Matpic
mathematics, in pictures
Concept

Hypercube

The shape whose corners are all the ways of choosing true or false for each of several variables, with edges between corners differing in one.

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

Also named here as normal form — the same set of essays touches all of them, so they are one junction rather than several.

000001010011100101110111(p ∨ q) ∧ ¬r on the 3-cube of assignments — 3 of 8 cornerscorners next to each other differ in one variable, which every edge here was checkedagainst

A formula is a corner of a cube

A formula about three letters is a set of eight rows. Written as a table that is a list; drawn on a cube it is a shape — and the shape is what almost every later question in this field turns out to be about.

logic · truth functions rspq00011110000111101110111011110010((p ∧ q) ∨ (r ∧ s)) ∨ (¬p ∧ ¬r) covered by 3 of its 6 primeimplicantsr∧s ∨ ¬p∧¬r ∨ p∧q — checked against the formula on all 16assignments

The map that puts neighbours side by side

Reorder the rows of a truth table so that neighbouring squares differ in one letter, and finding a short formula stops being algebra and becomes the problem of covering a shape with rectangles.

logic · truth functions

Named alongside it

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

Normal formTruth functionAssignmentConnectiveCoveringGray codeKarnaugh mapMinimalityParityPrime implicantPropositional formulaSatisfiability

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