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W-curve

Index W-curve

In geometry, a W-curve is a curve in projective ''n''-space that is invariant under a 1-parameter group of projective transformations. [1]

15 relations: Conic section, Felix Klein, Georg Scheffers, Helix, Homography, Invariant (mathematics), Klein's encyclopedia, Logarithm, Logarithmic spiral, One-parameter group, Projective space, Real projective plane, Sine, Sophus Lie, Straightedge.

Conic section

In mathematics, a conic section (or simply conic) is a curve obtained as the intersection of the surface of a cone with a plane.

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Felix Klein

Christian Felix Klein (25 April 1849 – 22 June 1925) was a German mathematician and mathematics educator, known for his work with group theory, complex analysis, non-Euclidean geometry, and on the associations between geometry and group theory.

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Georg Scheffers

Georg Scheffers was a German mathematician specializing in differential geometry.

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Helix

A helix, plural helixes or helices, is a type of smooth space curve, i.e. a curve in three-dimensional space.

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Homography

In projective geometry, a homography is an isomorphism of projective spaces, induced by an isomorphism of the vector spaces from which the projective spaces derive.

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Invariant (mathematics)

In mathematics, an invariant is a property, held by a class of mathematical objects, which remains unchanged when transformations of a certain type are applied to the objects.

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Klein's encyclopedia

Klein's encyclopedia is a German mathematical encyclopedia published in six volumes from 1898 to 1933.

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Logarithm

In mathematics, the logarithm is the inverse function to exponentiation.

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Logarithmic spiral

A logarithmic spiral, equiangular spiral or growth spiral is a self-similar spiral curve which often appears in nature.

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One-parameter group

In mathematics, a one-parameter group or one-parameter subgroup usually means a continuous group homomorphism from the real line \mathbb (as an additive group) to some other topological group G. That means that it is not in fact a group, strictly speaking; if \varphi is injective then \varphi(\mathbb), the image, will be a subgroup of G that is isomorphic to \mathbb as additive group.

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Projective space

In mathematics, a projective space can be thought of as the set of lines through the origin of a vector space V. The cases when and are the real projective line and the real projective plane, respectively, where R denotes the field of real numbers, R2 denotes ordered pairs of real numbers, and R3 denotes ordered triplets of real numbers.

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Real projective plane

In mathematics, the real projective plane is an example of a compact non-orientable two-dimensional manifold; in other words, a one-sided surface.

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Sine

In mathematics, the sine is a trigonometric function of an angle.

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Sophus Lie

Marius Sophus Lie (17 December 1842 – 18 February 1899) was a Norwegian mathematician.

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Straightedge

A straightedge or straight edge is a tool with a straight edge, used for drawing straight lines, or checking their straightness.

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References

[1] https://en.wikipedia.org/wiki/W-curve

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