An oblique cone connecting two parallel pipes of different diameters... the true size of the base is not given in the top view and must be revolved until parallel to H."—French, 1911

Oblique Cone by Triangulation Connecting to Two Parallel Pipes of Different Diameters

"An oblique cone connecting two parallel pipes of different diameters... the true size of the base is…

A development or rolled out oblique cone using triangulation. The method of triangulation is done by creating series of triangles respect to the base.

Development of Oblique Cone by Triangulation

A development or rolled out oblique cone using triangulation. The method of triangulation is done by…

Also known as Abies amabilis. A species of fir native to the Pacific Northwest of North America.

Pine Cone of Pacific Silver Fir

Also known as Abies amabilis. A species of fir native to the Pacific Northwest of North America.