Timeline for Can I detect the point of impact without looking at it?
Current License: CC BY-SA 2.5
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 6, 2010 at 10:28 | vote | accept | Andrew Stacey | ||
| Apr 6, 2010 at 10:28 | comment | added | Andrew Stacey | Thinking about this a little, I realised that the counterexample to Question 1 is what I was really looking for. Questions 2 and 3 seem still in the mindset of your first question (that c is unknown, rather than which c satisfy the condition). Working through the details of the counterexample then showed me how to adapt my proof that I can't detect the point of impact into a characterisation of those curves that satisfy the condition-the basic idea is that the y-value goes to 0 faster than any of the derivatives of the x-value. I'll put the details at the nlab. Thanks for the help! | |
| Mar 27, 2010 at 15:43 | comment | added | Bjorn Poonen | You're right; I could have just used xy. (I was worrying about a problem that doesn't exist.) | |
| Mar 27, 2010 at 12:48 | comment | added | Andrew Stacey | Excellent! I hadn't thought of using two (or r) functions simultaneously. That's an extremely useful tool to have learnt. Question (4) is still outstanding: is there some intrinsic characterisation of those curves c satisfying the condition (ie without reference to f). However, although that is my implicit question, it wasn't really the question in the question so I know I'm being a bit cheeky tacking it on the end! I'll have a think about what you've written and check that I understand it all. Incidentally, why use e^x y and not just x y? | |
| Mar 27, 2010 at 8:20 | history | answered | Bjorn Poonen | CC BY-SA 2.5 |