Equilateral triangles with vertices on a parabola

Timothy Sibbald

doi:10.1080/00255572.2026.2714222

August 13, 2026The Mathematical Gazette

Equilateral triangles with vertices on a parabola

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Key Points

To examine the algebraic and geometric conditions under which all three vertices of an equilateral triangle lie on a standard parabola.
Applied analytic geometry techniques and algebraic equations to model triangle coordinates on parabolic curves.
Framed solutions around secondary mathematics curriculum topics involving coordinate systems and conic sections.
Determined the necessary coordinate relationships and algebraic equations defining equilateral triangles with vertices on a parabola.
Provided instructional approaches for integrating conic sections with coordinate geometry problem solving.

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Implication

Mathematical analysis demonstrates conditions for inscribing equilateral triangles on a parabola, highlighting pedagogical connections in secondary coordinate geometry.

Abstract

This article arose while considering a high school mathematics problem that combines analytic geometry and parabolas. Instructionally these topics occur in the same year of high school in Ontario, ...

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Timothy Sibbald (2026) studied this question.

synapsesocial.com/papers/6a8019db75c2e31742c860a2 https://doi.org/10.1080/00255572.2026.2714222

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Equilateral triangles with vertices on a parabola

Key Points

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Implication

Abstract

Discussion

Cite This Study

Equilateral triangles with vertices on a parabola

Key Points

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Implication

Abstract

Discussion

Cite This Study

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