Who did not graph such equations as $y^2-x^2=1$ in secondary schoool?

THEREFORE: Algebraic geometry (since it is only about zero-sets of polynomials in several variables) is high-school-level stuff, not research-level. Right?

I asked if what graphs of polynomial functions of sine and cosine look like. This was closed as "high-school level" stuff. Is it? There was an intelligent comment from Neil Strickland, and also a comment that it's an imprecise question and should therefore be closed. Obviously anyone maintaining that imprecise questions have generally been unwelcome on mathoverflow would lose any debate about whether that's true. Maybe the other point is more substantial.

**Postscript:** Angelo draws parallels to the proposition that every question about zero sets of polynomials is on topic. That proposition is plainly false.

Angelo commits a logical error: The correct parallel is to the proposition that every question about zero sets of polynomials is off topic. That proposition is also plainly false.

**PPS:** The absence of Andy Putman, Mariano Suárez-Alvarez, David Roberts, Misha, and Gerry Myerson from this discussion would be impolite if they knew it was happening. I've just notified them by email. However, the fact that mathoverflow's notification system has no way to handle such a matter is a flaw. Some users' email addresses cannot readily be found.

**PPPS:** I wonder if anyone anywhere knows the answer to the question I posted, which was held not to be a research-level question. Just this morning I derived a simple result: The function $\theta\mapsto\tan(\theta/2)$ is the identity element in a structure that one naturally considers when thinking about this question. Maybe high-school-level in the sense that if one phrased it as a precise question, a bright high-school student would prove it. But I wouldn't be surprised it hasn't been noticed before. And it would take an even brighter high-school student to think of asking that question. Which raises a question that I'll ask on "main".

**PPPPS:** One should ask a "focused question" with a "specific goal". So says Anton Geraschenko below, and I agree. But he suggests that imprecise questions cannot also be "focused" questions having a "specific goal". Then he retreats from that position. Just to be clear, here are some **counterexamples**: i.e

**Examples of imprecise questions that are focused and have a specific goal and have large numbers of up-votes on mathoverflow:**

Proofs that require fundamentally new ways of thinking

nontrivial theorems with trivial proofs

Not especially famous, long-open problems which anyone can understand

Examples of common false beliefs in mathematics

(307 votes for this last.)

Most intricate and most beautiful structures in mathematics

(This last was asked by Richard P. Stanley, perhaps one of mathoverflow's most respected contributors.)

Examples of seemingly elementary problems that are hard to solve?

Theorems with unexpected conclusions

(Also asked by Richard P. Stanley, 55 votes.)

topicof the question (namely, the visual appearance of graphs of functions) was high-school level. And I stand by this. But I cannot answer your question myself because itisn't actually a well-posed mathematical question. If anything, this is even more pertinent to its closing than the level. See Anton's answer for what I mean by that. $\endgroup$reallygot my goat $\endgroup$dothink that down-votes and closureareone of the main ways to maintain quality on MathOverflow. Many is the idle question or philosophical musing that I havenotput on MO. $\endgroup$no circumstanceswould I want to receive email about such matters and sending them strikes me (but one might see this differenlty) as quite inapproriate . $\endgroup$23more comments