intersection
Pluralintersections
- 1The point where two or more roads, streets, or paths cross or join.
The city installed new traffic lights at the dangerous intersection downtown.
Several intersections along the highway were redesigned to reduce accidents.
Similarjunction, crossroads, crossing
Note
The street sense keeps the word's Latin shape in plain view. It came into English through Middle French from Latin intersectiō, and English speakers hear it as intersect plus -ion: the spot where one way cuts across another. Crossroads is its near-synonym. It is also the working term of accident investigation, as in the NTSB's 2024 report Intersection Crash Between Passenger Car and Combination Vehicle.
- 2A point of overlap, confluence, or crossover between different things.
The conference celebrated the intersection of food, music, and culture.
Modern medicine increasingly works at the intersection of biology and computing.
Similarcrossroads, confluence, convergence, overlap, nexus
Note
The figurative sense shifts its preposition with its number. In the singular it usually takes of and a list: the intersection of food, music, and culture. In the plural it often takes between, as when James Lambert, writing in 2015, describes a "melee of intersections between English and Cantonese" among bilingual students. The plural suits a meeting that is many-sided and untidy rather than a single crossing point.
- 3The point or set of points shared by two geometric objects, such as where two lines meet or two planes cross.
The students calculated the intersection of the two curves.
Where the plane cut the cone, the intersection formed an ellipse.
Note
Geometry cares what shape the shared part takes. Two distinct lines in a plane share at most a single point, while two planes that are not parallel share a whole line. An intersection need not be a point at all, and it can be empty. That is why mathematicians speak of the intersection of two curves or surfaces as an object to be found and described.
- 4The set containing all elements that belong to two or more sets at once.
The intersection of set A and set B contains only the numbers found in both.
If the two sets share no members, their intersection is empty.
Oppositeunion
Note
Set theory writes it with a symbol, A ∩ B. When one set sits wholly inside the other, their intersection is simply the smaller set. It is the general form of the geometric meaning: a figure is a set of points, so the points two figures share are exactly the intersection of those two sets.
- 5The element in which two or more straight lines of synchronized skaters pass through each other.
The squad's intersection drew applause as the two lines glided through one another.
A clean intersection requires precise timing from every skater on the ice.
Note
Synchronized skating borrows the word for one of its set pieces. Lines of skaters travel toward each other at speed and thread through one another. The element is judged on timing, on spacing, and on the angle at which the lines cross. In this sense the word is countable: a team performs an intersection as one element of its program.
- 6The subobject formed by the pullback of two monomorphisms that share a common codomain.
The intersection of two subobjects is defined as the pullback of their inclusion monics.
Here the intersection corresponds to the pullback completing the corner of the diagram.
Note
Category theory rebuilds the set idea with arrows instead of elements. In the category of sets, two subsets become monic arrows into the same set, and their pullback gives back the shared-elements meaning. A pullback of monics is itself monic, so the intersection is again a subobject. It is the largest subobject lying inside both, which makes it the meet in the ordering of subobjects.
Practice
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Origin
From Middle French "intersection" and its Latin source "intersectiō." By surface analysis, it can be read as "intersect" plus the suffix "-ion."