Matpic
mathematics, in pictures
Concept

Construction

A figure produced by a stated sequence of permitted operations, so that what is drawn is reachable rather than merely plausible.

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

[0, 1](0, 1)01½0 goes to a half and 1/n goes to 1/(n+2); every other point of [0, 1] stays where it is8 moved points drawn, all distinct, all inside (0, 1) — and the two endpoints are gone

Two injections make a bijection

If each of two collections fits inside the other without collisions, they are the same size. That sounds obvious and is not, because neither injection needs to be onto — and the proof is a rule for deciding which of the two to follow, one chain at a time.

logic · cardinality 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.

AngleBijectionCardinalityChain decompositionCountabilityCounterexampleEquilateral triangleExhaustive searchHilbert hotelInjectionIntervalInvariance

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