ÿþ<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN"> <HTML> <HEAD> <TITLE>Flatland</TITLE> <LINK REL=stylesheet HREF="images/style.css" TYPE="text/css"> </HEAD> <BODY style="font-family:arial; color=#000064; font-style:bold;" > <span lang=HE style='font-family:David'> <B><CENTER><H1>Flatland - ÞÙéÕèÙÔ<br></H1></CENTER></B><BR> <p class=MsoNormal dir=RTL style='margin-bottom:6.0pt;text-align:right; direction:rtl;unicode-bidi:embed'><span lang=HE style='font-family:David'>ÐÓÕÕÙß, Ð. ÐÑÕØ, ÒèáÔ âÑèÙê ×ÓéÔ: ÜÙÔ àèÒÓ, ÑÑÜ ÔÕæÐÔ ÜÐÕè, êÜ-ÐÑÙÑ, 2000</span></p> <p class=MsoNormal dir=RTL style='margin-bottom:6.0pt;text-align:right; direction:rtl;unicode-bidi:embed'><span lang=HE style='font-family:David'><STRONG>Ð×èÙê ÓÑè ÜÞÔÓÕèÔ ÔâÑèÙê: ÜÙÐÕ çÕèÙ</STRONG></span></p> <p class=MsoNormal dir=RTL style='margin-bottom:6.0pt;text-align:right; direction:rtl;unicode-bidi:embed'><span lang=HE style='font-family:David'>ÐÓÕÕÙß ÐÑÕØ ÐÑÕØ (1838-1926) ÜÐ ÔÙÔ ÔÐàÒÜÙ ÔÙ×ÙÓ, ÕÐäÙÜÕ ÜÐ ÔèÐéÕß, éäèáÝ äàØÖÙÔ ÞÑÕááê âÜ èâÙÕàÕê éÐÕÜÙÝ ÞâÕÜÝ ÔÞÓâ, ÕÔØÕÞàê Ñ×ÕÑÔ Þáè âÕçæàÙ éÜ ÑÙçÕèê ×ÑèêÙê ÕêèÑÕêÙê ÛÜäÙ ÑàÙ ÓÕèÕ. Ò'Õàê'ß áÕÕÙäØ, ÜÕÕÙá çÐèÕÜ Õ-Ô.Ò' ÕÕÜá ÔÝ éÜÕéÔ ÞÑÙß ÔéÞÕê ÔÑÕÜØÙÝ ÔàÕáäÙÝ éâÕÜÙÝ âÜ ÓâêàÕ ÑÔçéè ÔÖÔ. ÛÞÕ ÑÞçèÙÝ éÜ áÕÕÙäØ, çÐèÕÜ, Õ-ÕÕÜá, áäèÕ éÜ ÐÑÕØ, &quot;ÞÙéÕèÙÔ&quot;, ÖÛÔ, ÕâÓÙÙß ÖÕÛÔ, ÜÞÔÓÕèÕê Þ×ÕÓéÕê éÞÞéÙÛÕê ÜâÕèè ÓèÚ çÑâ âàÙÙß èÑ ÑÓÕèÕê ×ÓéÙÝ éÜ çÕèÐÙÝ àÜÔÑÙÝ. <o:p></o:p></span></p> <p class=MsoNormal dir=RTL style='text-align:right;direction:rtl;unicode-bidi: embed'><span lang=HE style='font-family:David'>ÐÑÕØ ÜÞÓ ÜÙÞÕÓÙÝ çÜÐáÙÙÝ ÑçÙÙÞÑèÙÓÒ'. ÜÐ×è ÔáÞÛêÕ ÜÛÞÕèÔ, ÔÕÐ ÞÕàÔ ÜÞàÔÜ ÑÑÙÔ&quot;á ÔÜÕàÓÕàÙ éÑÕ Ôê×àÚ</span><span dir=LTR></span><span lang=HE dir=LTR style='mso-bidi-font-family:David'><span dir=LTR></span> </span><span lang=HE style='font-family:David'>ÑÙÜÓÕêÕ. ÔÕÐ ÞÙÜÐ Ðê ÔêäçÙÓ ÑÞéÚ 25 éàÔ ÑÔæÜ×Ô ÙÕæÐê ÓÕäß éÔçàêÔ ÜÕ êÔÙÜÔ èÑÔ âÕÓ ÑÙÞÙ ×ÙÙÕ. ÔÕÐ èÐÔ Ñ×ÙàÕÚ Ðê ÔÛÜÙ ÔÞèÛÖÙ ÜçÙÓÕÝ ÕÜÙêè éÕÕÙÕß Ñ×ÑèÔ ÔÐàÒÜÙê, ÕâÜ Ûß ÔçÓÙé ÞÐÞæÙÝ ÛÔ èÑÙÝ ÜØÙäÕ× ×ÙàÕÚ âÜ äÙ ÔÑàêÕ. ÔÞäÕèáÝ ÞÑÙß êÜÞÙÓÙÕ ÔÙÔ ÔèÑèØ Ô. ÐáçÙê (</span><span dir=LTR style='mso-bidi-font-family:David'>H. H. Asquith</span><span dir=RTL></span><span lang=HE style='font-family:David'><span dir=RTL></span>), ÞÙ éÔÙÒâ ÜèÐéÕê ÞÞéÜê ÐàÒÜÙÔ, ÜÐ×è ÙÜÓÕê éÜ âÕàÙ, ÜÙÞÕÓÙÝ ÑÑÙê áäèÕ éÜ ÑÕØ, ÕÜÐ×è ÞÛß, ÜÙÞÕÓÙÝ ÐçÓÞÙÙÝ ÑÐÕçáäÕèÓ. ÐÕÜÝ, ÑÒÙÜ ×ÞÙéÙÝ ÐÑÕØ äèé ÞâÑÕÓêÕ Ô×ÙàÕÛÙê ÛÓÙ ÜÔçÓÙé Ðê ÛÜ ÖÞàÕ ÜÛêÙÑÔ. ÔÕÐ äèáÝ áäèÙ âÙÕß ÕÞ×çè èÑÙÝ, éÔÞäÕèáÝ ÞÑÙàÔÝ<span style="mso-spacerun: yes">  </span>âÕáç ÑÓÙçÓÕç ÔÐàÒÜÙ ÑÙæÙèêÕ éÜ éÙÙçáäÙè. Ðê ÓâÕêÙÕ ÔÑÙçÕèêÙÕê âÜ Ô×ÑèÔ ÔÕÙçØÕèÙÐàÙê ÔÕÐ ÔÑÙâ ÜÐ èç ÓèÚ ÐÜÒÕèÙÕê ÛÒÕß ÖÕ ÔÞÕäÙâÔ Ñ&quot;ÞÙéÕèÙÔ&quot;, ÐÜÐ ÒÝ ÑÐÕäß ÙéÙè ÕÑÔÖÓÞàÕÙÕê èÑÕê.<o:p></o:p></span></p> <p class=MsoNormal dir=RTL style='margin-bottom:6.0pt;text-align:right; direction:rtl;unicode-bidi:embed'><span lang=HE style='font-family:David'><![if !supportEmptyParas]>&nbsp;<![endif]><o:p></o:p></span></p> <p class=MsoNormal dir=RTL style='margin-bottom:6.0pt;text-align:right; tab-stops:right 217.3pt;direction:rtl;unicode-bidi:embed'><span lang=HE style='font-family:David'>ÔèâÙÕß ÔÞÓâÙ ÔÞèÛÖÙ éáÑÙÑÕ ÞêàÔÜ áäèÕ éÜ ÐÑÕØ ÔÕÐ ÔèâÙÕß éÜ ÔÞÙÞÓ ÔèÑÙâÙ ÕéÜ ÙÛÕÜêàÕ, ÛÙÙæÕèÙÝ Ô×ÙÙÝ ÑâÕÜÝ êÜê-ÞÙÓÞÙ, ÜÔÑÙß Ðê ÞéÞâÕêÕ. ÞÐÖ äÕèáÝ ÜèÐéÕàÔ &quot;ÞÙéÕèÔ&quot; Ñ-1884 âÑè ÔèâÙÕß éÜ ÔÞÙÞÓ ÔèÑÙâÙ ÒÜÒÕÜÙÝ èÑÙÝ ÑÔçéè ÔÞÓâÙ ÓÕÕçÐ. ÑàáÙÑÕê ÔÞéêàÕê éàçéèÕ ÐÜÙÕ, êéÕÞê ÜÙÑÝ éÜ çÕèÐÙ &quot;ÞÙéÕèÙÔ&quot; ÔÕäàêÔ ÐÜ Ôáäè ÛÜ äâÝ ÞÛÙÕÕàÙÝ éÕàÙÝ, é×ÜçÝ ÑÕÕÓÐÙ ÔÙÕ ÞäêÙâÙÝ Ðê ÔÞ×Ñè âÓ ÞÐÕÓ. ÔÓÕÒÞÔ ÔÑÕÜØê ÑÙÕêè ÜÛÚ çéÕèÔ ÜêÕèê ÔÙ×áÕê. êÕèÔ ÖÕ ÞâÕèèê ÑÓÞÙÕß ÔçÕÜçØÙÑÙ, ÙÕêè ÐÕÜÙ ÞÛÜ èâÙÕß ÞÓâÙ Ð×è, ÖÙçÔ ÙéÙèÔ ÜÞÕéÒ ÔÞÙÞÓ ÔèÑÙâÙ. çÕèÐÙÝ ÕÞÑçèÙÝ èÑÙÝ ÔæÑÙâÕ ÑèÑÕê ÔéàÙÝ âÜ ÔâÕÜÝ ÔÞêÕÐè Ñ&quot;ÞÙéÕèÙÔ&quot; ÛÐÜ ÐÜÒÕèÙÔ ÜâÕÜÝ ÔäÙÖçÜÙ Ô×Óé éêÕèê ÔÙ×áÕê ×éäÔ ÑäàÙàÕ. ÐÜÐ éÑäÕâÜ, ÛÞÕÑß, ÐÑÕØ ÛêÑ Ðê áäèÕ ÙÕêè ÞéÜÕéÙÝ éàÔ <b>ÜäàÙ </b>éÐÙÙàéØÙÙß äèáÝ Ðê ÞÐÞèÕ ÔèÐéÕß éâáç ÑÙ×áÕê. ÙêèÔ ÞÖÕ, ÑÛÜ ÞÐÞèÙÕ ÔèÐéÕàÙÝ Ñê×ÕÝ, ÐÙÙàéØÙÙß âæÞÕ ÜÐ çÙéè ÑÓèÚ ÛÜéÔÙ Ðê êÕèêÕ Ô×ÓéÔ ÜÞÕéÒ ÔÞÙÞÓ ÔèÑÙâÙ. ÜÔÙäÚ: êÒÕÑêÕ ÜçéèÙÝ ÔèÐéÕàÙÝ éÔÕæâÕ ÑÛÙÕÕß ÔÖÔ ÔÙÙêÔ éÜ Ó×ÙÙÔ ÞÕ×ÜØê. ÔèÐéÕß éäÙê× Ðê Ôçéè ÑÙß êÕèê ÔÙ×áÕê ÔäèØÙê ÜÑÙß èâÙÕß ÔÒÙÐÕÞØèÙÔ ÔÐèÑâÔ-ÞÙÞÓÙê ÔÙÔ ÔÞêÞØÙçÐÙ ÔèÞß ÞÙàçÕÑáçÙ (</span><span dir=LTR style='mso-bidi-font-family:David'>Hermann Minkowski</span><span dir=RTL></span><span lang=HE style='font-family:David'><span dir=RTL></span>) Ô×Ü Þ-1907, ÕÐÙÙàéØÙÙß èÐÔ ÑÛÚ ÔêÒàÓèÕê äÕèÞÜÙê ÕÞÙÕêèê éÜ ÞêÞØÙçÐÙÝ, éÜÐ ÔÙÔ ÑÔ ÕÜÐ ÛÜÕÝ ÛÓÙ ÜÔÕáÙã êÕÑàÕê äÙÖÙçÜÙÕê ×ÓéÕê ÜêÕèêÕ éÜÕ. àÓèéÕ âÕÓ Þáäè éàÙÝ éÜ âÑÕÓÔ ÕÔÑàê ÔéÜÛÕêÙÔ éÜ ÒÙéê ÞÙàçÕÑáçÙ ÛÓÙ éÐÙàéØÙÙß âæÞÕ ÙÐÞå Ðê ÔÒÙéÔ ÕÙÞéÙÚ Ðê äÙêÕ× êÕèê ÔÙ×áÕê ÞàçÕÓê ÔèÐÕê Ô×éÕÑÔ éÔÒÙéÔ ÔÖÕ ÞÐäéèê. ÕÐÖ ÛâÑÕè ÛÞÔ éàÙÝ, Ñ-1926 , äÕèáÞÔ ÞÔÓÕèÔ Þ×ÕÓéê éÜ &quot;ÞÙéÕèÙÔ&quot; âÜ èçâ ÔÔêâàÙÙàÕê ÔÒÕÑèê ÑêÕèê ÔÙ×áÕê ÕÑèâÙÕß ÔÞÙÞÓ ÔèÑÙâÙ ÔæÞÕÓ ÜÔ. ÞÜÐÛê ÛêÙÑê ÔÞÑÕÐ ÜÞÔÓÕèÔ ÔÔÙÐ éÜ &quot;ÞÙéÕèÙÔ&quot; àÞáèÔ ÜÙÓÙ ÔäÙÖÙçÐÙ ÕÕÙÜÙÐÝ ÒÐèàØ (</span><span dir=LTR style='mso-bidi-font-family:David'>William Garnett</span><span dir=RTL></span><span lang=HE style='font-family:David'><span dir=RTL></span>), ÕÛÚ ÔÙÔ ÒÝ ÑÞÔÓÕèÔ éÜ 1952, éÔÞÑÕÐ ÜÔ àÛêÑ â&quot;Ù ÔäÙÖÙçÐÙ Ñàé ÔÕäÞß</span><span dir=LTR></span><span dir=LTR style='mso-bidi-font-family: David'><span dir=LTR></span> (Banesh Hoffmann) </span><span dir=RTL></span><span lang=HE style='font-family:David'><span dir=RTL></span>. ÒÝ ÔÕäÞß ÕÒÝ ÒÐèØ ÔÓÒÙéÕ ÑÞÙÕ×Ó, ÑÞÑÕÐÕê éÛêÑÕ, Ðê ÔÔçéè éÜ êÕèê ÔÙ×áÕê ÕéÜ èâÙÕß &quot;âçÞÕÞÙÕê Ô×ÜÜ&quot;, ÕÔáÙÕâ ÔäÕØàæÙÐÜÙ éçèÙÐÔ ÑáäèÕ éÜ ÐÑÕØ ÙÛÕÜÔ ÜÔâàÙç ÜÔÑàêÝ éÜ ÐÜÔ.<span style="mso-spacerun: yes">  </span><o:p></o:p></span></p> <p class=MsoNormal dir=RTL style='margin-bottom:6.0pt;text-align:right; direction:rtl;unicode-bidi:embed'><span lang=HE style='font-family:David'>ÑÙß ÔÞÔÓÕèÕê ÔÞÐÕ×èÕê ÙÕêè éäÕèáÞÕ Ðäéè ÜæÙÙß Ðê ÖÕ Þ-1991, éÐê ÞÑÕÐÔ ÛêÑ ÔÞêÞØÙçÐÙ êÕÞá ÑàçÔÕã (</span><span dir=LTR style='mso-bidi-font-family:David'>Thomas Banchoff</span><span dir=RTL></span><span lang=HE style='font-family:David'><span dir=RTL></span>). ÔàÕéÐ Ô×Óé éÑàçÔÕã ÞÓÒÙé ÑÞÑÕÐÕ ÔÕÐ Ôçéè éÑÙß ÔÞÙÞÓ ÔèÑÙâÙ ÜÑÙß ÔÞ×éÑÙÝ ÔÐÜçØèÕàÙÙÝ Ô×ÓéÙÝ (ÓÐÖ), ÕÑäèØ, ÜÙÛÕÜêÝ éÜ ÐÜÔ ÜÐäéè ÜàÕ ÔææÔ, éÜÐ ÔÛèàÕ çÕÓÝ ÜÛß, ÜÙÙæÕÒÙÝ ÒèäÙÙÝ ÞâàÙÙàÙÝ éÜ ÞÙÞÓÙÝ éÞâÜ ÔÞÙÞÓ ÔéÜÙéÙ. ÑÐÞæâÕê ÔÞ×éÑ àÙêß ÜØäÜ ÑÐÕÑÙÙçØÙÝ ÓÞÙÕàÙÙÝ ÑâÜÙ ÐèÑâÔ ÞÙÞÓÙÝ ÕÜèÐÕê ÑæÕèÔ äéÕØÔ ÕÞâÙèê âÙàÙÙÝ ×êÛÙÝ &quot;èÕ×ÑÙÙÝ&quot; êÜê-ÞÙÞÓÙÙÝ, ÞÛÜ ÛÙÕÕß éàèæÔ, éÜ ÔÐÕÑÙÙçØÙÝ ÔÐèÑâÔ-ÞÙÓÞÙÙÝ ÔÜÜÕ. ÖÔ ÐÛß ÔâÙçèÕß éÐÑÕØ ÔÓÒÙÝ ÑáäèÕ, ÛÐéè êÕéÑ ÞÙéÕèÙÔ ÞêÕÕÓâ ÜâÕÜÝ ÔêÜê-ÞÙÞÓÙ ÓèÚ ×êÛÙÝ ÓÕ-ÞÙÞÓÙÙÝ éÜ ÔÛÓÕè. ×êÛÙÝ ÐÜÔ ÞÕäÙâÙÝ ÑâÕÜÝ ÔÓÕ-ÞÙÞÓÙ ÛÞâÒÜÙÝ ÑÒÕÓÜ ÞéêàÔ (ÛäÙ éÔçÕèÐ ÙÒÜÔ ÑçèÙÐêÕ ÑÔÞéÚ). ÕÛÚ, êÕÚ ÔäâÜê ÔÓÞÙÕß, ÐàÕ ÞÕÖÞàÙÝ ÜÞâéÔ ÜêÔÕê ÐÙÚ ÙÛÕÜàÕ ÐÕÜÙ ÜÑàÕê ÑÔÛèêàÕ ÔêÜê-ÞÙÞÓÙê ÙÙæÕèÙÝ ÞâÕÜÝ Ñß ÐèÑâÔ ÞÙÞÓÙÝ ÓèÚ ÔêÑÕààÕê Ñ×êÛÙÝ ÔêÜê-ÞÙÞÓÙÙÝ éÜÔÝ. ÔÞ×éÑ ÔÞÕÓèàÙ, ÛÚ ÞÓÒÙé ÑàçÔÕã ÑÞÑÕÐÕ, ÞæÙâ áÙÕâ ÞéÞâÕêÙ ÞÐÕÓ ÑÞÜÐÛÔ ÖÕ éÜ ÔäâÜê ÔÓÞÙÕß âÜ äÙ ÔÛÙÕÕß éÐÑÕØ ÔÓÒÙÝ ÑáäèÕ.<o:p></o:p></span></p> <p class=MsoNormal dir=RTL style='margin-bottom:6.0pt;text-align:right; direction:rtl;unicode-bidi:embed'><span lang=HE style='font-family:David'>ÞÔÓÕèÔ ×ÓéÔ âÕÓ ÙÕêè éÜ &quot;ÞÙéÕèÙÔ&quot; ÔÕäÙâÔ Ñ-1999 ÕÞÑÕÐÔ àÛêÑ â&quot;' äÙÖÙçÐÙ Þ-</span><span dir=LTR style='mso-bidi-font-family:David'>MIT</span><span dir=RTL></span><span lang=HE style='font-family:David'><span dir=RTL></span>, ÐÜß ÜÙÙØÞß (</span><span dir=LTR style='mso-bidi-font-family:David'>Alan Lightman</span><span dir=RTL></span><span lang=HE style='font-family:David'><span dir=RTL></span>)</span><span dir=LTR></span><span lang=HE dir=LTR style='mso-bidi-font-family:David'><span dir=LTR></span> </span><span dir=RTL></span><span lang=HE style='font-family:David'><span dir=RTL></span>, ÔÞÕÛè ÒÝ ÛáÕäè ÕÞáÐÙ ÞÕæÜ× ÑÖÛÕê âæÞÕ. ÑÓÑèÙÕ âÜ Ôáäè éÜ ÐÑÕØ, ÜÙÙØÞß ÔÜÚ âÕÓ æâÓ Ð×Ó çÓÙÞÔ ÕÛÑè ÔÖÛÙè Ðê ÔÖÙçÔ ÑÙß èâÙÕàÕêÙÕ éÜ ÐÑÕØ ÜÑÙß Ð×ê ÔêÕèÕê Ôà×éÕàÙÕê ÕÔéàÕÙÕê ÑÙÕêè ÑÞ×ÜÕçê éÜ ÔäÙÖÙçÔ ÑÙÞÙàÕ, &quot;êÕèê ÔÞÙØèÙÝ&quot; (</span><span dir=LTR style='mso-bidi-font-family:David'>String Theory</span><span dir=RTL></span><span lang=HE style='font-family:David'><span dir=RTL></span>). ÑêÕèÔ ÖÕ ÞêÕÐèÙÝ ÞèÛÙÑÙÕ ÔÙáÕÓÙÙÝ ÔÐÕÜØÙÞØÙÕÕÙÙÝ éÜ Ô×ÕÞè ÑÞÕà×ÙÝ éÜ ÙéÕÙÕê ÞêÞØÙÕê ÑâÜÕê ÜÐ ä×Õê ÞÐéè âéèÔ ÞÙÞÓÙÝ. ÔÔÕæÐÔ ÜÐÕè &quot;äàÒÕÕÙß&quot; ÞÕÓÙâÔ ÑÒÐÕÕÔ âÜ ÔâØÙäÔ éÔáäè, &quot;ÔÒÝ éàÛêÑ ÜäàÙ ÜÞâÜÔ ÞÞÐÔ éàÔ, Þ×ÑÙÐ ÑêÕÚ äÐèÕÓÙÔ ÞÑèÙçÔ âÜ Ô×ÑèÔ ÔÕÙçØÕèÙÐàÙê áäçÕÜæÙÕê âÜ ÔÙçÕÝ ÔÞÔÓÔÓÕê ÑêÕèê ÔÙ×áÕê éÜ ÐÙàéØÙÙß ÕÐã ÑêÕèê ÔÞÙØèÙÝ éÜ ÔØÑâ, ÔÞçÕÑÜê ÑÙÞÙàÕ.&quot;<o:p></o:p></span></p> <p class=MsoNormal dir=RTL style='margin-bottom:6.0pt;text-align:right; direction:rtl;unicode-bidi:embed'><span lang=HE style='font-family:David'>àéÐÜê Ûâê ÔéÐÜÔ: ÜÐÙÜÕ ÖÕÕÙÕê èÐÙÙÔ ×ÓéÕê âÜ àÕéÐ ÔÞÙÞÓ ÔèÑÙâÙ àÙêß ÜÔçÓÙé ÞÑÕÐ éÜ âÕÓ ÞÔÓÕèÔ éÜ &quot;ÞÙéÕèÙÔ&quot;, ÓÕÒÞê ÐÜÔ éÔÖÛèàÕ ÜâÙÜ? êéÕÑÔ ÐäéèÙê Ð×ê, ÛÞÕÑß, ÔÙÐ ÖÕ ÔÞêÙÙ×áê ÜÖÕÕÙê Ô×ÓéÔ ÔÞçÕÑÜê ÑÙÞÙàÕ ÜÛÜ æÕèÚ éÙÙÓèé: ÔÐÙàØèàØ ÕÔéäâêÕ Þè×Ùçê ÔÜÛê âÜ ÛÜ ê×ÕÝ éàÙêß ÜÔâÜÕê âÜ ÔÓâê. ÕÐÛß, ÞÔ ÜâéÕê, çÙÙÞÙÝ Ñèéê ÐêèÙÝ èÑÙÝ ÜÞÓÙ, éÞÐäéèÙÝ ÜÐÖè× ÔçØß, ÒÝ ÐÝ âÓ ÛÔ ÜÐ âÞÓÕ ÜèéÕêÕ ÔÐÞæâÙÝ ÕÔÙÓâ ÔÓèÕéÙÝ ÜÛÚ, ÜæäÕê ÑÐÕêÝ ×êÛÙÝ ÕÔÓÞÙÕê ÒèäÙÕê éÜ ÔÞÙÞÓ ÔèÑÙâÙ, éÑàçÔÕã ÞÖÛÙè ÑÞÑÕÐ éÜÕ. ÛêÕÑÕê ÜÐêèÙÝ ÛÐÜÔ ÞæÕèäÕê ÑáÕã ÔÞÑÕÐ ÔÖÔ, ÕÔçÕèÐÙÝ ÔÞâÕàÙÙàÙÝ ÙèÕÕ ÜÜÐ áäç à×ê ÕÙÖÕÐÜÙê ÞÑÙçÕè ÑÔÝ. ×ÙäÕé ÞÔÙè ÑÐÙàØèàØ ÙÒÜÔ ÒÝ éÔçéè ÑÙß &quot;ÞÙéÕèÙÔ&quot; ÜÑÙß êÕèê ÔÙ×áÕê éÕÞè âÜ ÐÙêàÕêÕ ÕÐÕÜÙ Ðã ÔêÒÑè Ñ×ÜÕã ÔéàÙÝ. ÛÚ ÜÞéÜ, ÑÐêè ÔáäèÙÝ Reader's Choice, ÑÞ×ÜçÔ &quot;ÞÓã ÔáäèÙÝ âÜ Ù×áÕê&quot;, ÞÕäÙâ &quot;ÞÙéÕèÙÔ&quot; ÑÞçÕÝ ÔéÑÙâÙ, Ù×Ó âÝ áäèÙÝ éÜ ÐÙàéØÙÙß âæÞÕ, éÜ ÓÙèÐç, ÕéÜ äÙÖÙçÐÙÝ ÕÞ×ÑèÙÝ ÞÕÛèÙÝ Ð×èÙÝ. <o:p></o:p></span></p> <p dir=RTL style='margin-top:0in;margin-right:0in;margin-bottom:6.0pt; margin-left:0in;text-align:right;direction:rtl;unicode-bidi:embed'><span lang=HE style='font-family:David'><![if !supportEmptyParas]>&nbsp;<![endif]><o:p></o:p></span></p> <p class=MsoNormal dir=RTL style='margin-bottom:6.0pt;text-align:right; direction:rtl;unicode-bidi:embed'><span lang=HE style='font-family:David'>âæÝ çÙÕÞß éÜ ÞÔÓÕèÕê èÑÕê ÕÞÕæÜ×Õê ÜÐÕèÚ ÔéàÙÝ, ÕÔÓÒéÙÝ ÔéÕàÙÝ éÔÕéÞÕ ÑÞÑÕÐÕê éàÛêÑÕ ÜÔß, ÞÓÒÙÞÕê ÞéÔÕ ÐÕÓÕê ÔâàÙÙß ÔèÑ ÕÔÞê×Óé, éèâÙÕß ÔÞÙÞÓÙÝ ÔâÜÙÕàÙÙÝ ÞâÕèè ÐæÜ æÙÑÕè èÑ éÜ çÕèÐÙÝ. ×éÕÑ âÝ ÖÐê ÜÔâÞÙÓ Ðê ÔÓÑèÙÝ ÑäèÕäèÕæÙÔ ÔèÐÕÙÔ ÕÜæÙÙß éÑÔçéè ÔÞÓâÙ Ôæè, ÔèâÙÕß éÜ ÔÞÙÞÓ ÔèÑÙâÙ ÞâÕèè ÐÞàÝ ÔêâàÙÙàÕê ÛÜéÔÙ, ÐÚ ÔÕÐ è×Õç ÞÜÔÙÕê àÕéÐ ÞáâÙè ÑÞÙÕ×Ó</span><span dir=LTR></span><span lang=HE dir=LTR style='mso-bidi-font-family:David'><span dir=LTR></span> </span><span dir=RTL></span><span lang=HE style='font-family:David'><span dir=RTL></span><span style="mso-spacerun: yes"> </span>ÕÑâÜ ×éÙÑÕê âÜÙÕàÔ. ÑÞ×æÙê ÔÞÐÔ ÔêéâÔ-âéèÔ, Ôêäê×ÕÙÕê äàÙÞÙÕê Ñ×çè ÔÒÙÐÕÞØèÙÔ, ÕÑâÙçè âÜÙÙêÝ éÜ ÞÔ éÞÛÕàÔ ÒÙÐÕÞØèÙÕê ÜÐ-ÐÐÕçÜÙÓÐÕê, ÔÕÜÙÓÕ Ðê ÔÔêâàÙÙàÕê ÔéÙØêÙê ÔèÐéÕàÔ ÑèâÙÕß ÔÞÙÞÓ ÔèÑÙâÙ. ÑÓèÛÙÝ éÕàÕê ÕÑÔÓèÒÔ, ÔêÕÕÓâÕ çÔÜÙÝ ÔÕÜÛÙÝ ÕÒÓÜÙÝ ÑèâÙÕß ÔÖÔ ÕÑÔéÜÛÕêÙÕ, ÕáÑÙè ÜÔàÙ× éÐÑÕØ âæÞÕ éÐÑ Ðê ÙÓÙâÕêÙÕ âÜÙÕ ÞÔÞçÕèÕê ÔéÕàÙÝ éâÞÓÕ ÜèéÕê ÔæÙÑÕè ÔÞéÛÙÜ (ÐÚ éÐÙàÕ âÕáç ÙéÙèÕê ÑÞÓâ) ÑêçÕäêÕ. ÐÛß, ÑéàÕê ÔéÑâÙÝ éÜ ÔÞÐÔ Ôêéâ-âéèÔ èÐÕ ÐÕè éÕèÔ ÐèÕÛÔ éÜ ÞÐÞèÙ äÕäÕÜèÙÖæÙÔ âÜ ÔàÕéÐ, éàÛêÑÕ â&quot;Ù ÞêÞØÙçÐÙÝ ÐàÒÜÙÙÝ ÞÕÑÙÜÙÝ, ÓÕÒÞê Ò'ÙÙÞá Ò'ÕÖã áÙÜÑáØè (</span><span dir=LTR style='mso-bidi-font-family: David'>James J. Sylvester</span><span dir=RTL></span><span lang=HE style='font-family:David'><span dir=RTL></span>) Õ-ÕÕÙÜÙÐÙÝ çÙàÓÕß çÜÙäÕèÓ</span><span dir=LTR></span><span dir=LTR style='mso-bidi-font-family:David'><span dir=LTR></span> (William K. Clifford) </span><span dir=RTL></span><span lang=HE style='font-family:David'><span dir=RTL></span>. ÞêÞØÙçÐÙÝ ÐÜÔ ÑÙçéÕ ÜäèáÝ ÑäàÙ ÔçÔÜ Ôè×Ñ éÜ çÕèÐÙ ÔÐàÒÜÙê Ðê ÔÔÙéÒÙÝ Ô×éÕÑÙÝ éÜ âÞÙêÙÔÝ ÔÒèÞàÙÙÝ ÒÐÕá</span><span dir=LTR></span><span lang=HE dir=LTR style='mso-bidi-font-family:David'><span dir=LTR></span> </span><span dir=LTR style='mso-bidi-font-family:David'>(C.F. Gauss) </span><span dir=RTL></span><span lang=HE style='font-family:David'><span dir=RTL></span>, èÙÞß</span><span dir=LTR></span><span dir=LTR style='mso-bidi-font-family:David'><span dir=LTR></span> (G.B. Riemann) </span><span lang=HE style='font-family:David'>ÕÔÜÞÔÕÜå</span><span dir=LTR></span><span dir=LTR style='mso-bidi-font-family:David'><span dir=LTR></span> (H. von Helmholtz) </span><span dir=RTL></span><span lang=HE style='font-family:David'><span dir=RTL></span><span style="mso-spacerun: yes">    </span>Ñê×ÕÝ. <o:p></o:p></span></p> <p class=MsoNormal dir=RTL style='margin-bottom:6.0pt;text-align:right; direction:rtl;unicode-bidi:embed'><span lang=HE style='font-family:David'>áäèÕ éÜ ÐÑÕØ ÞèÞÖ èç âÜ Ð×ê ÔÓèÛÙÝ éÑÔ ÔçÔÜ ÔÞÜÕÞÓ Ôè×Ñ ÐÙÞå Ðê ÔèâÙÕß éÜ ÔÞÙÞÓ ÔèÑÙâÙ ÑáÕã ÔÞÐÔ Ôêéâ-âéèÔ. ÜÑÓ ÞÔâàÙÙß ÔÞÓâÙ ÑÕ, ÕÔéÙÞÕé éÜ ÔèâÙÕß ÜæÕèÚ ÐÜÒÕèÙÕê ×ÑèêÙÕê ÛÒÕß &quot;ÞÙéÕèÙÔ&quot; ÐÕ &quot;ÞÛÕàê ÔÖÞß&quot; éÜ ÕÕÜá, Ôêäê×Ô êâéÙÙÔ ÜÐ ÞÑÕØÜê éÜ ×ÙÑÕèÙÝ ÔÞçéèÙÝ Ðê ÔÞÙÞÓ ÔèÑÙâÙ âÝ èâÙÕàÕê ÞÙáØÙÙÝ ÕâÜ-ØÑâÙÙÝ ÞáÕÒÙÝ éÕàÙÝ. ÑÞáÒèê ÖÕ àÙêß ÜÔÖÛÙè Ðê ÛêÑÙÔÝ ÔÞèÕÑÙÝ ÕèÑÙ-ÔÔéäâÔ éÜ ÔÐàÒÜÙ æ'èÜá ÔÐÕÕèÓ ÔÙàØÕß<span style="mso-spacerun: yes">  </span>(</span><span dir=LTR style='mso-bidi-font-family:David'>C.H. Hinton</span><span dir=RTL></span><span lang=HE style='font-family:David'><span dir=RTL></span>), éÜ ÔèÕáÙ ÐÕéäàáçÙ (</span><span dir=LTR style='mso-bidi-font-family:David'>P.D. Ouspensky</span><span dir=RTL></span><span lang=HE style='font-family:David'><span dir=RTL></span>), ÕéÜ ÔÐÞèÙçÐÙ ÑèÐÒÓÕß (</span><span dir=LTR style='mso-bidi-font-family:David'>Claude Bragdon</span><span dir=RTL></span><span lang=HE style='font-family:David'><span dir=RTL></span>). ÛêÑÙÔÝ ÔàÜÔÑÙÝ âÜ ÔÞÙÞÓ ÔèÑÙâÙ è×ÕçÙÝ Þè×ç èÑ Þß ÔèâÙÕàÕê ÔÞÓâÙÙÝ ÔÞçÕèÙÙÝ éÞÔÝ ÔÕÐ æÞ×, ÐÑÜ ÔÝ ÔÝ éâÖèÕ ÜÔäÙå ÐÕêÕ ÑèÑÙÝ, ÕÔäÛÕ ÐÕêÕ ÜÞØÑâ ÞçÕÑÜ Ñ×ÕÒÙÝ ÐÙàØÜçØÕÐÜÙÙÝ ÕÐÞàÕêÙÙÝ èÑÙÝ. ÑÞÑØ ÔÙáØÕèÙ àÙêß ÜÔÑ×Ùß ÑÑÔÙèÕê ÐÙÚ ÔÝ éäÙâÕ ÔéäâÔ Þè×Ùçê ÜÛê éêèÞÔ ÜÔÕÕæèÕê ÖèÞÙÝ ÞèÛÖÙÙÝ ÑÐÞàÕê ÔÞÕÓèàÙê, ÛÒÕß ÔçÕÑÙÖÝ ÕÔäÕØÕèÙÖÝ. âÜ ÛÜ ÐÜÔ, ÜÞèÑÔ Ôæâè, çæèÔ ÛÐß ÔÙèÙâÔ ÞÜäèØ, ÕÔçÕèÐ ÔÞâÕàÙÙß ÞÕäàÔ ÑÖÔ ÜèéÙÞê ÔáäèÙÝ ÔÞæÕèäê.<o:p></o:p></span></p> <p class=MsoNormal dir=RTL style='margin-bottom:6.0pt;text-align:right; direction:rtl;unicode-bidi:embed'><span lang=HE style='font-family:David'><![if !supportEmptyParas]>&nbsp;<![endif]><o:p></o:p></span></p> <p class=MsoNormal dir=RTL style='margin-bottom:6.0pt;text-align:right; direction:rtl;unicode-bidi:embed'><span lang=HE style='font-family:David'>&quot;ÞÙéÕèÙÔ&quot; ÔÕÐ áäè çæèæè ÐÚ éÕäâ èâÙÕàÕê, ÔçéèÙÝ, ÔäàÙÕê ÕèÞÙÖÕê. èÑÕê àÛêÑ âÜ ÔÔçéèÙÝ ÔÜÜÕ ÕèÑÕê âÕÓ ÙÙÛêÑ ÜÜÐ áäç. ÐÚ ÛèÒÙÜ ÑÞçèÙÝ ÛÒÕß ÖÔ, ÔÞÑ×ß Ô×éÕÑ ÔÕÐ ÑØâÙÞÔ. ÔçÕèÐ ÞÕÖÞß âÛéÙÕ ÜÔÞéÙÚ ÔÜÐÔ ÜÑÓÕ, ÕÜÔ×ÜÙØ ÑâæÞÕ ÔÐÝ Ôáäè âÕÞÓ ÑÞ×Ñß ÔÖÔ.<o:p></o:p></span></p> <p class=MsoNormal dir=RTL style='margin-bottom:6.0pt;text-align:right; direction:rtl;unicode-bidi:embed'><span lang=HE style='font-family:David'><![if !supportEmptyParas]>&nbsp;<![endif]><o:p></o:p></span></p> <p class=MsoNormal dir=RTL style='margin-bottom:6.0pt;text-align:right; direction:rtl;unicode-bidi:embed'><b><span lang=HE style='font-family:David'>ÜçèÙÐÔ àÕáäê:<o:p></o:p></span></b></p> <p class=MsoNormal>Linda D. Henderson, <i>The Fourth Dimension and non-Euclidean Geometry in Modern Art</i>, Princeton University Press (1983).<span dir=RTL></span><span lang=HE dir=RTL><span dir=RTL></span><o:p></o:p></span></p> <p class=MsoNormal>Rudy Rucker, <i>The Fourth Dimension: A Guided Tour of the Higher Universes</i>, Houghton Mifflin (1985). <span style='mso-bidi-font-family: David'><o:p></o:p></span></p> <p class=MsoNormal dir=RTL style='text-align:right;direction:rtl;unicode-bidi: embed'><b><span lang=HE style='font-family:David'><![if !supportEmptyParas]>&nbsp;<![endif]><o:p></o:p></span></b></p> <p class=MsoNormal dir=RTL style='text-align:right;direction:rtl;unicode-bidi: embed'><b><span lang=HE style='font-family:David'>ÜçØ ÐêèÙ ÐÙàØèàØ èÜÕÕàØÙÙÝ: <o:p></o:p></span></b></p> <p class=MsoNormal><span dir=LTR></span><span style='mso-bidi-font-family:David'><a href="http://www2.trincoll.edu/~ssmith3/">http://www2.trincoll.edu/~ssmith3/</a></span> <p class=MsoNormal><span style='mso-bidi-font-family:David'><a href="http://www.fractalwisdom.com/FractalWisdom/fourth.html">http://www.fractalwisdom.com/FractalWisdom/fourth.html</a><o:p></o:p></span></p> <p class=MsoNormal><span style='mso-bidi-font-family:David'><a href="http://www.lboro.ac.uk/departments/ma/gallery/hyper">http://www.lboro.ac.uk/departments/ma/gallery/hyper</a></span><span dir=RTL></span><span dir=RTL style='font-family:David'><span dir=RTL></span> </span><span dir=LTR></span><span style='mso-bidi-font-family:David'><span dir=LTR></span><span style="mso-spacerun: yes"> </span><a href="http://www.cyburban.com/~mrf">http://www.cyburban.com/~mrf</a></span><span <p class=MsoNormal><span style='mso-bidi-font-family:David'><a href="http://www.evl.uic.edu/EVL/VROOM/HTML/PROJECTS/13Hanson.html">http://www.evl.uic.edu/EVL/VROOM/HTML/PROJECTS/13Hanson.html</a></span><span dir=RTL></span><span dir=RTL style='font-family:David'><span dir=RTL></span> </span><span dir=LTR></span><span style='mso-bidi-font-family:David'><span dir=LTR></span><span style="mso-spacerun: yes"> </span><a href="http://forum.swarthmore.edu/mam/00/612/dimension/four.html">http://forum.swarthmore.edu/mam/00/612/dimension/four.html</a></span><span dir=RTL></span><span dir=RTL style='font-family:David'><span dir=RTL></span> </span><span dir=LTR></span><span style='mso-bidi-font-family:David'><span dir=LTR></span><span style="mso-spacerun: yes"> </span><a href="http://www.geocities.com/CapeCanaveral/7997/">http://www.geocities.com/CapeCanaveral/7997/</a><o:p></o:p></span></p> <p class=MsoNormal><span style='mso-bidi-font-family:David'><a href="http://www.cwru.edu/artsci/engl/VSALM/mod/ricca/index.html">http://www.cwru.edu/artsci/engl/VSALM/mod/ricca/index.html</a><o:p></o:p></span></p> <p class=MsoNormal><span style='mso-bidi-font-family:David'><a href="http://www.comp-help.com/ciuca/ho00003.html">http://www.comp-help.com/ciuca/ho00003.html</a><o:p></o:p></span></p> </span> </BODY> </HTML>