Electronic Proceedings of the Seventh Annual International Conference on Technology in Collegiate Mathematics

Orlando, Florida, November 17-20, 1994

Paper C033

Dimension of Maximum Volume

Robert Kreczner

University of Wisconsin-Stevens Point
Stevens Point, WI 54481
Phone: (715) 346-3754

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Technology has already established itself well in College-Mathematics. No one today tries to deny its benefits and positive impacts on learning and teaching Mathematics. However, there are growing needs for the problems and examples that are suitable for present powerful mathematical software. The problems where good Mathematics and powerful application of technology intertwine with each other in complementary manner, without excluding or belittling each other, are in great demand. In this article we will present an example of such a problem. It is about how to find a formula for the dimension in which a unit ball determined by l_p-norm obtains its maximum volume. The use of technology, specifically Mathematica program, is not only indispensable to find this solution but also leads us to new unexpected mathematical discoveries. The ideas and problems investigated in this article might be used by the students in Advanced Calculus course.

Keyword(s): calculus, Mathematica