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.

Advertisements

Author: Joseph Nebus

I was born 198 years to the day after Johnny Appleseed. The differences between us do not end there.

5 thoughts on “A Summer 2015 Mathematics A To Z: locus”

Please Write Something Good

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s