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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

At Netflix we engage in what we call consumer science: we test new ideas with real customers, at scale, and we measure for statistically significant differences in how they engage with our product. Are members staying with the service longer? Are they instantly watching more TV shows and movies from us?

As an employee, the results of these tests are more important than your confidence in what the outcome will be, what your title is, or your ability to persuade. I’ve seen even our best product minds bet wrong on such tests on occasion. We absolutely believe we couldn’t build one of the best loved internet brands in the world without consumer science at the core of our product development methodology.

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:

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.