T is for . . .

This month I'm posting Mad-Cool-Math Nuggets.

T is for tangent. Writers and/or their characters go off on tangents all the time, meaning we pursue a somewhat related or irrelevant course while neglecting the main subject. (The Free Dictionary) Take my character, Audrey Ericsson. She goes off on tangents all the time, but it's too be expected since she suffers from ADHD. And her son has autism. And boy, this has totally morphed into an advert for my new short story.

See what I did there? I went off on a tangent.

So what's a mathematical tangent? A tangent line touches a curve at one point without cutting across the curve (at that point). Imagine I ask you to balance a long spike on your head. Hopefully, you would opt to lay it somewhat horizontally on top of your head and not stab it into your skull. Same idea.

A tangent line can and often does intersect a curve at some other point as seen below. (Math is fun.) That's the source, but also a true statement. For some people. People like me who like math and can't stop going off on tangents. Gotcha!

Image source: Wikicommons

In this image, the red line is tangent to the black curve at the red dot (not where the red line crosses the black curve).

Lines can be tangent to circles too. Circles can be tangent to other circles. Planes can be tangent to spheres. It all happens the same way: the two items in question touch at one point.

Keep in mind that you can draw a tangent line at any point along a continuous curve. The video below shows many tangent lines to various points along a curve. The green lines are tangents with a positive slope (going up), the red lines signify a tangent with a negative slope (going down), and the black lines happen when the slope of the tangent line is zero (also known as a horizontal line.)

Is it just me, or does this look like someone riding a roller coaster while carrying a vaulting pole? Wheee! And speaking of roller coasters . . .




Source: By en:User:Dino (English Wikipedia) [Public domain], via Wikimedia Commons

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If you want to know more about Audrey Ericcson, stop by from tomorrow (4/24) through Monday (4/27) for a free download of the novella Ghosts of a Benevolent Place.