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題 名 | On a Curious Property of N-dimensional Sphere=N維球體的一個奇妙性質 |
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作 者 | 余長義; | 書刊名 | 銘傳學刊 |
卷 期 | 10:3 1999.07[民88.07] |
頁 次 | 頁295-298 |
分類號 | 316 |
關鍵詞 | 圓盤; 圓週長; 球體體積; 球面積; 面積分; 三角代換法; Disk; Circumference; Spherical volume; Spherical area; Surface integral; Trigonometric substitution; |
語 文 | 英文(English) |
中文摘要 | 在N維球體其其邊界之間有一個奇秒的性質。首先,觀察有趣的現象,圓盤的面積對於半徑的導數等於其圓週長,類似地,球的體積對於半徑的導數等於其表面積,最後,證明奇妙的性質,N維球體體積對於半徑的導數等於其N維球面積。 |
英文摘要 | There is a curious property between n-dimensional sphere and its boundary. It is interesting that the derivative of the disk area with respective to radius is equal to its circumference. Similarly, the derivative of the spherical volume with respective to radius is equal to its spherical area. At last, it is proved that the derivative of the n-dimensional spherical volume with respective radius is equal to its n-dimensional spherical area. |
本系統中英文摘要資訊取自各篇刊載內容。