Saddle point in German for a line in plane

Asked May 02 '17 at 21:12

Active May 12 '17 at 12:52

Viewed 71 times

In German Sattelpunkt (= saddle-point) refers to a point that has inflection parallel to x-axis.

$$ y' =0, y^{''}=0 $$

for a line in the plane.

In English it is a point of a surface of negative curvature.

Why the is the same translated word so conceptually different ?

In a monkey-saddle $ (K<0) $ at its center there is an inflection point, is that why ?

edited May 12 '17 at 12:52

asked May 02 '17 at 21:12

Narasimham

40,495

Your location is : USA, India and you are asking German. Strange :P – Jaideep Khare May 02 '17 at 21:18
2

Wikipedia says it: a saddle point is a stationary point that is not an extremum. This holds in 1D and higher dimensions. – May 02 '17 at 21:19
as @YvesDaoust says, saddle point should have a universal meaning. Germans would not change it. Can you give the source of information? – Seyhmus Güngören May 02 '17 at 21:20
@SeyhmusGüngören: see German Wikipedia. – May 02 '17 at 21:22
You probably misunderstood one of the Wikipedia articles, as both use the same definition. – user251257 May 02 '17 at 21:37
There is no visible saddle in 1D case, so in this special case it's better to call it Terrassenpunkt and keep the notion of saddle point to minimax. – A.Γ. May 02 '17 at 21:50
@YvesDaoust Yes, but the use of this notion is minor compared to the "critical point with indefinite Hessian", which is central in optimization and game theory. – A.Γ. May 03 '17 at 09:03
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@YvesDaoust No, the game saddle point has nothing to do with "critical not extremum". For example, a monkey saddle is not a saddle point. – A.Γ. May 03 '17 at 10:28
One can see the difference between eye vision and mathematical eye (logik) vision. – Narasimham May 03 '17 at 11:01
@ A.Γ. but I thought monkey saddle is composed of all saddle points except at the center where ( here monkey bottom contacts ) it is a singularity. Is it right? – Narasimham May 03 '17 at 16:12
@Narasimham It is negative curvature at all points, but for the saddle point is should be a critical point. – A.Γ. May 03 '17 at 16:44
Negative curvature point and saddle point are quite the same.. only different words – Narasimham May 03 '17 at 18:18

Saddle point in German for a line in plane

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