On Minimum Distance Problem
Keywords:
minimum distance formula, geometrical construction, extreme-value theorem, optimizationAbstract
This study provides a clear-cut solution to a minimum distance problem, in particular, the problem of finding the minimum distance from a point to a line to another point on the same side of the line. The straightforward solution is a Pythagorean relation or formula which can be derived through geometrical construction and reasoning, and analytical approach using differentiation, particularly, the application of extreme-value theorem. Such formula is vital in solving minimum distance problems with greater ease, accuracy and speed. This will lessen the cost and waste of materials in practical engineering and business applications.
References
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[2] J.L. Berggren. “Mathematics” in Funk & Wagnalls New Encyclopedia, Vol. 17, p. 97, 1990.
[3] R.T. Seeley. Calculus of One Variable. Illinois: Scott, Foresman and Company, 1968.
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[2] J.L. Berggren. “Mathematics” in Funk & Wagnalls New Encyclopedia, Vol. 17, p. 97, 1990.
[3] R.T. Seeley. Calculus of One Variable. Illinois: Scott, Foresman and Company, 1968.
[4] K. Kalmanson and P.C. Kenschaft. Calculus: A Practical Approach. New York: Worth Publishers, Inc., 1975.
[5] T.P. Dick and C.M. Patron Calculus. Boston: PWS-KENT Publishing Company, 1992.
[6] N.M. Mame. Development of Corollaries to Basic Theorems on Derivatives of Algebraic Functions. Masters Thesis, Batangas State University, 2004.
[7] E.E. Moise and F.L. Dawas Jr. Geometry. Massachussetts: Addison-Wesley Publishing Company, Inc., 1975.
[8] A. Schwartz. Analytic Geometry and Calculus. New York: Holt, Rinehart and Winston, 1960.
[9] L. Leithold. The Calculus 7. Massachussetts: Addison-Wesley Publishing Company, Inc., 1996.
[10] H. Anton. Calculus with Analytic Geometry. New York: John Wiley & Sons, Inc., 1995.
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Published
2015-02-17
How to Cite
Castillo, R. C., Mendoza, E. E., & Comia, J. B. (2015). On Minimum Distance Problem. American Scientific Research Journal for Engineering, Technology, and Sciences, 11(1), 84–95. Retrieved from https://asrjetsjournal.org/index.php/American_Scientific_Journal/article/view/591
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