## A Summer 2015 Mathematics A To Z: locus

## Locus.

A locus is a collection of points that all satisfy some property. For example, the locus of points that are all equally distant from some center point is a circle. Or maybe it’ll be a sphere, or even a hypersphere. That depends whether we’re looking at points in a plane, in three-dimensional space, or something more. When we draw lines and parabolas and other figures like that in algebra we’re drawing locuses. Those locuses are the points that satisfy the property “the values of the coordinates of this point make that equation true”.

The idea is a bit different in connotation from “the curve of an equation”. We might not be talking about points that can be conveniently, or sensibly, described by an equation. We might want something like “the shape made by the reflection of this rectangle across this cylindrical mirror”. Or we might want “the points in space from which a space probe will crash into the moon, instead of crashing into Earth”. It’s convenient to have a shorthand way of talking about that idea. Using this word avoids necessarily tying ourselves to drawings or figures we might not be able to produce even in theory.

## Barb Knowles 1:02 am

onSunday, 21 June, 2015 Permalink |And a math neophyte like I can understand it better…

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## Joseph Nebus 2:27 am

onMonday, 22 June, 2015 Permalink |Good! I hope it helps.

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## A Summer 2015 Mathematics A to Z Roundup | nebusresearch 3:03 pm

onFriday, 24 July, 2015 Permalink |[…] Locus. […]

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## Mathematics A to Z: Part 3 | Mean Green Math 11:09 am

onSunday, 13 September, 2015 Permalink |[…] L is for locus, a word that’s unfamiliar to today’s math majors but was hammered into my head when I was a student. I distinctly remember learning the definition of an ellipse as the locus of points so that the sum of the distances from two fixed points to that point is a constant. […]

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