This is TeX, Version 3.14159 (Web2C 7.3) (format=latex 1999.4.27) 13 JUN 2000 23:11 **kakeya.tex (kakeya.tex LaTeX2e <1998/12/01> Babel and hyphenation patterns for american, french, german, ngerman, n ohyphenation, loaded. (/net/fern/m4/tex/teTeX-0.9/share/texmf/tex/latex/base/latex209.def File: latex209.def 1998/05/13 v0.52 Standard LaTeX file Entering LaTeX 2.09 COMPATIBILITY MODE ************************************************************* !!WARNING!! !!WARNING!! !!WARNING!! !!WARNING!! This mode attempts to provide an emulation of the LaTeX 2.09 author environment so that OLD documents can be successfully processed. It should NOT be used for NEW documents! New documents should use Standard LaTeX conventions and start with the \documentclass command. Compatibility mode is UNLIKELY TO WORK with LaTeX 2.09 style files that change any internal macros, especially not with those that change the FONT SELECTION or OUTPUT ROUTINES. Therefore such style files MUST BE UPDATED to use Current Standard LaTeX: LaTeX2e. If you suspect that you may be using such a style file, which is probably very, very old by now, then you should attempt to get it updated by sending a copy of this error message to the author of that file. ************************************************************* \footheight=\dimen102 \@maxsep=\dimen103 \@dblmaxsep=\dimen104 \@cla=\count79 \@clb=\count80 \mscount=\count81 (/net/fern/m4/tex/teTeX-0.9/share/texmf/tex/latex/base/tracefnt.sty Package: tracefnt 1997/05/29 v3.0j Standard LaTeX package (font tracing) \tracingfonts=\count82 LaTeX Info: Redefining \selectfont on input line 83. ) \symbold=\mathgroup4 \symsans=\mathgroup5 \symtypewriter=\mathgroup6 \symitalic=\mathgroup7 \symsmallcaps=\mathgroup8 \symslanted=\mathgroup9 LaTeX Font Info: Redeclaring math alphabet \mathbf on input line 275. LaTeX Font Info: Redeclaring math alphabet \mathsf on input line 276. 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(/net/fern/m4/tex/teTeX-0.9/share/texmf/tex/latex/base/ulasy.fd File: ulasy.fd 1998/08/17 v2.2eLaTeX symbol font definitions ))) (/net/fern/m4/tex/teTeX-0.9/share/texmf/tex/latex/base/article.cls Document Class: article 1999/01/07 v1.4a Standard LaTeX document class (/net/fern/m4/tex/teTeX-0.9/share/texmf/tex/latex/base/size12.clo File: size12.clo 1999/01/07 v1.4a Standard LaTeX file (size option) ) \c@part=\count83 \c@section=\count84 \c@subsection=\count85 \c@subsubsection=\count86 \c@paragraph=\count87 \c@subparagraph=\count88 \c@figure=\count89 \c@table=\count90 \abovecaptionskip=\skip41 \belowcaptionskip=\skip42 Compatibility mode: definition of \rm ignored. Compatibility mode: definition of \sf ignored. Compatibility mode: definition of \tt ignored. Compatibility mode: definition of \bf ignored. Compatibility mode: definition of \it ignored. Compatibility mode: definition of \sl ignored. Compatibility mode: definition of \sc ignored. LaTeX Info: Redefining \cal on input line 488. LaTeX Info: Redefining \mit on input line 489. \bibindent=\dimen105 ) (/net/fern/m4/tex/teTeX-0.9/share/texmf/tex/latex/amsfonts/amssymb.sty Package: amssymb 1996/11/03 v2.2b (/net/fern/m4/tex/teTeX-0.9/share/texmf/tex/latex/amsfonts/amsfonts.sty Package: amsfonts 1997/09/17 v2.2e \@emptytoks=\toks14 \symAMSa=\mathgroup11 \symAMSb=\mathgroup12 LaTeX Font Info: Overwriting math alphabet `\mathfrak' in version `bold' (Font) U/euf/m/n --> U/euf/b/n on input line 133. )) (/u/sonia/h1/fa/tao/tex/MathMacro.tex) \c@theorem=\count91 \c@proposition=\count92 \c@lemma=\count93 \c@corollary=\count94 \c@remark=\count95 (kakeya.aux) \openout1 = `kakeya.aux'. LaTeX Font Info: Checking defaults for OML/cmm/m/it on input line 42. LaTeX Font Info: ... okay on input line 42. LaTeX Font Info: Checking defaults for T1/cmr/m/n on input line 42. LaTeX Font Info: ... okay on input line 42. LaTeX Font Info: Checking defaults for OT1/cmr/m/n on input line 42. LaTeX Font Info: ... okay on input line 42. LaTeX Font Info: Checking defaults for OMS/cmsy/m/n on input line 42. LaTeX Font Info: ... okay on input line 42. LaTeX Font Info: Checking defaults for OMX/cmex/m/n on input line 42. LaTeX Font Info: ... okay on input line 42. LaTeX Font Info: Checking defaults for U/cmr/m/n on input line 42. LaTeX Font Info: ... okay on input line 42. LaTeX Font Info: Try loading font information for U+msa on input line 71. (/net/fern/m4/tex/teTeX-0.9/share/texmf/tex/latex/amsfonts/umsa.fd File: umsa.fd 1995/01/05 v2.2e AMS font definitions ) LaTeX Font Info: Try loading font information for U+msb on input line 71. (/net/fern/m4/tex/teTeX-0.9/share/texmf/tex/latex/amsfonts/umsb.fd File: umsb.fd 1995/01/05 v2.2e AMS font definitions ) [1 ] LaTeX Font Info: Try loading font information for OMS+cmr on input line 83. (/net/fern/m4/tex/teTeX-0.9/share/texmf/tex/latex/base/omscmr.fd File: omscmr.fd 1998/03/27 v2.5g Standard LaTeX font definitions ) LaTeX Font Info: Font shape `OMS/cmr/m/n' in size <17.28> not available (Font) Font shape `OMS/cmsy/m/n' tried instead on input line 83. Overfull \hbox (7.31908pt too wide) in paragraph at lines 87--88 []\OT1/cmr/m/n/17.28 A pos-si-ble con-nec-tion with the Fal-coner dis-tance pro b- [] [2] Overfull \hbox (0.61118pt too wide) in paragraph at lines 101--102 []\OT1/cmr/m/n/17.28 One can phrase this for ei-ther the Minkowski or Haus- [] [3] Overfull \hbox (33.57465pt too wide) in paragraph at lines 117--118 []\OT1/cmr/m/n/17.28 In two di-men-sions the Kakeya con-jec-ture is true (C^^So rdoba, [] Overfull \hbox (20.4611pt too wide) in paragraph at lines 119--120 \OT1/cmr/m/n/17.28 men-sion at least $(\OML/cmm/m/it/17.28 n \OT1/cmr/m/n/17.28 + 1)\OML/cmm/m/it/17.28 =\OT1/cmr/m/n/17.28 2$ (Christ, Drury, Duandikotxea, [] [4] Overfull \hbox (29.36505pt too wide) in paragraph at lines 137--138 \OT1/cmr/m/n/17.28 planes around the stem line seg-ment, and us-ing C^^Sordoba' s [] [5] [6] [7] [8] Overfull \hbox (10.32138pt too wide) in paragraph at lines 187--188 \OT1/cmr/m/n/17.28 metic com-bi-na-torics which im-proves on Wolff's Kakeya [] [9] [10] Overfull \hbox (4.51082pt too wide) in paragraph at lines 221--222 \OT1/cmr/m/n/17.28 tremely close to $5\OML/cmm/m/it/17.28 =\OT1/cmr/m/n/17.28 2 $. This im-plies a sur-pris-ing amount [] [11] [12] [13] (kakeya.aux) ) Here is how much of TeX's memory you used: 967 strings out of 10896 9508 string characters out of 71883 50550 words of memory out of 263001 3904 multiletter control sequences out of 10000+0 22736 words of font info for 87 fonts, out of 200000 for 1000 15 hyphenation exceptions out of 1000 25i,4n,24p,576b,198s stack positions out of 300i,100n,500p,30000b,4000s Output written on kakeya.dvi (13 pages, 17596 bytes).