Mediaspace scheduled maintenance: Aug 25, 2026 07:00 - 12:00 AM. During this time, videos will be temporarily unavailable. Check status updates.

Lecture

Sphere, Cone, and Cylinder: Descriptive Geometry

Description

This lecture covers the definitions and properties of spheres, cones, and cylinders, including sections of a sphere, projections, and apparent contours. It also discusses intersections of lines with spheres, as well as cones and cylinders as ruled surfaces. Special cases such as circular cones and cylinders are explored, along with the intersection of a line with a cone. The lecture concludes with sections on conic sections, including ellipses, parabolas, and hyperbolas, and their asymptotes. Practical applications and examples are provided throughout the lecture.

Official source

Ontological neighbourhood

Mathematics

Geometry: Euclidean geometry

Related concepts (32)

Parabola

In mathematics, a parabola is a plane curve which is mirror-symmetrical and is approximately U-shaped. It fits several superficially different mathematical descriptions, which can all be proved to define exactly the same curves. One description of a parabola involves a point (the focus) and a line (the directrix). The focus does not lie on the directrix. The parabola is the locus of points in that plane that are equidistant from the directrix and the focus.

Sphere

A sphere () is a geometrical object that is a three-dimensional analogue to a two-dimensional circle. Formally, a sphere is the set of points that are all at the same distance r from a given point in three-dimensional space. That given point is the centre of the sphere, and r is the sphere's radius. The earliest known mentions of spheres appear in the work of the ancient Greek mathematicians. The sphere is a fundamental object in many fields of mathematics. Spheres and nearly-spherical shapes also appear in nature and industry.

Confocal conic sections

In geometry, two conic sections are called confocal if they have the same foci. Because ellipses and hyperbolas have two foci, there are confocal ellipses, confocal hyperbolas and confocal mixtures of ellipses and hyperbolas. In the mixture of confocal ellipses and hyperbolas, any ellipse intersects any hyperbola orthogonally (at right angles). Parabolas have only one focus, so, by convention, confocal parabolas have the same focus and the same axis of symmetry.

Conic section

A conic section, conic or a quadratic curve is a curve obtained from a cone's surface intersecting a plane. The three types of conic section are the hyperbola, the parabola, and the ellipse; the circle is a special case of the ellipse, though it was sometimes called as a fourth type. The ancient Greek mathematicians studied conic sections, culminating around 200 BC with Apollonius of Perga's systematic work on their properties. The conic sections in the Euclidean plane have various distinguishing properties, many of which can be used as alternative definitions.

Cylinder

A cylinder () has traditionally been a three-dimensional solid, one of the most basic of curvilinear geometric shapes. In elementary geometry, it is considered a prism with a circle as its base. A cylinder may also be defined as an infinite curvilinear surface in various modern branches of geometry and topology. The shift in the basic meaning—solid versus surface (as in ball and sphere)—has created some ambiguity with terminology. The two concepts may be distinguished by referring to solid cylinders and cylindrical surfaces.

Related lectures (31)

Intrinsic Geometry of Regular Surfaces

Explores the intrinsic geometry of regular surfaces and isometric transformations, including spheres and cylinders.

Conic Sections: Determining Parameters

Explores the determination of conic section parameters and the laws of Kepler in celestial mechanics.

Dandelin Theorem: Ellipse Construction Log in to Mediaspace to watch this video

Explores ellipse construction using the Dandelin theorem and properties of conics in space.

Geometric Surfaces: Paraboloids and Hyperboloids in Architecture Log in to Mediaspace to watch this video

Explores the geometric properties of paraboloids and hyperboloids in architecture, emphasizing their design implications and practical applications.

Conics in the Plane: Uniform Description of 3 Conics Log in to Mediaspace to watch this video