Timeline for Wanted, dead or alive: Have you seen this curve? (circular variant of cardioid)
Current License: CC BY-SA 3.0
16 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 4, 2020 at 18:48 | vote | accept | Andrew Stacey | ||
| Jan 25, 2016 at 23:57 | answer | added | Gro-Tsen | timeline score: 13 | |
| Jan 25, 2016 at 20:00 | comment | added | Andrew Stacey | @Gro-Tsen I'll try the polar form, thanks for the suggestion. In the meantime, your second comment was absolutely correct. The outer half is then the inversion in the unit circle of the inner half. I think you should post that as an answer since although it doesn't answer the "has this been seen before" part, it's a very useful point of view on the curve and not one I'd've thought of (I know of the Poincaré disc model but hadn't heard of the Beltrami-Klein one, and the passage between the two is lovely and geometric). | |
| Jan 24, 2016 at 22:47 | comment | added | Gro-Tsen | If you say the straight-line version draws a cardioid, then the curve you describe, or at least the "inside" half of it, should be the transform of the cardioid under the transformation that takes the Beltrami-Klein model of projective space to the Poincaré disk model (because the points on the unit circle are preserved by this transformation, which then maps the line segment to the circle arc, and tangency will be preserved). Maybe there is no better description. | |
| Jan 24, 2016 at 22:43 | comment | added | Steven Landsburg | (CONTINUED) She even said something about trying to figure out what it means for two computations to be essentially different. When I praised her exactly as you propose to praise your students ("Wow! That's exactly the kind of question a real mathematician might ask!"), she said: "Really? A real mathematician might ask a question like this". I said yes. And she said --- this is verbatim, because I wrote it down instantly: "Wow! What a soul-deadening job THAT must be." | |
| Jan 24, 2016 at 22:41 | comment | added | Steven Landsburg | Not really relevant but I feel compelled to share this: When my daughter was the same age as your students, I found her staring at a piece of paper on which she'd drawn many copies of the same right triangle in a variety of configurations. I asked what she was doing, and she said she was trying to figure out how many different ways there are to compute the area of the same triangle --- she had fit two together to make a rectangle, four together to make a different rectangle, etc. (CONTINUED) | |
| Jan 24, 2016 at 22:38 | comment | added | Gro-Tsen | You should try to compute a polar equation for the curve, this will make it easier to look up. Try to find it in this site, which seems to list an unreasonable number of historical curves and constructions thereof, and, if you can't, try contacting its author. | |
| Jan 24, 2016 at 22:08 | history | edited | user9072 |
edited tags
|
|
| Jan 24, 2016 at 21:50 | history | edited | Gerhard Paseman | CC BY-SA 3.0 |
more detail in tile makes it easier to find and link. Hopefully circular is a good adjective.
|
| Jan 24, 2016 at 21:44 | comment | added | Gerhard Paseman | While you are most likely to get an informed answer here, if you don't, try matheducators.stackexchange next week. Even if they don't have a pointer to the geometry literature, something in education of geometry might appear. Gerhard "Cast Net Far And Wide" Paseman, 2016.01.24 | |
| Jan 24, 2016 at 21:40 | history | edited | Andrew Stacey | CC BY-SA 3.0 |
The equation wasn't technically an equation (I'd left off the '=0' part).
|
| Jan 24, 2016 at 21:39 | comment | added | Andrew Stacey | Oh, and here's a link to the geogebra worksheet that made that picture: ggbtu.be/m2473555 | |
| Jan 24, 2016 at 21:36 | comment | added | Andrew Stacey | Here's the MSE link: math.stackexchange.com/q/1618523/2907 (and I've linked in the other direction too) | |
| Jan 24, 2016 at 21:16 | comment | added | YCor | Please give the MSE link and also write a link to this MO question on the MathSE question. | |
| Jan 24, 2016 at 21:11 | comment | added | Andrew Stacey | PS I did ask this on Maths-SE and on G+ a week ago but to no avail. I thought it best to write more context for MO than for MSE rather than just ask for the question to be migrated. | |
| Jan 24, 2016 at 21:10 | history | asked | Andrew Stacey | CC BY-SA 3.0 |