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A comment on Post your proofs: Given five points on a sphere, four of them lie on a closed hemisphere..

Re:Post your proofs: Given five points on a sphere, four of ... by cperciva on Tuesday December 04, 2007 @01:13PM (#86006)
Answer ROT13ed, see http://www.rot13.com/ to translate:

Gnxr nal gjb bs gur svir cbvagf, naq pnyy gurz N naq O. Pnyy gur bgure guerr cbvagf P, Q, naq R.

Abj pbafgehpg n cynar K cnffvat guebhtu N, O, naq gur pragre bs gur fcurer (vs N naq O ner rdhny, gurer ner vasvavgryl znal fhpu cynarf; bgurejvfr gurer vf cerpvfryl bar). Gur cynar K qvivqrf gur fcurer F vagb gjb bcra urzvfcurerf F_1 naq F_2, naq gur pvepyr F_3 juvpu vf gur vagrefrpgvba bs F naq K. Abgr gung F_3 pbagnvaf obgu N naq O.

Abj qrsvar G_1 = F_1 H F_3 naq G_2 = F_2 H F_3; ol vafcrpgvba, gurfr ner obgu pybfrq urzvfcurerf. Fvapr F_3 pbagnvaf obgu N naq O, G_1 naq G_2 obgu pbagnva obgu N naq O. Shegurezber, G_1 H G_2 = F_1 H F_2 H F_3 = F, naq gurersber gur cbvagf P, Q, naq R rnpu yvr ba bar be zber bs G_1 naq G_2.

Ol gur cvtrbaubyr cevapvcyr, ng yrnfg bar bs G_1 naq G_2 pbagnvaf ng yrnfg gjb bhg bs gur guerr cbvagf P, Q, naq R. Pnyy guvf bar G. Fvapr jr nyernql xabj gung G pbagnvaf obgu N naq O, jr pbapyhqr gung G vf n pybfrq urzvfcurer pbagnvavat ng yrnfg sbhe bhg bs gur svir cbvagf N, O, P, Q, naq R.

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Re:Post your proofs: Given five points on a sphere, four of ... by viergroupie on Tuesday December 04, 2007 @03:13PM (#86071)
Qbrf guvf cebbs nyfb jbex gb fubj gung nal A-1 bs A cbvagf qenja ba n fcurer jvyy funer n urzvfcurer?
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Re:Post your proofs: Given five points on a sphere, four of ... by tomjen on Tuesday December 04, 2007 @04:04PM (#86093)
Ab ohg vg pna or hfrq gb cebir gung sbe sbhe cbvagf ba n pvepyr, guerr bs gurfr cbvagf zhfg or va gur fnzr frzvpvepyr.

Zl uhapu vf gung sbe rnpu qvzrafvba lbh nqq, lbh pna vapernfr a ol bar, gung vf gb fnl lbh pbhyq unir 6 cbvagf va gur 4 qvzrafvba. Guvf vf onfrq ba gur vqrn gung vg gnxrf a cbvagf gb znxr na a qvzrafvbany cynar, fb lbh pna cynpr 4 cbvagf va gur pragre sbe gur frzvsvther va gur 4gu qvzrafvba.

Gura vg vf snveyl fvzcyr gb ernyvfr gung cynpvat 2a+1 vgrzf vagb 2 tebhcf zrnaf gung ng yrnfg bar tebhc zhfg unir ng yrnfg a+1 vgrzf.

Gb hfr guvf onfvf sbe gur agu qvzrafvba, lbh zhfg erzbir a cbvagf yrnivat bayl 3 cbvagf. Vs nalobql pna znxr n cebbs guvf gubhtu V jbhyq ybir gb frr vg.

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Re:Post your proofs: Given five points on a sphere, four of ... by gambling8nt on Tuesday December 04, 2007 @05:18PM (#86125)
Va x-qvzrafvbany fcnpr, gnxvat x-1 cbvagf abg nyy ba gur fnzr x-2 fcurer qrgrezvarf n x-1 fcurer pbapragevp jvgu bhe bevtvany x-fcurer. Fhpu n x-1 fcurer qvivqrf bhe bevtvany x-fcurer vagb gjb x-urzvfcurerf (vs lbh qba'g oryvrir guvf, fvzcyl er-bevrag lbhe onfvf fb gung bar qverpgvba vf begubtbany gb gur x-1 fcurer; gur gjb x urzvfcurerf ner gura gur cbvagf ba gur x-fcurer jurer guvf pbbeqvangr vf abaartngvir, naq gur cbvagf ba gur x-fcurer jurer guvf pbbeqvangr vf abacbfvgvir. Ohg gura vs jr jnag y cbvagf va bhe x-urzvfcurer, jr pna thnenagrr gurve cerfrapr vs jr unir 2(y-(x-1)-1 = 2y-2x+1 cbvagf yrsg. Ohg guvf vf gur fnzr nf fgnegvat jvgu 2y-x cbvagf ba gur fhesnpr bs gur fcurer va x-qvzrafvbany fcnpr, fb gung vf gur zvavzhz ahzore jr arrq gb thnenagrr (hfvat guvf nethzrag) y bs gurz ba n pybfrq x-qvzrafvbany urzvfcurer. Abgr gung guvf erfhyg zngpurf gung bs gur 3-qvzrafvbany pnfr.

Gur vagrerfgvat cneg bs guvf erfhyg vf abg qverpgyl jung vg fnlf, ohg jung vg fnlf nobhg fcnprf jr pna rzorq va gur fhesnpr bs n x-qvzrafvbany fcurer...gung 2y-x cbvagf va fhpu n fcnpr ner pbirerq ol gur cer-vzntr (haqre gur rzorqqvat) bs n urzvfcurer--sbe rzorqqvatf jvgu avpr-ybbxvat cer-vzntrf bs urzvfcurerf, guvf pbhyq pbaprvinoyl npghnyyl or n hfrshy erfhyg.

Edit: Vs lbh pna'g pubbfr fhpu n frg bs x-1 cbvagf, gura nyy lbhe cbvagf snyy ba gur fnzr x-2 fcurer, juvpu pna or rkgraqrq gb n x-1 fcurer gung vf hfrq nf n obhaqnel orgjrra gjb x-urzvfcurerf; nyy lbhe cbvagf ner ba gur obhaqnel bs obgu.

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Re:Post your proofs: Given five points on a sphere, four of ... by Xichekolas on Wednesday December 05, 2007 @10:57AM (#86300)
You guys keep going like this and I'm going to be able to read rot13 without needing the translator...
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Re:Post your proofs: Given five points on a sphere, four of ... by brlewis on Tuesday December 04, 2007 @03:24PM (#86074)
Ab, sbe 6 cbvagf guvf cebbs jbhyq fgvyy bayl cebir 4 bs gurz gb or va gur fnzr urzvfcurer.

The leet key Firefox extension is fun.

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Re:Post your proofs: Given five points on a sphere, four of ... by cperciva on Tuesday December 04, 2007 @03:58PM (#86091)
Ab, vg cebirf gung bhg bs 2A-1 cbvagf ba n fcurer, A+2 jvyy funer n urzvfcurer.
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Re:Post your proofs: Given five points on a sphere, four of ... by viergroupie on Wednesday December 05, 2007 @10:26PM (#86494)
Oh right, I'm an idiot.
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