Geometric Construction of Some Lehmer Means

Ralph Høibakk, Dag Lukkassen, Annette Meidell and Lars-Erik Persson
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Ralph Høibakk: Department of Computer Science and Computational Engineering, Faculty of Engineering Science and Technology, UiT the Arctic University of Norway, Lodve Langesgate 2, N8505 Narvik, Norway
Dag Lukkassen: Department of Computer Science and Computational Engineering, Faculty of Engineering Science and Technology, UiT the Arctic University of Norway, Lodve Langesgate 2, N8505 Narvik, Norway
Annette Meidell: Department of Computer Science and Computational Engineering, Faculty of Engineering Science and Technology, UiT the Arctic University of Norway, Lodve Langesgate 2, N8505 Narvik, Norway
Lars-Erik Persson: Department of Computer Science and Computational Engineering, Faculty of Engineering Science and Technology, UiT the Arctic University of Norway, Lodve Langesgate 2, N8505 Narvik, Norway

Mathematics, 2018, vol. 6, issue 11, 1-18

Abstract: The main aim of this paper is to contribute to the recently initiated research concerning geometric constructions of means, where the variables are appearing as line segments. The present study shows that all Lehmer means of two variables for integer power k and for k = m 2 , where m is an integer, can be geometrically constructed, that Lehmer means for power k = 0 , 1 and 2 can be geometrically constructed for any number of variables and that Lehmer means for power k = 1 / 2 and − 1 can be geometrically constructed, where the number of variables is n = 2 m and m is a positive integer.

Keywords: means; Lehmer means; geometric construction; crossed ladders diagram (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2018
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