Matpic
mathematics, in pictures
Concept

Perpendicular bisector

The line of points equally far from two given ones, at right angles to the segment joining them.

Named by 2 essays across one field — each of them below, with the objects they name alongside it.

The plane, divided by whoever is nearest

Scatter some points and colour every other point of the plane by which one is closest. The result is a tiling nobody designed, and its dual triangulation has a property that no part of the construction mentions.

geometry · voronoi Hcentremidpoints of the sides · feet of the altitudes · midpoints up to Hall nine sit at 97.0 from the centre, which is half the 194.1 of the circle through thecornerschecked again on 240 further triangles, every one of which puts its own nine on onecircle

Nine points on one circle

Three midpoints, three feet of altitudes and three more midpoints. Nine points defined in three unrelated ways, on an arbitrary triangle, and all nine sit on one circle — checked here on two hundred and forty triangles as well as on the drawn one.

geometry · triangle centres

Named alongside it

The objects these essays reach for when they reach for this one.

CircleAltitudeConvexityCounterexampleDelaunay triangulationDualityEuler characteristicIncidenceInscribed angleInvariantLocusNearest neighbour

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