A Summer 2015 Mathematics A To Z: 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.

A Brief Word for the Comic Pages

There’s legitimate mathematical content linked from here, but mostly, I want to promote what seems to be a little-known comic strip that’s working very hard at making me love it. Part of that work has been in producing a couple of mathematics-oriented strips. Grant Snider’s Incidental Comics, part of the gocomics.com comics empire, is a roughly twice-a-week strip filling the page with lots of detail humor. It’s the sort of comic strips which assumes you will remember Ludwig Miles van der Rohe’s Farnsworth House. (However, I did see a Lego block version of the Farnsworth House in Barnes and Noble the other day, so maybe Miles van der Rohe has gone and become all trendy while I wasn’t looking.

Relevant to the nominal base for this little blog, though, is that Snider has posted a few comics based on mathematics jokes. The most recent is that from January 23, titled “Axes of Evil”, and mixes descriptive statistics with horror that is somehow not associated with calculating standard deviations. A little farther back is the December 12, 2011, strip, titled “Function World”, which adapts graphs of some popular functions, such as hyperbolas, the natural logarithm, and the inverse cosine (which is not actually popular, but don’t tell it) into amusement park rides. Do enjoy.

I am not certain how far in the archives people who haven’t got gocomics.com accounts can go before they’re nagged into getting gocomics.com accounts.

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