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Spiric section, the Glossary

Index Spiric section

In geometry, a spiric section, sometimes called a spiric of Perseus, is a quartic plane curve defined by equations of the form Equivalently, spiric sections can be defined as bicircular quartic curves that are symmetric with respect to the x and y-axes.[1]

Table of Contents

  1. 17 relations: Cassini oval, Circle, Circular algebraic curve, Ellipse, Geometry, Hippopede, Hyperbola, Imaginary number, Lemniscate of Bernoulli, Orthoptic (geometry), Perseus (geometer), Plane curve, Polar coordinate system, The Ancient Tradition of Geometric Problems, Toric section, Torus, Wilbur Knorr.

  2. Plane curves
  3. Quartic curves
  4. Spiric sections
  5. Toric sections

Cassini oval

In geometry, a Cassini oval is a quartic plane curve defined as the locus of points in the plane such that the product of the distances to two fixed points (foci) is constant. Spiric section and Cassini oval are plane curves, quartic curves and spiric sections.

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Circle

A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.

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Circular algebraic curve

In geometry, a circular algebraic curve is a type of plane algebraic curve determined by an equation F(x, y).

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Ellipse

In mathematics, an ellipse is a plane curve surrounding two focal points, such that for all points on the curve, the sum of the two distances to the focal points is a constant. Spiric section and ellipse are plane curves.

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Geometry

Geometry is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures.

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Hippopede

In geometry, a hippopede is a plane curve determined by an equation of the form where it is assumed that and since the remaining cases either reduce to a single point or can be put into the given form with a rotation. Spiric section and hippopede are quartic curves and spiric sections.

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Hyperbola

In mathematics, a hyperbola is a type of smooth curve lying in a plane, defined by its geometric properties or by equations for which it is the solution set.

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Imaginary number

An imaginary number is the product of a real number and the imaginary unit, is usually used in engineering contexts where has other meanings (such as electrical current) which is defined by its property.

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Lemniscate of Bernoulli

In geometry, the lemniscate of Bernoulli is a plane curve defined from two given points and, known as foci, at distance from each other as the locus of points so that. Spiric section and lemniscate of Bernoulli are plane curves, quartic curves and spiric sections.

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Orthoptic (geometry)

In the geometry of curves, an orthoptic is the set of points for which two tangents of a given curve meet at a right angle.

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Perseus (geometer)

Perseus (Περσεύς; 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.

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Plane curve

In mathematics, a plane curve is a curve in a plane that may be a Euclidean plane, an affine plane or a projective plane. Spiric section and plane curve are plane curves.

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Polar coordinate system

In mathematics, the polar coordinate system is a two-dimensional coordinate system in which each point on a plane is determined by a distance from a reference point and an angle from a reference direction.

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The Ancient Tradition of Geometric Problems

The Ancient Tradition of Geometric Problems is a book on ancient Greek mathematics, focusing on three problems now known to be impossible if one uses only the straightedge and compass constructions favored by the Greek mathematicians: squaring the circle, doubling the cube, and trisecting the angle.

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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. Spiric section and toric section are quartic curves and toric sections.

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Torus

In geometry, a torus (tori or toruses) is a surface of revolution generated by revolving a circle in three-dimensional space one full revolution about an axis that is coplanar with the circle.

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Wilbur Knorr

Wilbur Richard Knorr (August 29, 1945 – March 18, 1997) was an American historian of mathematics and a professor in the departments of philosophy and classics at Stanford University.

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See also

Plane curves

Quartic curves

Spiric sections

Toric sections

References

[1] https://en.wikipedia.org/wiki/Spiric_section

Also known as Persian curve, Spiric Sections, Spiric curve.