数学杂志
數學雜誌
수학잡지
JOURNAL OF MATHEMATICS
2005年
4期
355-357
,共3页
陈方维%赵雪华%周家足
陳方維%趙雪華%週傢足
진방유%조설화%주가족
曲率%法曲率%测地曲率
麯率%法麯率%測地麯率
곡솔%법곡솔%측지곡솔
Curvature%normal curvature%geodesic curvature
经典的欧拉公式描述了两曲面交线的曲率和曲面的法曲率以及曲面夹角之间的关系.本文给出了R3中曲面的法曲率的欧拉公式的简单证明.并得到一个关于曲面交线曲率及曲面测地曲率的类似的欧拉公式.
經典的歐拉公式描述瞭兩麯麵交線的麯率和麯麵的法麯率以及麯麵夾角之間的關繫.本文給齣瞭R3中麯麵的法麯率的歐拉公式的簡單證明.併得到一箇關于麯麵交線麯率及麯麵測地麯率的類似的歐拉公式.
경전적구랍공식묘술료량곡면교선적곡솔화곡면적법곡솔이급곡면협각지간적관계.본문급출료R3중곡면적법곡솔적구랍공식적간단증명.병득도일개관우곡면교선곡솔급곡면측지곡솔적유사적구랍공식.
The classic Euler formula describes the relationships between the curvature of the intersection curve of two surfaces and the normal curvatures of surfaces and the angle between surfaces. In this paper, we give simplified proofs of the Euler formula for normal curvatures of surfaces of R3. We derive an analogue of Euler formula for geodesic curvatures of surfaces.
