Timeline for Parametrically Defined Curves: $f'$ and $g'$ Are Not Simultaneously Zero
Current License: CC BY-SA 4.0
13 events
| when toggle format | what | by | license | comment | |
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| Jul 20, 2018 at 15:11 | comment | added | The Pointer | @DavidC.Ullrich Yes, I think I understand now. See my comment on your answer. | |
| Jul 20, 2018 at 15:11 | comment | added | David C. Ullrich | @ThePointer This is undesirable behavior because if we don't disallow this behavior we find the the curve $y=|x|$ is "differentiable", as I showed in my answer. We certainly don't want that - if $y=|x|$ is a "differentiable" curve then differentiable curves are nothing like what we think they should be. | |
| Jul 20, 2018 at 14:55 | comment | added | user65203 | @ThePointer: because the direction of the curve is an essential property in many problems. | |
| Jul 20, 2018 at 14:53 | comment | added | The Pointer | Hmm, so why is this undesirable behaviour? Let's say the direction is undefined: so what? What are the consequences for a parameterised curve that exhibits this behaviour? | |
| Jul 20, 2018 at 14:52 | comment | added | user65203 | @ThePointer: I'd prefer to say where the direction is undefined. | |
| Jul 20, 2018 at 14:51 | history | edited | user65203 | CC BY-SA 4.0 |
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| Jul 20, 2018 at 14:50 | comment | added | The Pointer | So the reason for this condition is to avoid parameterisations where the direction changes abruptly? | |
| Jul 20, 2018 at 14:50 | comment | added | user65203 | @ThePointer: "in one direction" means following a straight line. I doubt this is what you have in mind. But I have completely rephrased my answer. | |
| Jul 20, 2018 at 14:49 | history | edited | user65203 | CC BY-SA 4.0 |
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| Jul 20, 2018 at 14:47 | comment | added | user65203 | @ThePointer: what do you mean by unidirectional ? | |
| Jul 20, 2018 at 14:45 | comment | added | The Pointer | Thanks for the response. So the reason for this condition is that we want the parameterised curve to be unidirectional? | |
| Jul 20, 2018 at 14:44 | comment | added | The Pointer | Singular point: mathworld.wolfram.com/SingularPoint.html | |
| Jul 20, 2018 at 14:39 | history | answered | user65203 | CC BY-SA 4.0 |