Euclidean Geometry

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5 domain-specific abstractions whose origin domain is Euclidean Geometry.

• Acute and obtuse triangles — A Euclidean triangle classification based on whether all angles are below a right angle or exactly one angle exceeds it.
• Fixed points of isometry groups in Euclidean space — The common-fixed-point set of a Euclidean isometry group, which is either empty or an affine subspace.
• Orthocentric system — A planar set of four points in which each point is the orthocenter of the triangle formed by the other three.
• Right triangle — Specify a triangle with exactly one right angle, making the opposite side the hypotenuse and coupling its sides, acute angles, altitude, circumcircle, and similarity relations through Euclidean constraints.
• Tangential quadrilateral — A convex quadrilateral whose four sides are tangent to one inscribed circle.