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Paper folding is one of the tasks that was chosen to teach children about multiplicative relationships. The act of operating on the paper itself will help students in articulating reasoning, testing and revising their conjectures and developing multiplicative reasoning.

Abstract. A model of a cone can be constructed from a piece of paper by removing a wedge and taping the edges together. The paper models discussed here expand on [...]

A brief overview of Tukey's paper, 'The Future of Data Analysis' after 40 years by various authors is discussed considering the debates regarding whether statistics is a science and ways to attract bright students by showing excitement and rewards of applied work. It is argued that beyond the ideas of data analysis, one should look at how data is analyzed by others and the key concept should be statistical thinking.

Byline: David E. Rowe (1) Author Affiliation: (1) Fachbereich 17--Mathematik, Johannes Gutenberg University, D55099, Mainz, Germany Article History: Registration Date: 07/11/2008

Byline: L.L. Stacho (1), Gy. Domotor (2), M.I. Ban (2) Keywords: Elber--Karplus procedures; reaction path-following; DDRP method Abstract: The flaws in the 'Reply' [1] to our paper [2] have been pointed out. Elber and Karplus (EK) have not disproved our irrefutable global statement that the energy average cannot be minimized which rebuts the theoretical background of EK-type calculations. Another statement of ours has shown that even a curve for which the average energy is locally minimal for all directional perturbations in the sense of classical variational calculus cannot be identical with the reaction path (RP) defined as a steepest descent path (SDP). EK found an error in the early preprint of our theoretical paper [3] and because of this error they qualified our correct variational statement as false for all the SDPs consisting of a straight line each. Mixing global and variational arguments, EK refuted our criticism in a logically incorrect manner. In this Comment we prove that both of our earlier statements invariably remain in force and the criticism included in those has been as well-established and solid as was before. Author Affiliation: (1) Bolyai Institute, JATE University of Szeged, H-6720, Szeged, Aradi Vertanuk tere 1, Hungary (2) Institute of Physical Chemistry, JATE University of Szeged, H-6720, Szeged, POB 105, Hungary Article History: Registration Date: 09/10/2004

Kolmogorov-Arnold-Moser (or KAM) theory was developed for conservative dynamical systems that are nearly integrable. Integrable systems in their phase space usually contain lots of invariant tori, and KAM theory establishes persistence results for such tori, which carry quasi-periodic motions. We sketch this theory, which begins with Kolmogorov's pioneering work.

It is shown that an approach earlier used by the author for classification of closed simply connected 6-manifolds (reduction to the problem of calculating certain bordism groups) can also be [...]

The construction in a way that enables the description of other related paper folding constructions as alternative geometrical front-ends to the sound mathemathetical base created by Peter Hilton and Jean Pederson is summarized. It is recommended to try the constructions presented with real paper.

The rock-paper-scissors problem is an entertaining methods to developm students' understanding of the principle of probability. How to use the rock-paper-scissors problem for math instruction is discussed.

Problems that offer multiple revelations during its investigations and that can be approached mathematically in more than one way often involve paper folding and conic sections. These problems can be easily demonstrated with a sheet of wax paper or emulated by the geometer's sketchpad.

The goal of the elementary mathematics program is to create an environment that supports the active exploration of mathematical ideas while demonstrating the connections between mathematics and everyday life. Many [...]

Congruences mod p for a prime p and partial products of the numbers 1, ..., p - 1 are obtained. Bibliography: 2 titles., UDC 511 1. FULL FACTORIALS In accordance with the Wilson theorem, for a positive rational prime number p, the factorial of p - 1 satisfies the congruence (p - 1)! [...]

A method to derive the appropriate aperiodic sequence of folding moves in construction of irrational acute angles in paper-folding is presented. The approach uses a connection between a simple dynamical system and the folding construction to generate the sequence of angles.

A theory of divisibility, including greatest common divisors (gcd), which presents a new gcd algorithm for Gaussian integers suited to paper-and pencil computation is presented. This establishes that any two Gaussian integers have a greatest common divisor, and it is interesting to see that this result has an odd-even proof.

A simulated total eclipse situation is created in the laboratory wherein the students have to mathematically evaluate the same. However, this evaluation shows that the primary mathematical models could be improved with the help of additional real world variables.

A study is conducted about the two distinct coordinate systems that are suited to graph the conic sections. These are an outcome of the focus-directrix definition and the focus-focus definition of conics. These two systems can help students to understand the relationship among the linear equations in two lines and the quadratic equations in two variables.

Students find it difficult to relate their mathematical knowledge with the real world experience. The print-shop paper cutting method, with the help of ratios, help students to interpret and create an accurate scale drawing.

New journals spring up with overwhelming and almost tiresome frequency these days. But Discrete Analysis is different. This journal is online-only--but it will contain no papers. Rather, it will provide [...]

Essays in Econometrics: Collected Papers of Clive W. J. Granger (Vols. 1 and 2).* Eric GHYSELS, Norman R. SWANSON, and Mark W. WATSON (Eds.). New York: Cambridge University Press, 2001. [...]

The Rock-Paper-Scissors play is designed for students to help them in investigating the game who with their reasoning judge on its fairness and examine the outcomes.

UDC 515.164 (Journal of Mathematical Sciences, Vol. 159, No. 6, pp. 753-760 (2009)) There is a misprint in the formulation of Lemma 3. Instead of the dimension constraints n-k = [...]

To authenticate to the full-text of this article, please visit this link: http://dx.doi.org/10.3982/ECTA786FORTH

To authenticate to the full-text of this article, please visit this link: http://dx.doi.org/10.3982/ECTA785FORTH

To authenticate to the full-text of this article, please visit this link: http://dx.doi.org/10.3982/ECTA784FORTH

To authenticate to the full-text of this article, please visit this link: http://dx.doi.org/10.3982/ECTA783FORTH