Toric section

Toric section

A toric section is an intersection of a plane with a torus, just as a conic section is the intersection of a plane with a cone.

Mathematical formulae

In general, toric sections are fourth-order (quartic) plane curvesof the form

:left( x^{2} + y^{2} ight)^{2} + a x^{2} + b y^{2} + cx + dy + e = 0.

piric sections

A special case of a toric section is the spiric section (σπειρα = torus in ancient Greek), in which the intersecting plane is parallel to the rotational symmetry axis of the torus. They were discovered by the ancient Greek geometer Perseus in roughly 150 BC. Well-known examples include the hippopede and the Cassini oval and their relatives, such as the lemniscate of Bernoulli.

General toric sections

More complicated figures such as an annulus can be created when the intersecting plane is perpendicular or oblique to the rotational symmetry axis.


Wikimedia Foundation. 2010.

Игры ⚽ Поможем сделать НИР

Look at other dictionaries:

  • toric — adjective Pertaining to or shaped like a torus, or a section of a torus; toroidal …   Wiktionary

  • Spiric section — A spiric section is a special case of a toric section, which is the intersection of a plane with a torus (σπειρα in ancient Greek). Spiric sections are toric sections in which the intersecting plane is parallel to the rotational symmetry axis of… …   Wikipedia

  • Perseus (geometer) — Perseus (c. 150 BC) was an ancient Greek geometer, who invented the concept of spiric sections, in analogy to the conic sections studied by Apollonius of Perga. Few details of Perseus life are known, as he is mentioned only by Proclus and… …   Wikipedia

  • Torus — Not to be confused with Taurus (disambiguation). This article is about the surface and mathematical concept of a torus. For other uses, see Torus (disambiguation). A torus As the distance to th …   Wikipedia

  • Quartic plane curve — A quartic plane curve is a plane curve of the fourth degree. It can be defined by a quartic equation::Ax^4+By^4+Cx^3y+Dx^2y^2+Exy^3+Fx^3+Gy^3+Hx^2y+Ixy^2+Jx^2+Ky^2+Lxy+Mx+Ny+P=0.This equation has fifteen constants. However, it can be multiplied… …   Wikipedia

  • List of mathematics articles (T) — NOTOC T T duality T group T group (mathematics) T integration T norm T norm fuzzy logics T schema T square (fractal) T symmetry T table T theory T.C. Mits T1 space Table of bases Table of Clebsch Gordan coefficients Table of divisors Table of Lie …   Wikipedia

  • Hippopede — In geometry, a hippopede (from ἱπποπέδη meaning horse fetter in ancient Greek) is a plane curve determined by an equation of the form (x2 + y2)2 = cx2 + dy2, where it is assumed that c>0 and c>d since the remaining cases either reduce to a… …   Wikipedia

  • Contact lens — Contacts redirects here. For the software application, see Address book. A pair of contact lenses, positioned with the concave side facing upward …   Wikipedia

  • Mirror symmetry (string theory) — In physics and mathematics, mirror symmetry is a relation that can exist between two Calabi Yau manifolds. It happens, usually for two such six dimensional manifolds, that the shapes may look very different geometrically, but nevertheless they… …   Wikipedia

  • Resolution of singularities — Strong desingularization of Observe that the resolution does not stop after the first blowing up, when the strict transform is smooth, but when it is simple normal crossings with the exceptional divisors. In algebraic geometry, the problem of… …   Wikipedia

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”