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Sinitsky, Ilya; Stupel, Moshe; Sinitsky, Marina – International Journal of Mathematical Education in Science and Technology, 2018
The paper explores the division of a polygon into equal-area pieces using line segments originating at a common point. The mathematical background of the proposed method is very simple and belongs to secondary school geometry. Simple examples dividing a square into two, four or eight congruent pieces provide a starting point to discovering how to…
Descriptors: Geometric Concepts, Plane Geometry, Arithmetic, Mathematics Instruction
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Griffiths, Martin; MacHale, Des – International Journal of Mathematical Education in Science and Technology, 2017
We study here an aspect of an infinite set "P" of multivariate polynomials, the elements of which are associated with the arithmetic-geometric-mean inequality. In particular, we show in this article that there exist infinite subsets of probability "P" for which every element may be expressed as a finite sum of squares of real…
Descriptors: Arithmetic, Geometry, Geometric Concepts, Algebra
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de Alwis, Amal – International Journal of Mathematical Education in Science and Technology, 2012
The article begins with a well-known property regarding tangent lines to a cubic polynomial that has distinct, real zeros. We were then able to generalize this property to any polynomial with distinct, real zeros. We also considered a certain family of cubics with two fixed zeros and one variable zero, and explored the loci of centroids of…
Descriptors: Arithmetic, Algebra, Mathematical Formulas, Geometric Concepts
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Mortici, Cristinel – International Journal of Mathematical Education in Science and Technology, 2011
The aim of this article is to establish some interesting inequalities involving arithmetic functions.
Descriptors: Arithmetic, English (Second Language), Mathematics, Mathematics Education
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Persky, Ronald L. – International Journal of Mathematical Education in Science and Technology, 2003
In 1968, Leon Gerber compared (1 + x)[superscript a] to its kth partial sum as a binomial series. His result is stated and, as an application of this result, a proof of the arithmetic mean-geometric mean inequality is presented.
Descriptors: Arithmetic, Mathematical Logic, Geometric Concepts, Validity
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Qi, Feng – International Journal of Mathematical Education in Science and Technology, 2003
For any nonnegative integer "k" and natural numbers "n" and "m," the equations presented in this paper demonstrate the inequalities obtained on the ratio for the geometric means of a positive arithmetic sequence with unit difference, where alpha epsilon [vertical bar]0,1[vertical bar] is a constant. Using the ideas and methods of Chen (2002),…
Descriptors: Geometric Concepts, Arithmetic, Validity, Mathematical Logic
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Blest, David C.; Jamil, Tariq – International Journal of Mathematical Education in Science and Technology, 2003
Computer operations involving complex numbers, essential in such applications as Fourier transforms or image processing, are normally performed in a "divide-and-conquer" approach dealing separately with real and imaginary parts. A number of proposals have treated complex numbers as a single unit but all have foundered on the problem of the…
Descriptors: Arithmetic, Numbers, Computation, Computer Uses in Education