> Is there some theory in which the tangent curve has its +/- infinities connected? I'm sure there are much simpler ways in which this can be done, but one nee

> Is there some theory in which the tangent curve has its +/- infinities connected? I'm sure there are much simpler ways in which this can be done, but one need only regard the tangent function as valued in the one-point compactification (https://en.wikipedia.org/wiki/One-point_compactification https://en.wikipedia.org/wiki/One-point_compactification) of `\mathbb R`, which is a circle. In this sense, the graph of the tangent function is a subset of the cylinder `\mathbb R \times S^1`; and the usual graph comes from making a slice through the "`\infty` section" `\mathbb R \times \{\infty\}` and unrolling.