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November 4

Truncated (or censored) data and tests of statistical significance

Are there any technical reasons why I can't judge the statistical significance of consistency between a truncated data set (those with sized above a threshold) and a model statistical distribution which is truncated to the same threshold? Or to put it another way, do test of significance assume no trunction? Attic Salt (talk) 14:52, 4 November 2018 (UTC)[reply]

Could we build a mathematical discipline on other triangles instead of right triangles?

I get that triangles are central: the simplest polygon, you can decompose all other polygons into it. But how come that right triangles are central to loads of stuff? If we used another coordinated system, instead of the Cartesian, would it make any difference? If we worked really hard analysing properties of triangles with a 60 degrees angle, would that lead us anywhere? --Doroletho (talk) 18:06, 4 November 2018 (UTC)[reply]

Any triangle can be decomposed in two right triangles. So, why to try in invent something much more complicated if you can use an existing simpler theory? Ruslik_Zero 20:21, 4 November 2018 (UTC)[reply]

Back in the day (at least 100 years ago) it wasn't assumed automatically that the x and y axes where at right angles, so you'd have a chapter in textbooks devoted to the 'skew axes' case. Everything proceeds as normal except that formulas for distance, area, angles, etc get more complicated. The crux of the issue is the law of cosines with it's cos θ term; measurement becomes simpler when the cos θ = 0 and you can drop that term. There are certain cases though where computation for a given problem is more natural when you have axes at an angle, usually it involves having two given fixed lines off which the rest of the problem is built. One example is the Joachimsthal tetracuspid. (See [1], middle of the page, for a short description.) There are also cases in higher math where the most natural set of axes does not have right angles; see for example Coxeter group and Leech lattice. --RDBury (talk) 00:26, 5 November 2018 (UTC)[reply]

(Topic drift!) The description of the Joachimsthal tetracuspid conflicts with the diagram there! The end of the short segment is not moving along the base line if it reaches beyond that line at the corners. —Tamfang (talk) 20:10, 5 November 2018 (UTC)[reply]

The Joachimsthal tetracuspid does some unexpected things. in particular you sometimes have to extend the line segment to get the entire envelope. The diagram shows the extended line segment which is why it extends beyond the axis at times. The diagram is perhaps a bit misleading, but the wording of the description is correct if you read it carefully. Going further off topic -- http://www.mathcurve.com has been around for a while now, but only recently have they added English translations of the pages. --RDBury (talk) 00:18, 6 November 2018 (UTC)[reply]

Further topic drift: Our current tetracuspid page redirects to an article about only one type of tetracuspid, and this discussion is the only page in the whole 'pedia where the Joachimsthal type is even mentioned - articles that need to be written, but unfortunately I'm nowhere near competent to do it. Roger (Dodger67) (talk) 09:18, 9 November 2018 (UTC)[reply]

(drifting again) You might like a puzzle about 'right wiggly triangles'. These can have bendy lines as sides but the sum of the angles at the three corners must add up to 180 degrees. If a vertex is on a side the side must be straight through there. Show one can't decompose a circle into right wiggly triangles. And then actually decompose a circle that way ;-) Dmcq (talk) 10:35, 9 November 2018 (UTC)[reply]