论文标题
割线平面的表面切线悖论和差异矢量商
The surface tangent paradox and the difference vector quotient of a secant plane
论文作者
论文摘要
如果单变量函数足够光滑，则其图的速度线的极限位置是切线线。类比，人们期望两种可变性平滑函数的割线平面的极限位置是其图形的平面。令人惊讶的是，即使函数是一个简单的多项式，这也不一定是正确的。尽管存在这种悖论，但我们表明，只要我们使用特定的向量产品：Clifford的几何形状，与单变量的情况仍然存在于多变量上下文中。
If a one-variable function is sufficiently smooth, then the limit position of secant lines its graph is a tangent line. By analogy, one would expect that the limit position of secant planes of a two-variable smooth function is a plane tangent to its graph. Amazingly, this is not necessarily true, even when the function is a simple polynomial. Despite this paradox, we show that some analogies with the one-variable case still hold in the multi-variable context, provided we use a particular vector product: the Clifford's geometric one.
