Brain Teaser - Minimum distance between two curves
01-02-2016, 06:14 PM
Post: #14
 quinyu Junior Member Posts: 44 Joined: Dec 2015
RE: Brain Teaser - Minimum distance between two curves
1. The coordinates at f(x) are (x,x^2+1); at g(y) are (y,sqrt(y)). Using a global minimization for the distance, the lowest distance possible is ~0.427592 where x=~0.331695 and y=~0.568071.
2. This x is the (real) root of the equation 4*x^5+6*x^3-x^2=1/8
3. More precisely y is ~0.5680712803530178751565860996, but I could not find a single proper closed form for this.

Done with Mathematica/WolframAlpha.
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 Messages In This Thread Brain Teaser - Minimum distance between two curves - CR Haeger - 11-18-2015, 04:35 PM RE: Brain Teaser - Minimum distance between two curves - Vtile - 11-18-2015, 05:50 PM RE: Brain Teaser - Minimum distance between two curves - Gerald H - 11-18-2015, 06:18 PM RE: Brain Teaser - Minimum distance between two curves - Vtile - 11-18-2015, 06:24 PM RE: Brain Teaser - Minimum distance between two curves - Jonathan Cameron - 11-18-2015, 06:40 PM RE: Brain Teaser - Minimum distance between two curves - CR Haeger - 11-18-2015, 07:06 PM RE: Brain Teaser - Minimum distance between two curves - Jonathan Cameron - 11-18-2015, 11:47 PM RE: Brain Teaser - Minimum distance between two curves - Vtile - 11-18-2015, 07:23 PM RE: Brain Teaser - Minimum distance between two curves - Werner - 11-18-2015, 10:19 PM RE: Brain Teaser - Minimum distance between two curves - CR Haeger - 11-19-2015, 12:30 AM RE: Brain Teaser - Minimum distance between two curves - Thomas Klemm - 11-21-2015, 01:46 AM RE: Brain Teaser - Minimum distance between two curves - Jonathan Cameron - 11-21-2015, 05:37 PM RE: Brain Teaser - Minimum distance between two curves - Bunuel66 - 11-21-2015, 09:39 PM RE: Brain Teaser - Minimum distance between two curves - quinyu - 01-02-2016 06:14 PM RE: Brain Teaser - Minimum distance between two curves - Pekis - 01-12-2016, 09:40 AM

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