Some cubic curves associated with a triangle

Cundy, H. Martyn; Parry, Cyril F.

doi:10.1007/bf01224039

Cited by 14 publications

(13 citation statements)

References 4 publications

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“…Hence (9) shows that x, y satisfy an equation of degree 3, that is the locus of P is a cubic, c2. The following study shows that it is the McCay cubic [3].…”

Section: -First Problemmentioning

confidence: 98%

On some geometrical problems of paperfolding

Justin

1999

Annali di Matematica pura ed applicata

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“…Hence (9) shows that x, y satisfy an equation of degree 3, that is the locus of P is a cubic, c2. The following study shows that it is the McCay cubic [3].…”

Section: -First Problemmentioning

confidence: 98%

On some geometrical problems of paperfolding

Justin

1999

Annali di Matematica pura ed applicata

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“…However, first we shall extend the domains of ϕ and ψ : It is easy to check that there remain three additional points for which (1) fails and three for which (2) fails. These points are identified in a further extension of domains:…”

Section: Vertices Of Central Triangles Reference Trianglementioning

confidence: 99%

“…The class of cubics Z have been widely studied [1][2][3][4][5]10]. Among their salient properties are these:…”

Section: Vertices Of Central Triangles Reference Trianglementioning

confidence: 99%

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Rubio cubics and generalized Cundy–Parry mappings

Kimberling

2009

J. Geom.

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Rubio's mappings between the Thomson and Darboux cubics are generalized for pairs of cubics of the form pα(β 2 − γ 2 )+ qβ(γ 2 − α 2 ) + rγ(α 2 − β 2 ) = 0, where p, r, q, α, β, γ are functions of a triple (a, b, c) of variables or indeterminates. Methods include symbolic substitutions, such as (a, b, c) → (bc, ca, ab). Connections between the generalized Rubio mappings with generalized Cundy-Parry mappings are described.Mathematics Subject Classification (2010). 51N20.

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“…It and other triangle cubics have the potential to be useful geometrical tools for understanding elliptic curves. See [1], [2], [3], [4], [5] and [6] for background on triangle cubics.…”

Section: Metrical Views Of Cubicsmentioning

confidence: 99%

Neuberg cubics over finite fields

Wildberger

2008

Algebraic Geometry and Its Applications

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The framework of universal geometry allows us to consider metrical properties of affine views of elliptic curves, even over finite fields. We show how the Neuberg cubic of triangle geometry extends to the finite field situation and provides interesting potential invariants for elliptic curves, focussing on an explicit example over F23. We also prove that tangent conics for a Weierstrass cubic are identical or disjoint.

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Some cubic curves associated with a triangle

Cited by 14 publications

References 4 publications

On some geometrical problems of paperfolding

On some geometrical problems of paperfolding

Rubio cubics and generalized Cundy–Parry mappings

Neuberg cubics over finite fields

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