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[½»Á÷] ¡¾·ÖÏí¡¿Flatland: Romance of Many Dimensions

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ÉϵÛ(Äã)»îÔÚ3ά¶È¿Õ¼äÀï, µ±È»Äã¿ÉÒÔ¿´, ´¥Ãþ, ¸Ð¾õÁ¢Ìå (3D), µ«ÄãÏëÂïÄãÊÇÉϵÛŶ, ´´ÔìÁ˸öÊÀ½ç, ×ܲ»ÄÜÈÃÄÇЩÉúÎïºÍÄãÒ»Ñù´ÏÃ÷°É!
ËùÒÔÄã¾ö¶¨ÏÞÖÆÄǹú¶ÈµÄά¶ÈÓÚ2ά¶È(2D). ËùÒÔÎÒÃǽÐËüFlatland. »îÔÚÕâ¶ùµÄÈËÂï, µ±È»È«ÊÇÆ½ÃæµÄ¿©! ¾ÍÊÇÄã¿´ÉÏÈ¥ËûÃÇÈ«ÊDZâ±âµÄÀ²! »îÔÚÄǶùµÄÉúÎﵱȻ,ËûÃǸù±¾Ã»ÓÐÁ¢ÌåµÄ¸ÅÄî (ÊÇÄã²»ÏëÈÃËûÃÇÓеÄÂï)!
ÔÚFlatlandÀï, Ö»ÓÐ, ¶«Î÷Äϱ±×óÓÒǰºó, ȴûÓÐÉÏÏÂŶ! ÄÇЩÉúÎï¾Í½ÐËûÃÇFlatlanderºÃÁË! סÔÚÄĶùµÄFlatlander, ¶¼ÊÇÐ©Æ½Ãæpolygon, Èç3½ÇÐÎÀ², 4·½ÐÎÀ²µÄ. µ±È»ÄãÊÇÉÏ´´ÔìÁËÕû¸öFlatland, ÓÖ¿ÉÒԸоõµÚÈýά¶È, Òª±æ±ðÄÇЩÉá÷á3½ÇÐÎÀ², 4·½ÐÎÀ², ´óÈý½ÇÐÐÀ², СÈý½ÇÐÎÀ² ... ²¢²»ÄÑ. µ«ÊÔÏëÏëÄÇЩFlatlander×Ô¼º¿´×Ô¼ºÈ˵½µØÊÇÔõ¸öÑù°¡? Ò»ÌõÖ±ÏßÀ², ¾ÍºÃÏñÄãÄÃÒ»ÕÅA4Ö½·Åµ½×ÀÃæÉÏ, ´ÓÉÏÃæ¿´ÊÇÔ²ÐÎ, ÈçÂýÂý°ÑÊÓÏßÒÆµ½×À½Ç, ÄÇÖ½ÊDz»ÊDZäÁ˸öÖ±Ïß? ¾ÍÊÇÕâÖÖ¸ÅÄîÀ²!

סÔÚÄǶùµÄÈËÈ«¶¼ÊÇpolygon¶øÇÒ»¹ÊÇÈ«µÈ±ßµÄŶ(regular polygon). Flatlander ÓкÜÇ¿µÄ½×¼¶¸ÅÄî! ×îµÍ¼¶µÄ¾ÍÊÇÈý½ÇÐÎÁË, ¶¼ÊÇÊôÓÚÄÇЩ, Ê¿±øÀ², À͹¤À²Ö®ÀàµÄ. ÓÃÀ´´òÕÌ»ò¿ª·¢ÍÁµØÉá÷áµÄ, ÐèÒªÀÍÁ¦µÄ¾Í¶ÔÁËÀ²! ½ÓÏÂÀ´µ±È»ÓÐÕý·½ÐÎÀ², Õý5½ÇÐÎ, Õý6½ÇÐεȵȵÄ, ÊôÓÚÖеȽ׼¶µÄ.  
ÔÚFlatlandÀï, ÖÇ»ÛÂï¾ÍÒÔpolygonµÄÄڽǴóС¶ø¶¨, µ±È»×îûÖǻ۵ľÍÊÇÈý½ÇÐο©! 5½ÇÐÎÂï¾Í±ÈÕý·½ÐÎÓÐÖÇ»ÛÁË. 7½Ç8½ÇÐÎÒ²ÓÐ, ÊÇÊôÓڸ߼¶Flatlander, ÊÜÆäËûFlatlander³ç°ÝºÍ¾´ÑöµÄһȺ, ´ó¶àÊÇÂÉʦÀ², ´óѧ½ÌÊÚÀ²µÄ. ºÇºÇ ...³¬¹ý10½ÇµÄ¾Ã¾Ã²Å³öÏÖÒ»Á½¸ö. ÊÇÊôÓÚÖǻ۳¬·²Õß,×Ú½ÌÁìÐä»ò´´°ìÕß. µ«ÓÐÖǻ۲»ÒÔ¶¨ÓгɾÍŶ! ÓÐЩÈËÂï³Ö×Å×Ô¼ºÓÐÒ»µãС´ÏÃ÷, ½á¹û»¹²»ÊÇÒ»ÍÅÔã. ÔÚÈËÀàÊÀ½çÈç´Ë, ÔÚFlatlandµ±È»Ò²Èç´ËÀ²!

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[ Last edited by RyanPCH on 2009-11-14 at 15:28 ]
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ÔÚFlatlandÀïÂïÓÐÒ»¸ö¼¸ºÎѧÕß, Dr. Square, ÊÇÕý·½ÐÎ(ÖÇ»ÛÓÐ90¶È). ¶àÄêÀ´Ä¬Ä¬¸ûÔÅ, ËäÈ»ÖÇ»ÛÆÕÆÕͨͨ, µ«¶àÄêÀ´Ò²¸øËû»ìÁ˸öPhD. ËûÒ»Ö±ºÜÈÈÖÔÓÚ¼¸ºÎѧÑо¿Å¶! Äê½×40ÓÐÓà, ÓÐλÆÞ×Ó. Å®ÈËÂïÔÚÕâÊÀ½çÀïÊÇÊôÓÚÒ»ÌõÖ±ÏßŶ, ûÉá÷áµØÎ», ¶øÇÒÊÇ×îûÄÔµÄŶ - Ö±ÏßÄÄÓÐÄڽǰ¡? (±ðÂîÎÒ, È¥Âî Edwin Abbott).
Dr. SquareºÜϲ»¶ÂÃÐÐŶ! µ«ÊÇÔÚFlatlanderÓм¸¸öµØ·½ÊÇûÈ˸ÒÈ¥µÄŶ! ÒòΪÒÔǰÓкܶàÂÃÕßÈ¥Á˾Íûһ¸ö»ØÀ´ÁË. ¾ÍÊÇÄϼ«,±±¼«, ¶«¼«, Î÷¼«. ËùÒԺܶàÈ˶¼²»¸ÒÅÜÀëFlatlandÖÐÐÄ̫Զ! ËûÃÇÈÏΪÄÇ4¸ö½ÇÂä, Òª²»Ã»Óо¡Í·, Òª²»Âï¾ÍÊÇÓпÖÁú¹ÖÊÞÉá÷áµÄ, °ÑÄÇЩÂÃÕß¶¼¸ø³ÔÁË!

Dr. Square ÓÐλ¸ç¸ç(Ò²ÊÇÕý·½ÐÎ), ÉúÁ˸ö¾ø¶¥´ÏÃ÷µÄСֶ¶ù! (ÖÇ»ÛÓÐ120¶ÈÒ², ÖªµÀËûÊÇÉáÐÎ×´Á˰É). ´ó¼Ò¶ÔËûµÄÆÚÍûÒ²ÕæµÄºÜ¸ß, Dr. Squareÿ´Îµ½Ëû¸ç¸ç¼ÒÓÃÍêÍí²Í, ¶¼»á»¨µãʱ¼ä½Ìµ¼ÏÂÖ¶¶ùÊýÀí, ²Å²»¹ý¶Ì¶ÌÁùÆßÄê, Сֶ¶ùµÄÄÔ´üÀïÒÔ×°ÂúÁË, +,-,¡Á,¡Â, »ù±¾´úÊý·¨Ò²¸ù±¾ÄѲ»µ¹ËûÁË!
½ñÌìÊÇСֶ¶ùÉúÈÕŶ, Dr. Square ÓÖºÍËûµÄ̫̫һͬµ½Ëû¸ç¸ç¼ÒÀïÈ¥×ö¿ÍÁË! ½ñÌìÓе㲻ͬ, ´ó¼Ò¿ª¿ªÐÄÐĵijÔÍêÍí²Í, Dr. SquareÐÄÀíÔÚÏë:"°¡! ʱ¼ä¹ýµÄÒ²Õæ¿ì°¡, Сֶ¶ùһתÑÛ¾Í8ËêÁË! ´Ë×ÓÄ꼶ССÒѶ®ÊýÀí, ÒÔºóǰ;ÎÞ¿ÉÏÞÁ¿ÄØ , µÃºÃºÃÔÔÅàËû²ÅÐÐ! ÏëÏëÊÇʱºò½ÌËû»ù±¾¼¸ºÎÁË"

To be continue...
3Â¥2009-11-14 15:35:24
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