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Tangents to a cubic
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Hi.
In the file, the cubic was created with the command Cubic[A,B,C,3]. The theory says that the circumcenter (D) is on the curve. If you try to draw the tangent to the curve at the point D, you get a set of lines. On a mac OSX, GG 4.2.3.0 Java: 1.6.0_37.
jtico
Files:
ct.png
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What were you expecting?
D isn't a point fixed on the cubic (in the sense of Point[cubic])  it could move off. (and GeoGebra can't tell that it in fact can't without doing some very hard maths which would slow everything down... and wouldn't work in all circumstances anyway...)
Hi.
I'm not sure that I understand your answer. As a user, I feel that this is an inconsistent behaviour of GG. From your answer, it looks like it's not easy to change this, so here is a workaround. Just hide the unwanted tangents.
jtico
Hi,
what we could consider doing is
* detect that D belongs to d symbolically  as Mike says, this is a performance killer
* detect that D belongs to d numerically / probabilistically  won't be very stable
* make sure that at least Tangent[ClosestPoint[d,D],d] works  I guess we can do that
Cheers,
Zbynek
Hi Zbynek. Thanks for your answer. Now I understand that as developers you are concerned about stability.
I was wondering. What about Distance[Point,Object]?. It looks like this is a robust numerical test for deciding if a point is on a curve or not.
Cheers, jtico.
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