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Dana-Picard, Thierry; Zeitoun, David – International Journal of Mathematical Education in Science and Technology, 2017

We study a 1-parameter family of trigonometric definite integrals, showing how the joint usage of Information and Communication Technologies and paper-and-pencil work lead to different outputs, revealing different mathematical meanings and different concrete meanings. This family of integrals is useful for describing a phenomenon in soil…

Descriptors: Trigonometry, Information Technology, Computation, Soil Science

Dana-Picard, Thierry; Zeitoun, David G. – International Journal of Mathematical Education in Science and Technology, 2012

We present a sequence of improper integrals, for which a closed formula can be computed using Wallis formula and a non-straightforward recurrence formula. This yields a new integral presentation for Catalan numbers.

Descriptors: Mathematical Formulas, Numbers, Mathematics Instruction, Teaching Methods

Dana-Picard, Thierry; Zeitoun, David G. – International Journal of Mathematical Education in Science and Technology, 2012

We compute closed forms for some parametric integrals. The tools used are MacLaurin developments and other infinite series. Finally, Stirling numbers appear. (Contains 1 figure.)

Descriptors: Mathematics Instruction, Numbers, Equations (Mathematics), Computation

Dana-Picard, Thierry – International Journal of Mathematical Education in Science and Technology, 2011

Looking for closed forms for an integral depending on one parameter, we obtain integral identities and new integral presentations of Catalan numbers. Wallis formula appears as an important tool.

Descriptors: Computation, Mathematics Education, College Students, Mathematical Logic

Dana-Picard, Thierry – International Journal of Mathematical Education in Science and Technology, 2010

We compute in three different ways the same definite parametric integral. By-products are the derivation of a combinatorial identity and two integral presentations of Catalan numbers. One of them leads to a presentation using the [gamma] function.

Descriptors: Mathematics Instruction, Mathematical Formulas, Numbers, Computation

Dana-Picard, Thierry; Zeitoun, David G. – International Journal of Mathematical Education in Science and Technology, 2009

We compute closed forms for two multiparameter families of definite integrals, thus obtaining combinatorial formulas. As a consequence, a surprising formula is derived between a definite integral and an improper integral for the same parametric function.

Descriptors: Computation, Mathematical Formulas, Calculus, Mathematical Concepts

Dana-Picard, Thierry – International Journal of Mathematical Education in Science and Technology, 2009

This is the third part of a study of plane transformations described in a complex setting. After the study of homotheties, translations, rotations and reflections, we proceed now to the study of plane similarities, either direct or inverse. Their group theoretical properties are described, and their action on classical geometrical objects is…

Descriptors: Geometry, Mathematics Instruction, Geometric Concepts, Mathematical Logic

Dana-Picard, Thierry – International Journal of Mathematical Education in Science and Technology, 2007

This paper is the second part of a study of plane transformations using a complex setting. The first part was devoted to homotheties and translations, now attention is turned towards plane isometries. The group theoretic properties of plane isometries are easy to derive and images of classical geometrical objects by these transformations are…

Descriptors: Geometry, Mathematics Education, Mathematical Concepts, Geometric Concepts

Dana-Picard, Thierry – International Journal of Mathematical Education in Science and Technology, 2005

Catalan numbers are defined by combinatorial properties, in numerous situations. Here, an integral representation for these Catalan numbers is computed.

Descriptors: Numbers, Nonparametric Statistics

Steiner, Joseph M.; Dana-Picard, Thierry – International Journal of Mathematical Education in Science and Technology, 2004

Despite the ready availability of computer algebra packages, from a pedagogical point of view, the authors still feel that integration should be taught extensively the classical way, by means of carefully selected examples which combine as many fundamental techniques as possible for their evaluation. Furthermore, whenever possible, these examples…

Descriptors: Mathematics Instruction, Teaching Methods, Computer Assisted Instruction, Algebra

Dana-Picard, Thierry – International Journal of Mathematical Education in Science and Technology, 2004

Closed forms are computed for parametric integrals, generally using induction formulas. It is shown that these integrals can be core activities, mixing hand-work, computations with a computer algebra system and experimental mathematics with an interactive website.

Descriptors: Computation, Mathematical Formulas, College Mathematics, Statistics

Dana-Picard, Thierry; Naiman, Aaron – International Journal of Mathematical Education in Science and Technology, 2002

Geometric constructions have previously been shown that can be interpreted as rays of light trapped either in polygons or in conics, by successive reflections. The same question, trapping light in closed Fermat curves, is addressed here. Numerical methods are used to study the behaviour of the reflection points of a triangle when the degree of the…

Descriptors: Geometric Concepts, Light, Geometry, Equations (Mathematics)