Matpic
mathematics, in pictures
Concept

Tangency

The meeting of a curve and a line or another curve that touch without crossing at the point of contact.

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

11122113233231142535344353524115 fractions, all in lowest terms, none of them twiceand left to right they are already in order

Every fraction, exactly once

Take two fractions, add the tops and add the bottoms. That is not how fractions are added, it is not an average, and repeating it produces every positive rational exactly once, already in lowest terms.

number · stern brocot 13 rays leave the left focus in 13 directions and every one of them arrives at the rightfocuseach path is the same total length — 2.90 drawing units — which is the property thatdefines the ellipse and the reason the reflection works

Every ray comes back to the other focus

An ellipse has two foci and one property everybody remembers: the distances to them add to a constant. What that property forces is stranger and more useful — a mirror shaped like an ellipse sends every ray leaving one focus, in every direction, through the other.

geometry · conic sections

Named alongside it

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

BijectionConicContinued fractionsCounting two waysDandelin spheresDirectrixEccentricityEllipseFarey sequenceFocusFord circlesLowest terms

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