9 ms·
The author tells the story of typical undergraduate instruction for the integrals of tan(x) and sec(x). I would have thought that such a setting would have incl
by rm445 6y ago
The author tells the story of typical undergraduate instruction for the integrals of tan(x) and sec(x). I would have thought that such a setting would have included that these were improper integrals, because of the infinities in the functions. i.e. if you evaluate the definite integral for any particular interval, it will give you the right answer except if you've gone through the part where the graph goes up to plus infinity and back through minus infinity.
Can someone more mathematically literate than me shed any light on whether it matters? I guess it's still useful even if the integral is undefined at certain points off the edges of the map.
- deleted 6y ago[deleted]
- the_origami_fox 6y agoIt matters here in the sense that to show the poles, you need to stretch the Mercator map to infinity, because the function sec(x) is undefined at 90 degrees. This is clearly absurd, so map makers get around the problem by cutting the top of the map off, usually around the 85 degrees parallel. I chose not to include this detail in the article. To slightly misquote the great Richard Feynman, "It turns out that it's possible to sweep the infinities under the rug by a certain crude skill." :)