Matpic
mathematics, in pictures
Concept

Angle — where it appears

The amount of turning between two rays from a common point, measured as a fraction of a full turn or in degrees or radians.

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

120°60°ABPthe same chordat the apex: 60°at the centre: 120°one is half the other,wherever P is put

An angle that does not care where it stands

Fix two points on a circle and look at them from anywhere else on the far arc. The angle is the same from every one of those places, and it is exactly half the angle at the centre.

geometry · inscribed angle 78°54°48°the outer triangle's angles are 78°, 54°, 48° and have nothing equal about them; the innertriangle's three sides are 0.152693, 0.152693, 0.152693the three corners are found by intersecting the trisectors, and the three lengths are thenmeasured off those corners — nothing in the construction asked for them to be equal

Three trisectors and a triangle nobody expected

Cut every angle of a triangle into three. The trisectors nearest each side meet in three points, and those three points are always the corners of an equilateral triangle — for every triangle there is, with no exceptions and no reason anybody finds obvious.

geometry · morley

Named alongside it

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

Central angleCircleConstructionCounterexampleCyclic quadrilateralEquilateral triangleExhaustive searchHypotenuseInscribed angleInvarianceIsosceles triangleLocus

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