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mathematics, in pictures
Concept

Degree

The highest power appearing in a polynomial, or the number of edges meeting a vertex in a graph.

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

Ndegree 3Idegree 5Edegree 3Sdegree 3

Seven bridges, and the invention of throwing things away

Euler solved a puzzle about a Prussian city by deleting the city. What survived the deletion was a new branch of mathematics.

discrete · eulerian paths radius 0.40 turns0 roots insideradius 10 turns0 roots insideradius 1.42 turns2 roots insideradius 23 turns3 roots insidep(z) = z³ − 2z + 2 — as the circle grows, the number of turns steps up from 0 to 3the count can only change by the image crossing the origin, and a crossing is a root

A loop that cannot miss the middle

Feed a circle into a polynomial and a closed loop comes out. A small circle gives a loop that does not enclose the origin; a large one gives a loop that goes round it as many times as the degree. Something has to happen in between, and that something is a root.

algebra · polynomial roots

Named alongside it

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

AbstractionClosed curveComplex numbersContinuityExistence proofFundamental theoremGraphHierholzer's algorithmMatrixNonconstructiveParityPolynomial

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