The Renewal Equation

A math odyssey

A Little Frustration

Today I read the review of conics and did the first section of exercises. Conics was my least favorite of the topics covered by my math education. Although I’m sure we learned other things, my memory of second year algebra is of endless repetitive graphing of parabolas, ellipses, and hyperbolas. The exercises for this section proved a bit like that, unfortunately. Find vertex, focus, directrix and graph…find vertex, focus, directrix and graph…

Furthermore, near the end of my study time I found that I had been doing the exercises correctly and producing accurate graphs, but consistently transposing $x$ and $y$ when writing down the coordinates of points. That’s something I recall from the past, as well.

Responses

  1. Tim McL

    I’ve read that Descartes’s coordinate system was something like ours rotated 90° clockwise, so y was horizontal and x pointed down. (It’s more than possible I have this wrong. Wikipedia says Descartes used a single coordinate axis.) That’s why we, like Descartes, write lines $y=mx+b$. The $y$-intercept $b$ is the Base, and $m$ is the Montée, the climb. I love the fact that we are so profoundly conservative. After more than four centuries we still say $y=mx+b$, even though $y$ is no longer the base and “slope” doesn’t start with m.

    Reply
    1. Olly

      I like the way a variety of natural languages have left an imprint on mathematical terms and conventions. There’s also $\mathbb{Z}$ for “Zahlen,” of course. And I was thinking the other day about the word “directrix,” which appears to be a feminine Latin noun. My guess is that the name was originally “linea directrix.”

      Reply

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