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Schröder Points Database / Darij Grinberg

This page contains some results and questions about the Schröder points of a triangle and configuration related to these. The dates are the dates of last changes.

The idea of this page was to collect all known results about the Schröder points of a triangle from different sources (Hyacinthos messages, MathLinks discussions). Feel free to mail me (see main site for address) if you have something to add.

[Schroeder2] The Schröder points, Darij Grinberg, 4 Jul 2004 [Schroeder3] Incentral Triangle Question, Darij Grinberg, 27 Feb 2004 [Schroeder4] Re: Incentral Triangle Question, Eric Danneels, 3 May 2003 [Schroeder5] Poristically fixed points, Darij Grinberg, 25 Mar 2004 [Schroeder6] Re: Incentral Triangle Question, Darij Grinberg, 27 Feb 2004 [Schroeder7] Some newer results from MathLinks, Darij Grinberg, 4 Jul 2004

[Schroeder2] [Schroeder3] [Schroeder4] [Schroeder5] [Schroeder6] [Schroeder7]
[Schroeder2] The Schröder points 1. The Schröder point by inversion Schröder point 2. Trilinears of the Schröder point Gergonne-Schröder point X(1155) = SCHRÖDER POINT 3. Jean-Pierre Ehrmann's approach 4. The Schröder point as inversive image of X(55) Weill point 5. The Nagel-Schröder point Nagel-Schröder point 6. The Stutensee point Stutensee point 7. The Mitten-Schröder points Mitten-Schröder points 8. The Bevan-Schröder point Bevan point Bevan-Schröder point 9. Trilinears of the Bevan-Schröder point 10. Some synthetic conjectures about the Bevan-Schröder point 11. Poristically fixed points poristically fixed Fundamental Poristic Theorem. 12. A generalization of the Schröder and Bevan-Schröder points leading to the Darboux cubic Schoute point Longchamps-Schröder point 13. A generalization of the Schröder and Nagel-Schröder points and the Feuerbach hyperbola Droussent pivot
[Schroeder3] Incentral Triangle Question
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Job number one for our product-focused engineers is to effectively innovate for Netflix members. The product we built in 2006 would not satisfy our members today. The best product in our market in 2015 will be far better than Netflix is today. It is our fundamental challenge to figure out what a better product can be on behalf of our members, and to build it.

Innovation involves a lot of failure. If we’re never failing, we aren’t trying for something out on the edge from where we are today. In this regard, failure is perfectly acceptable at Netflix. This wouldn’t be the case if we were operating a nuclear power plant or manufacturing cars. The only real failure that’s unacceptable at Netflix is the failure to innovate.

So if you’re going to fail, fail cheaply. And know when you’ve failed, vs. when you’ve gotten it right.

Product development at Netflix starts with a hypothesis, which typically goes something like this:

Algorithm/feature/design X will increase member engagement with our service, and ultimately member retention.

The idea may be a way to increase the relevance of our search results, a new design for device UIs, or a new feature, such as showing members what their Facebook friends are watching from Netflix. This is the crucial first step in our creative process, from which any improvement we can hope to deliver starts. Our intuition and imagination in how better to serve our members fuels our entire product development approach.

The second step is to design a test that will measure the impact of the hypothesis. Sometimes this simply means build it, but often we can build a prototype more quickly that captures the essence of the concept. Maybe the back end isn’t fully scalable; maybe it lacks polish or all of the bells and whistles we’d like to include if we roll it out for everyone.

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