勾股定理：修订间差异 - 求闻百科，共笔求闻

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[[古埃及]]在[[公元前]]2600年的[[纸莎草]]記載有<math>(3,4,5)</math>这一组[[勾股数]]，而[[古巴比伦]]泥板紀錄的最大的一个勾股数组是<math>(12709,13500,18541)</math>。

有些參考資料提到法国和比利時將勾股定理称为[[驴桥定理]]，但驴桥定理是指[[等腰三角形]]的二底角相等，非勾股定理<ref>{{Cite web|author=蔡聰明|url=http://www.bamboosilk.org/Wssf/2002/wangjiaxiang01.htm|title=從畢氏學派到歐氏幾何的誕生|~~deadurl=yes~~|~~archiveurl=https://web.archive.org/web/20131110075429/http://www.bamboosilk.org/Wssf/2002/wangjiaxiang01.htm~~|~~archivedate=2013-11-10~~|accessdate=2013-08-21}}</ref>。

有些參考資料提到法国和比利時將勾股定理称为[[驴桥定理]]，但驴桥定理是指[[等腰三角形]]的二底角相等，非勾股定理<ref>{{Cite web|author=蔡聰明|url=http://www.bamboosilk.org/Wssf/2002/wangjiaxiang01.htm|title=從畢氏學派到歐氏幾何的誕生||||accessdate=2013-08-21}}</ref>。

勾股定理有四百多個證明，如微分證明，面積證明等。

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|publisher= 中国人民大学书报資料社

|page = 49

|

|url = http://books.google.com.tw/books?id=6bcrAAAAMAAJ&q=%E5%8B%BE%E8%82%A1%E5%AE%9A%E7%90%86%E6%98%AF%E9%A4%98%E5%BC%A6%E5%AE%9A%E7%90%86%E4%B8%AD%E7%9A%84%E4%B8%80%E5%80%8B%E7%89%B9%E4%BE%8B&dq=%E5%8B%BE%E8%82%A1%E5%AE%9A%E7%90%86%E6%98%AF%E9%A4%98%E5%BC%A6%E5%AE%9A%E7%90%86%E4%B8%AD%E7%9A%84%E4%B8%80%E5%80%8B%E7%89%B9%E4%BE%8B&hl=en&sa=X&ei=dAYUUvnELsKkkAXezYDACQ&redir_esc=y

}}</ref>。勾股定理現約有400種[[数学证明|证明]]方法，是[[數學定理]]中證明方法最多的定理之一<ref>{{cite book

|author= 李信明

第35行：

|ISBN = 9575671511

|page = 106

|

|url = http://books.google.com.tw/books?id=TZmAAAAAIAAJ&q=%E5%8B%BE%E8%82%A1%E5%AE%9A%E7%90%86%E6%98%AF%E6%95%B8%E5%AD%B8%E5%AE%9A%E7%90%86%E4%B8%AD%E8%AD%89%E6%98%8E%E6%96%B9%E6%B3%95%E6%9C%80%E5%A4%9A%E7%9A%84%E5%AE%9A%E7%90%86%E4%B9%8B%E4%B8%80&dq=%E5%8B%BE%E8%82%A1%E5%AE%9A%E7%90%86%E6%98%AF%E6%95%B8%E5%AD%B8%E5%AE%9A%E7%90%86%E4%B8%AD%E8%AD%89%E6%98%8E%E6%96%B9%E6%B3%95%E6%9C%80%E5%A4%9A%E7%9A%84%E5%AE%9A%E7%90%86%E4%B9%8B%E4%B8%80&hl=en&sa=X&ei=fwAUUtW2J8O2kgXZm4DYAQ&redir_esc=y

}}</ref>。

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勾股定理是由[[欧几里得几何]]的公理推导出来的，其在非欧几里得几何中是不成立的<ref name=false>{{cite book |title=''cited work'' |author=Stephen W. Hawking |page=4 |~~url = http://books.google.com/books?id=3zdFSOS3f4AC&pg=PA4~~ |ISBN = 0-7624-1922-9 |year=2005}}</ref>。因为勾股定理的成立涉及到了[[平行公设]]。<ref name=Parallel>{{cite book |title=CRC concise encyclopedia of mathematics |author= Eric W. Weisstein |~~url = http://books.google.com/books?id=aFDWuZZslUUC&pg=PA2147~~ |page=2147 |quote=The parallel postulate is equivalent to the ''Equidistance postulate'', ''Playfair axiom'', ''Proclus axiom'', the ''Triangle postulate'' and the ''Pythagorean theorem''. |edition=2nd |isbn=1-58488-347-2 |year=2003}}</ref><ref name= Pruss>{{cite book |title=The principle of sufficient reason: a reassessment |author= Alexander R. Pruss |quote=We could include...the parallel postulate and derive the Pythagorean theorem. Or we could instead make the Pythagorean theorem among the other axioms and derive the parallel postulate. |ISBN = 0-521-85959-X |year=2006 |publisher=Cambridge University Press |page=11 |~~url = http://books.google.com/books?id=8qAxk1rXIjQC&pg=PA11~~}}</ref>

勾股定理是由[[欧几里得几何]]的公理推导出来的，其在非欧几里得几何中是不成立的<ref name=false>{{cite book |title=''cited work'' |author=Stephen W. Hawking |page=4 ||ISBN = 0-7624-1922-9 |year=2005}}</ref>。因为勾股定理的成立涉及到了[[平行公设]]。<ref name=Parallel>{{cite book |title=CRC concise encyclopedia of mathematics |author= Eric W. Weisstein ||page=2147 |quote=The parallel postulate is equivalent to the ''Equidistance postulate'', ''Playfair axiom'', ''Proclus axiom'', the ''Triangle postulate'' and the ''Pythagorean theorem''. |edition=2nd |isbn=1-58488-347-2 |year=2003}}</ref><ref name= Pruss>{{cite book |title=The principle of sufficient reason: a reassessment |author= Alexander R. Pruss |quote=We could include...the parallel postulate and derive the Pythagorean theorem. Or we could instead make the Pythagorean theorem among the other axioms and derive the parallel postulate. |ISBN = 0-521-85959-X |year=2006 |publisher=Cambridge University Press |page=11 |}}</ref>

== 参考文献 ==

@@ 第13行： / 第13行： @@
 [[古埃及]]在[[公元前]]2600年的[[纸莎草]]記載有<math>(3,4,5)</math>这一组[[勾股数]]，而[[古巴比伦]]泥板紀錄的最大的一个勾股数组是<math>(12709,13500,18541)</math>。
-有些參考資料提到法国和比利時將勾股定理称为[[驴桥定理]]，但驴桥定理是指[[等腰三角形]]的二底角相等，非勾股定理<ref>{{Cite web|author=蔡聰明|url=http://www.bamboosilk.org/Wssf/2002/wangjiaxiang01.htm|title=從畢氏學派到歐氏幾何的誕生|deadurl=yes|archiveurl=https://web.archive.org/web/20131110075429/http://www.bamboosilk.org/Wssf/2002/wangjiaxiang01.htm|archivedate=2013-11-10|accessdate=2013-08-21}}</ref>。
+有些參考資料提到法国和比利時將勾股定理称为[[驴桥定理]]，但驴桥定理是指[[等腰三角形]]的二底角相等，非勾股定理<ref>{{Cite web|author=蔡聰明|url=http://www.bamboosilk.org/Wssf/2002/wangjiaxiang01.htm|title=從畢氏學派到歐氏幾何的誕生||||accessdate=2013-08-21}}</ref>。
 勾股定理有四百多個證明，如微分證明，面積證明等。
@@ 第26行： / 第26行： @@
  |publisher= 中国人民大学书报資料社
  |page = 49
+ |
- |url = http://books.google.com.tw/books?id=6bcrAAAAMAAJ&q=%E5%8B%BE%E8%82%A1%E5%AE%9A%E7%90%86%E6%98%AF%E9%A4%98%E5%BC%A6%E5%AE%9A%E7%90%86%E4%B8%AD%E7%9A%84%E4%B8%80%E5%80%8B%E7%89%B9%E4%BE%8B&dq=%E5%8B%BE%E8%82%A1%E5%AE%9A%E7%90%86%E6%98%AF%E9%A4%98%E5%BC%A6%E5%AE%9A%E7%90%86%E4%B8%AD%E7%9A%84%E4%B8%80%E5%80%8B%E7%89%B9%E4%BE%8B&hl=en&sa=X&ei=dAYUUvnELsKkkAXezYDACQ&redir_esc=y
  }}</ref>。勾股定理現約有400種[[数学证明|证明]]方法，是[[數學定理]]中證明方法最多的定理之一<ref>{{cite book
  |author= 李信明
@@ 第35行： / 第35行： @@
  |ISBN = 9575671511
  |page = 106
+ |
- |url = http://books.google.com.tw/books?id=TZmAAAAAIAAJ&q=%E5%8B%BE%E8%82%A1%E5%AE%9A%E7%90%86%E6%98%AF%E6%95%B8%E5%AD%B8%E5%AE%9A%E7%90%86%E4%B8%AD%E8%AD%89%E6%98%8E%E6%96%B9%E6%B3%95%E6%9C%80%E5%A4%9A%E7%9A%84%E5%AE%9A%E7%90%86%E4%B9%8B%E4%B8%80&dq=%E5%8B%BE%E8%82%A1%E5%AE%9A%E7%90%86%E6%98%AF%E6%95%B8%E5%AD%B8%E5%AE%9A%E7%90%86%E4%B8%AD%E8%AD%89%E6%98%8E%E6%96%B9%E6%B3%95%E6%9C%80%E5%A4%9A%E7%9A%84%E5%AE%9A%E7%90%86%E4%B9%8B%E4%B8%80&hl=en&sa=X&ei=fwAUUtW2J8O2kgXZm4DYAQ&redir_esc=y
  }}</ref>。
@@ 第208行： / 第208行： @@
 {{Main|非欧几里得几何}}
-勾股定理是由[[欧几里得几何]]的公理推导出来的，其在非欧几里得几何中是不成立的<ref name=false>{{cite book |title=''cited work'' |author=Stephen W. Hawking |page=4 |url = http://books.google.com/books?id=3zdFSOS3f4AC&pg=PA4 |ISBN = 0-7624-1922-9 |year=2005}}</ref>。因为勾股定理的成立涉及到了[[平行公设]]。<ref name=Parallel>{{cite book |title=CRC concise encyclopedia of mathematics |author= Eric W. Weisstein |url = http://books.google.com/books?id=aFDWuZZslUUC&pg=PA2147 |page=2147 |quote=The parallel postulate is equivalent to the ''Equidistance postulate'', ''Playfair axiom'', ''Proclus axiom'', the ''Triangle postulate'' and the ''Pythagorean theorem''. |edition=2nd |isbn=1-58488-347-2 |year=2003}}</ref><ref name= Pruss>{{cite book |title=The principle of sufficient reason: a reassessment |author= Alexander R. Pruss |quote=We could include...the parallel postulate and derive the Pythagorean theorem. Or we could instead make the Pythagorean theorem among the other axioms and derive the parallel postulate. |ISBN = 0-521-85959-X |year=2006 |publisher=Cambridge University Press |page=11 |url = http://books.google.com/books?id=8qAxk1rXIjQC&pg=PA11}}</ref>
+勾股定理是由[[欧几里得几何]]的公理推导出来的，其在非欧几里得几何中是不成立的<ref name=false>{{cite book |title=''cited work'' |author=Stephen W. Hawking |page=4 ||ISBN = 0-7624-1922-9 |year=2005}}</ref>。因为勾股定理的成立涉及到了[[平行公设]]。<ref name=Parallel>{{cite book |title=CRC concise encyclopedia of mathematics |author= Eric W. Weisstein ||page=2147 |quote=The parallel postulate is equivalent to the ''Equidistance postulate'', ''Playfair axiom'', ''Proclus axiom'', the ''Triangle postulate'' and the ''Pythagorean theorem''. |edition=2nd |isbn=1-58488-347-2 |year=2003}}</ref><ref name= Pruss>{{cite book |title=The principle of sufficient reason: a reassessment |author= Alexander R. Pruss |quote=We could include...the parallel postulate and derive the Pythagorean theorem. Or we could instead make the Pythagorean theorem among the other axioms and derive the parallel postulate. |ISBN = 0-521-85959-X |year=2006 |publisher=Cambridge University Press |page=11 |}}</ref>
 == 参考文献 ==