This is the first guest post from John Chase’s dad, also a math teacher. Thanks, son, for letting me post to your blog.
Gene Chase: I was taking a shower today when I figured out why I always confused the words “sequence” and “series.” 2, 3, 4, 5, … is a sequence; 2+3+4+5 is a series. Until today, I thought that my confusion was because “series” and “sequence” both begin with “s.” Now I see the real problem! Teachers would say “sum the following series.” They should have said “evaluate the following series,” since the series is already a sum.
Comment from John Chase: In non-mathematical contexts we don’t differentiate between the two. We think of “television series” and a “series” of cars in a line at an intersection. How mathematically sloppy!
Gene Chase: Yes, usually mathematical language is general language made more precise, not less precise. For example, if you tell a story elliptically, you leave things out of it; if you tell the story parabolically, you give an analog of the story; if you tell the story hyperbolically, you embellish it. The corresponding geometric figures have eccentricities which are either between 0 and 1 (ellipse), precisely equal to 1 (parabola), or greater than 1 (hyperbola).
This makes sense when you remember that “elliptic” is Greek for “defective,” “para” is Greek for “along side,” and “hyper” is Greek for “beyond.”