斜邊

一個直角三角形和它的斜邊h直角邊c1c2

斜邊希臘語ὑποτείνουσα),亦稱作,是直角三角形中最長的一條邊,位於直角(90°角)對面。斜邊的長度通常使用勾股定理計算。

弦一詞來源

即“勾三股四弦五”,是勾股定理的一種特例,其中的指直角三角形的斜边[1]。勾股形一詞源於古代中國人測量天文時會豎起一根稱為「表」(圭表)的木竿,以光令「表」產生陰影,「表」與日影構成直角三角形兩條直角邊。此後,古代中國人便稱「表」為股,陰影稱為勾,兩者間的斜邊稱為弦,只要測量勾、股長度便能粗略估計太陽高度[2]

斜邊一詞來源

斜邊(hypotenuse)一詞出自古希臘語 ὑποτείνουσα(hypoteinousa),是底部和斜邊的意思[3]。另一個古希臘語的解釋是意思是由斜邊和其底部結合成。[4]

計算勾股定理

斜邊長度通常是用平方根計算出來。舉例說,如果x長3米,平方後就等於9平方米,y長4米的話,平方後則等於16平方米,兩數相加後等於25平方米,將25平方米開方便能得出斜邊長5米,數學標示為

有些科學計數機提供笛卡兒坐標系極坐標系的轉換功能:當給予xy的值後,這功能給出斜邊的長度和斜邊與底線(即c1)相交的角。

參見

註釋

  1. ^ 勾股定理. [2009-01-30]. (原始内容存档于2010-05-07). 
  2. ^ 勾股形. [2009-01-30]. (原始内容存档于2010-05-07). 
  3. ^ Schwartzman, Steven The Words of Mathematics, An Etymological Dictionary of Mathematical Terms used in English, Published by the Mathematical Association of America.
  4. ^ Anderson, Raymond. Romping Through Mathematics. Faber. 1947: 52. 

參考文獻

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