Thursday, April 23, 2015

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 . . .


Graph of sliding derivative line

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.

33 comments:

  1. I didn't know the term "tangent" was also used in math. It's true that you learn something new every day. :)

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    1. I thought that might be the case for lots of writers and readers, so I hoped to show how, if you follow a tangent, it leads you away from the curve, just like following a tangent in writing or thought, it leads you away from your subject.

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  2. Your story sounds promising! ADHD plus Autism equals lots of tension, tangents and conflict:)

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  3. You lost me at "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.” :)
    I liked the video, though, quite cool!

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    1. Sorry about that. There are plenty of pictures on the Wikipedia page, but I didn't want to make this post any longer by including them all.

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  4. It's probably one of the most important concepts in all of mathematics. Tangents (or derivatives) is a measure of change, and that's what all of theoretical physics is about; modeling change in terms of differential equations. Cool movie. Very nice to use for someone teaching highschool math >:)

    Cold As Heaven

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    1. As a math student, then professor, I think I must have calculated the slope of tangent lines and/or derivatives a couple thousand times.

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    2. Me too. I do it every day at work

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  5. I definitely know how to go off on tangents, but didn't know all that much about the math kind.

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  6. I had no idea about that - not surprising of course! When someone says they are going off at a tangent I'll be able to tell them what they are actually doing now!

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  7. It does look like a roller coaster. Can't ride them though. Sorry, just went off on a tangent.
    And sorry, Tamara! I thought I was following you. No wonder your blog doesn't show up in my Feedly Reader. Following you now.

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    1. Thanks Alex! Welcome to the show. I feel honored.

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  8. That little graphic is quite hypnotic! Not only do I go off on a tangent, my stories tend to be the curved line, rather than the straight one.

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  9. So glad to have found you and promise faithfully to catch up on the maths from now on in. I'm only teaching basic maths right now but , as you would expect, my lovely students are brilliant at going offf on tangents--may use this and see what happens :-)

    Anne at
    Author Support - Tips for New Authors from A to Z

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  10. I thought I was good at math until I had to take pre-calc and it was assumed everyone knew how to find a tangent line. . . not me.

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  11. My life is a tangent. Great explanation about this, and I enjoyed the interweaving of your literary and mathematical selves.

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  12. Math is fun! Yes, I'm a math geek. And I did know about tangents. Both types.

    Liz A. from Laws of Gravity

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