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Connecting the Inner and Outer Product of Vectors Based on the History of Mathematics  

Oh, Taek-Keun (Gyeonggi Science High School for the Gifted)
Publication Information
Journal of Educational Research in Mathematics / v.25, no.2, 2015 , pp. 177-188 More about this Journal
Abstract
In this paper, I investigated the historical development process for the product of two vectors in the plane and space, and draw implications for educational guidance to internal and external product of vectors based on it. The results of the historical analysis show that efforts to define the product of the two line segments having different direction in the plane justified the rules of complex algebraic calculations with its length of the product of their lengths and its direction of the sum of their directions. Also, the efforts to define the product of the two line segments having different direction in three dimensional space led to the introduction of quaternion. In addition, It is founded that the inner product and outer product of vectors was derived from the real part and vector part of multiplication of two quaternions. Based on these results, I claimed that we should review the current deployment method of making inner product and outer product as multiplications that are not related to each other, and suggested one approach for connecting the inner and outer product.
Keywords
History; Product of Vectors; Inner product; Outer product; Quaternion;
Citations & Related Records
Times Cited By KSCI : 6  (Citation Analysis)
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