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hint: two additional straight lines on #348 solution picture help.bleaug
See my full worked out solution:http://home.kpn.nl/henkreuling/solutions8foxes/349_8foxes_solution.pdf
similar to henkie's solution:http://bleaug.free.fr/8foxes/8foxes349.pngby construction:a(ADE)=a(BCE)=a(CFE)=a(DGE)let O = midpoint of DC. Symmetry centered in O sends DGH in CG'H'. Hence a(DGE)=a(DHE)+a(DGH)=a(DHE)+a(CG'H')Therefore:a(CDE)=a(CFE)+a(DHE)+a(CG'H')+a(FHH'G')=2*a(ADE)+a(FHH'G') > 2*a(ADE) > 1.96*a(ADE). Claim is wrong.bleaug
http://imageshack.us/photo/my-images/850/fox349.jpg/jyu
Good solutions...We have another one with totally analytic expressions. Some day, we may compile all of these into a single post. May be later...-8foxes
hint: two additional straight lines on #348 solution picture help.
ReplyDeletebleaug
See my full worked out solution:
ReplyDeletehttp://home.kpn.nl/henkreuling/solutions8foxes/349_8foxes_solution.pdf
similar to henkie's solution:
ReplyDeletehttp://bleaug.free.fr/8foxes/8foxes349.png
by construction:
a(ADE)=a(BCE)=a(CFE)=a(DGE)
let O = midpoint of DC. Symmetry centered in O sends DGH in CG'H'. Hence a(DGE)=a(DHE)+a(DGH)=a(DHE)+a(CG'H')
Therefore:
a(CDE)=a(CFE)+a(DHE)+a(CG'H')+a(FHH'G')=2*a(ADE)+a(FHH'G') > 2*a(ADE) > 1.96*a(ADE). Claim is wrong.
bleaug
http://imageshack.us/photo/my-images/850/fox349.jpg/
ReplyDeletejyu
Good solutions...
ReplyDeleteWe have another one with totally analytic expressions. Some day, we may compile all of these into a single post. May be later...
-8foxes