A logarithmic mean and intersections of osculating hyperplanes
Abstract
We discuss a special case of a family of means defined using intersections of osculating hyperplanes to curves in Rn. Let C be the curve in Rn with vector equation xk(t)=t(ln t)k-1,k=1,...,n. Let Ok be the osculating hyperplane to C at ak,k=1,...,n. Then we show that O1,...,On have a unique point of intersection, P=(i1,...,in), and in particular, i1 equals the logarithmic mean in n variables of Neuman.
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