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An Elementary Proof of Niven's Theorem via the Tangent Function
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Paolillo, Bonaventura; Vincenzi, Giovanni – International Journal of Mathematical Education in Science and Technology, 2021
In this paper, we propose an elementary proof of Niven's Theorem in which the tangent function will have a primary role.
Descriptors: Validity, Mathematical Logic, Mathematics Instruction, Scientific Concepts
An Application of Probability to Combinatorics: A Proof of Vandermonde Identity
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Paolillo, Bonaventura; Rizzo, Piermichele; Vincenzi, Giovanni – International Journal of Mathematical Education in Science and Technology, 2017
In this paper, we give possible suggestions for a classroom lesson about an application of probability using basic mathematical notions. We will approach to some combinatoric results without using "induction", "polynomial identities" nor "generating functions", and will give a proof of the "Vandermonde…
Descriptors: Probability, Mathematical Logic, Validity, Foreign Countries
Tribonacci-Like Sequences and Generalized Pascal's Pyramids
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Anatriello, Giuseppina; Vincenzi, Giovanni – International Journal of Mathematical Education in Science and Technology, 2014
A well-known result of Feinberg and Shannon states that the tribonacci sequence can be detected by the so-called "Pascal's pyramid." Here we will show that any tribonacci-like sequence can be obtained by the diagonals of the "Feinberg's triangle" associated to a suitable "generalized Pascal's pyramid."…
Descriptors: Mathematics Instruction, Equations (Mathematics), Mathematical Concepts, Generalization