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The cutting and skiving stock problem (CSSP) as encountered in the paper industry is examined. CSSP is considered one of the most interesting generalizations of the uni-dimensional cutting stock problem. The MAJIQTRIM commercial software package is used to solve the problem using heuristic and linear techniques. The software has proven to be superior to manually generated solutions in terms of quality and performance.

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.

The application of mathematical theorems to the paper folding techniques encountered in origami, the Japanese art of paper folding, reveals the shapes that can be constructed and those that cannot be constructed. Shapes such as cubes with double the volume of the given cube cannot be constructed. The mathematical characterization of origami is identical to the 17th problem developed by David Hilbert.

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.

An alternative approach to dealing with problems regarding disputed authorship is shown. The approach utilizes linear programming, a mathematical tool developed by mathematicians K.P. Bennett and O.L. Mangasarian. Applying the approach to the famous 'The Federalist' paper issue, where the authorship of several publications are being disputed, some of the steps involve the association of each paper with a point in 70-dimensional space, and the search for a hyperplane which separates the papers credited to Alexander Hamilton from those credited to James Madison.

Nikolai Nikolaevich Luzin's work on continuous functions in the early 20th century was influenced by French textbooks, especially the research of J. L. Lagrange and A. L. Cauchy. Attempts to restore infinitesimals derive directly from Luzin's thought.

Paper folding techniques used in combination with the computer simulation program The Geometer's Sketchpad as described in 'Exploring Conic Sections with The Geometer's Sketchpad' are an excellent way to teach students how to discover the underlying patterns in conics. By modeling the ellipse, hyperbola, and parabola, students can learn the underlying geometry needed to create models and can explore more possibilities. The Sketchpad models help students locate tangency points and connect the models to the concept of conics.

Ideas for using dot paper in the teaching of geometry are presented. Dot paper has wider uses than geoboards, although geoboards are useful for younger pupils. Dot paper allows students to learn about geometrical properties and relationships for themselves. Dot paper is particularly suited to learning about triangles, non-square parallelograms and squares, and to area calculations. Perimeters, medians and altitudes, congruent and similar figures are appropriate items for study.

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.

A break symmetry-based recursive investigation of Catalan number parenthesization reveals a direct link between CG-arrangements and bracketings by providing recursive mappings between the two at the break point. Each of the arrangements is then mapped to a bracketing, and a final manipulation process reassembles these bracketings. The break point of alpha in any CG-arrangement is the first point after the beginning of alpha, going from left to right, where every pair of parenthesis that has been opened is again closed. An inductive process gives one-to-one correspondences.

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 popular children's game of Scissors, Paper and Stone is extended to games with any number of opposing objects. Thus, the optimal strategy for each type of game is obtained. A game is first symbolized by a tournament, which is a directed graph with nodes representing objects and an arc between each pair of nodes pointing towards the winner. Thus, the games qualify as tournament games. These games are played many times, with their optimal strategies random in nature. However, this study is able to derive a unique strategy that uses an odd number of nodes.

Charles Jeffries' claim that Poynting's vector for energy transfer in static electromagnetic fields gives incorrect results is due to a misunderstanding of Poynting's identity. The new vector which he proposes as a replacement predicts values and diverges considerably from experimental results. Poynting's vector is directly derived from Maxwell's equations and remains valid even in static fields. Engineers and scientists can continue to use this method with confidence.

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 [...]

T. S. FERGUSON, L. S. SHAPLEY, and J. B. MACQUEEN (Eds.). Hayward, CA: Institute of Mathematical Statistics, 1996. ISBN 0-940600-42-0. xiv + 407 PP. $32 (P). This book is a [...]

A description is presented of an exercise which can be given to students of mathematics which involves an investigation of the limit of angle measures which can be formed through repeatedly folding a piece of paper.

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.

A paper folding technique to trisect an angle, that uses folding operations defined by five origami axioms, is presented. The technique utilizes the concept of similar triangles. The origami axioms fail to include all possible paper folding operations, thus requiring another axiom for folding two points onto nonparallel lines. Other origami constructions include other trisections, cube duplication and heptagon folding.

The use of paper is focussed in a classroom activity for graders 2 to 4 as students are asked to keep a record of their paper use for a week and the results are tabulated and entered in a graph. Students compare their results at the end of the week and answer questions about the amount paper used and the necessity for the use. The validity of the answers are checked by the students themselves. The activity aims at gathering and graphically presenting information as a data bank for future use., Background Using paper is a traditional part of classroom life. Efforts to conserve may start with a careful look at paper use. This activity requires students to keep track of [...]

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. [...]