A mechanically-based proof of the arithmetic mean harmonic mean inequality

被引：0
|
作者：
Padron, Miguel A. [1 ]
Plaza, Angel [2 ]
机构：
[1] Univ Las Palmas Gran Canaria, IUMA, Las Palmas Gran Canaria, Spain
[2] Univ Las Palmas Gran Canaria, Dept Math, Canarias 20,1, Las Palmas Gran Canaria 35002, Las Palmas, Spain
来源：
INTERNATIONAL JOURNAL OF MATHEMATICAL EDUCATION IN SCIENCE AND TECHNOLOGY | 2021年 / 52卷 / 08期
关键词：
Arithmetic mean; harmonic mean; inequality;
D O I：
10.1080/0020739X.2020.1827175
中图分类号：
G40 [教育学];
学科分类号：
040101 ; 120403 ;
摘要：
Many proofs of the arithmetic mean harmonic mean inequality have been proposed based on the rich connections between mathematics and physics. Sometimes the Arithmetic Mean Harmonic Mean inequality is proved by using electric networks. In this note, we use a simple set of two springs, instead of four springs which would be the equivalent set to those using electric networks.
引用
收藏
页码：1250 / 1252
页数：3
相关论文
共 50 条
  • [31] ON THE ARITHMETIC-GEOMETRIC MEAN INEQUALITY
    Hassani, Mehdi
    TAMKANG JOURNAL OF MATHEMATICS, 2013, 44 (04): : 453 - 456
  • [32] GENERALIZATION OF INEQUALITY OF ARITHMETIC AND GEOMETRIC MEAN
    HERING, F
    MONATSHEFTE FUR MATHEMATIK, 1973, 77 (01): : 31 - 42
  • [33] ON THE ARITHMETIC-GEOMETRIC MEAN INEQUALITY
    LUCHT, LG
    AMERICAN MATHEMATICAL MONTHLY, 1995, 102 (08): : 739 - 740
  • [34] On the arithmetic-geometric mean inequality
    Kwon, EG
    Shon, KH
    FINITE OR INFINITE DIMENSIONAL COMPLEX ANALYSIS, 2000, 214 : 233 - 235
  • [35] THE GEOMETRIC, LOGARITHMIC, AND ARITHMETIC MEAN INEQUALITY
    BURK, F
    AMERICAN MATHEMATICAL MONTHLY, 1987, 94 (06): : 527 - 528
  • [36] ARITHMETIC-GEOMETRIC MEAN INEQUALITY
    SCHMEICH.EF
    AMERICAN MATHEMATICAL MONTHLY, 1970, 77 (07): : 782 - &
  • [37] ON THE ARITHMETIC-GEOMETRIC MEAN INEQUALITY
    Sababheh, Mohammad
    Furuichi, Shigeru
    Heydarbeygi, Zahra
    Moradi, Hamid Reza
    JOURNAL OF MATHEMATICAL INEQUALITIES, 2021, 15 (03): : 1255 - 1266
  • [38] AN ARITHMETIC-GEOMETRIC-HARMONIC MEAN INEQUALITY INVOLVING HADAMARD-PRODUCTS
    MATHIAS, R
    LINEAR ALGEBRA AND ITS APPLICATIONS, 1993, 184 : 71 - 78
  • [39] Tightening and reversing the arithmetic-harmonic mean inequality for symmetrizations of convex sets
    Brandenberg, Rene
    von Dichter, Katherina
    Merino, Bernardo Gonzalez
    COMMUNICATIONS IN CONTEMPORARY MATHEMATICS, 2023, 25 (09)
  • [40] COMPARISON OF HARMONIC MEAN VERSUS ARITHMETIC MEAN CLEARANCE VALUES
    SCHAAF, LJ
    LAM, FC
    PERRIER, DG
    JOURNAL OF PHARMACEUTICAL SCIENCES, 1986, 75 (04) : 427 - 429
12345