Results 221 to 230 of about 509,522 (270)
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1978
In the statistician’s world arithmetic is rarely simple and a desk or pocket calculator is often needed. But many problems are easier than one thinks and this chapter will show the way.
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In the statistician’s world arithmetic is rarely simple and a desk or pocket calculator is often needed. But many problems are easier than one thinks and this chapter will show the way.
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2003
The power means are defined using the convex, or concave, power, logarithmic and exponential functions. In this chapter means are defined using arbitrary convex and concave functions by a natural extension of the classical definitions and analogues of the basic results of the earlier chapters are investigated.
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The power means are defined using the convex, or concave, power, logarithmic and exponential functions. In this chapter means are defined using arbitrary convex and concave functions by a natural extension of the classical definitions and analogues of the basic results of the earlier chapters are investigated.
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Proof Without Words: Arithmetic Mean of Two Means
The College Mathematics Journal, 2016We provide a visual proof that the arithmetic mean of two positive numbers is greater or equal than the arithmetic mean of the geometric mean and the root mean square.
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The Arithmetic-Geometric Mean of Gauss
1997This paper is an expository account of the arithmetic-geometric mean M(a,b) of two numbers a,b. For \(a,b>0\) define \(a_ 0=a\), \(b_ 0=b\) and \(a_{n+1}=(a_ n+b_ n)/2,\quad b_{n+1}=(a_ nb_ n)^{1/2},\quad n=0,1,2,\ldots.\) It follows by elementary methods that the two sequences \(a_ n\), \(b_ n\) have a common limit M(a,b).
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International Journal of Mathematical Education in Science and Technology, 2011
The aim of this article is to establish some interesting inequalities involving arithmetic functions.
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The aim of this article is to establish some interesting inequalities involving arithmetic functions.
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Understanding Meanings in Arithmetic
The Arithmetic Teacher, 1958During the last twenty years a great deal has been written about “meaningful arithmetic.” Although there is some confusion over the terminology surrounding meaningful arithmetic as well as difference of opinion as to what constitutes a program of meaningful arithmetic, the term itself has been generally accepted by teachers and administrators. There is
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Generalized Weighted Arithmetic Means
2011Means which are the sum of single variable functions are considered. It is shown among other that if such a mean is weighted quasi-arithmetic, or subtranslative or subadditive then it must be a weighted quasi-arithmetic mean. Conditions under which the functions of the form f(x) = ax + b are affine or convex with respect to such a mean are presented ...
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