what is inversion? :D 2009/9/29 Zx.MYS <[email protected]>
> > I got it!Thank you Takaki! > > Takaki wrote: > > Hi zx.mys! > > > > This is my interpretation of the contest analysis solution: > > > > Originally, you have 3 circles of radii r1, r2 and r3 (say r1 is the > > smallest). The solution says to subtract the radii of the two larger > circles > > to r2 - r1 and r3 - r1. These circles will be outside the smallest > circle, > > so after inversion, they will be contained within the smallest circle. > The > > tangents mean the straight lines that touch the two inverted circles > (they > > won't necessarily go through the smallest circle's centre). Like this: > > > > ____O_o___ > > > > When inverted back, the tangents will map to circles which touch the > r2-r1 > > and r3-r1 circles (because tangency is preserved by inversion) and goes > > through the centre of the smallest circle (lines map to circles that pass > > through origin), so the radius can be increased by r1 to get a circle > which > > touches all three plants. > > > > I hope this helps! If you're not too familiar with inversion, I think > > wikipedia explains it quite well: > > http://en.wikipedia.org/wiki/Inversive_geometry > > > > > > > > On Mon, Sep 28, 2009 at 3:00 PM, Zx.MYS <[email protected]> wrote: > > > > > > > > quoted from Contest Analysis > > > > > > "We can subtract from the radius of each of the three plants the > > > radius of the smallest plant, then compute an inversion about that > > > plant's center. Then we find appropriate tangents to the two inverted > > > plants, re-invert to find the corresponding circle, and add back the > > > radius of the smallest plant. " > > > > > > I got puzzled when trying to understand this(may caused by my poor > > > English). > > > Why doing all these inversions? Doe "appropriate tangents" mean a > > > tangents go through the smallest plant's center? > > > And finally,how does this solution work? > > > > > > > > > > > > > --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "google-codejam" group. To post to this group, send email to [email protected] To unsubscribe from this group, send email to [email protected] For more options, visit this group at http://groups.google.com/group/google-code?hl=en -~----------~----~----~----~------~----~------~--~---
