Showing papers in "The Mathematical Gazette in 1997"
125 citations
TL;DR: This paper addresses the question: ‘can you “win” the game Tetris?’
Abstract: Tetris is a computer game which has obsessed many computer users and attracted much attention, despite the simplicity of its rules. This paper addresses the question: ‘can you “win” the game Tetris?’ Designed by Soviet mathematician Alexey Pazhitnov in the late eighties and imported to the United States by Spectrum Holobyte, Tetris won a record number of software awards in 1989. Versions of Tetris are sold for most personal computers. There are Tetris arcade games, Tetris Nintendo cartridges, and hand-held Tetris games; Tetris has been played on machines ranging from mainframes to calculators. The game's success has prompted the invention of several similar games, including Hextris, Welltris, and Wordtris.
72 citations
52 citations
TL;DR: In this article, the authors propose a set of transformations of vectors, bases, and inner product spaces, which are then transformed into normal and duality, respectively, in order to solve the problem of Hints and solutions.
Abstract: 1. Scalars 2. Vectors 3. Bases 4.Transformations 5. Duality 6. Similarity 7. Canonical forms 8. Inner product spaces 9. Normality 10. Hints and solutions.
41 citations
28 citations
TL;DR: In this article, the authors propose a solution of the problem of algebraic Eigenvalue problem in the context of Numerical Processes and Non-Linear Equations Differences, Interpolation and Differentiation Solution of Algebraic Equations AlgebraIC Eigen value Problem Approximation Theory Quadrature Ordinary Differential Equations Integral Equations Partial DifferentialEquations Optimization Methods Appendices References Indexes
Abstract: Introduction to Numerical Processes and Non-Linear Equations Differences, Interpolation and Differentiation Solution of Algebraic Equations Algebraic Eigenvalue Problem Approximation Theory Quadrature Ordinary Differential Equations Integral Equations Partial Differential Equations Optimization Methods Appendices References Indexes.
27 citations
TL;DR: The history of the Fundamental Theorem of Arithmetic (FTA) and its application in Greek arithmetic can be traced back to c. 300BC as mentioned in this paper, when the natural numbers can be expressed as products of primes.
Abstract: There are hints of unique factorisation in Greek arithmetic. Indeed, some commentators have seen the Fundamental Theorem of Arithmetic (FTA), that the natural numbers can be expressed as products of primes in a unique way, lurking in Euclid’s Elements (c. 300BC). What can be said with certainty is that the history of the FTA is strangely obscure. It is not too much of an exaggeration to say that the result passed from being unknown to being obvious without a proof passing through the head of any mathematician.
23 citations
22 citations
17 citations
17 citations
TL;DR: The extremum problem has a long and interesting history since it was formulated by Fermat in the 17th century as mentioned in this paper, and Torricelli found the solution: P should be situated so that the angles between the half-lines PA, PB and PC are all 120° (except when one angle of the triangle ABC is greater than or equal to 120°).
Abstract: This extremum problem is really a classical beauty. It has had a long and interesting history since it was formulated by Fermat in the 17th century. Given three points A, B and C, the task is to find a point P such that the sum of distances PA + PB + PC is minimal; (see Figure 1). After a few years Torricelli found the solution: P should be situated so that the angles between the half-lines PA, PB and PC are all 120° (except when one angle of the triangle ABC is greater than or equal to 120°). The solution has then been rediscovered many times in new and interesting ways.
TL;DR: Cassini as mentioned in this paper will follow a convoluted path which will take it past Venus in April 1998 and again in June 1999 before it repasses close to Earth in August 1999, and after passing Jupiter at the end of the millennium (i.e. at the beginning of the year 2000) it should reach Saturn on 25 June 2004, where it will spend four years studying that planet and its satellites.
Abstract: On 6 October 1997 NASA plans to launch a space probe named Cassini which, if all goes to plan, will follow a convoluted path which will take it past Venus in April 1998 and again in June 1999 before it repasses close to Earth in August 1999. By then it will have gained enough speed to set out to more distant planets and after passing Jupiter at the end of the millennium (i.e. at the end of the year 2000) it should reach Saturn on 25 June 2004, where it will spend four years studying that planet and its satellites.
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TL;DR: The authors used a notebook that I kept in grade school when I ‘studied’ paper dolls, and the figures are based on dolls found pressed between the pages of the notebook.
Abstract: When a parent sees a little girl sitting on the floor cutting paper dolls, many thoughts may come to mind: ‘She’s keeping out of trouble’ or ‘She’s making a mess’ or even ‘There go my tax returns’. The thought that should have come to my parent’s mind, however, was ‘One day she’ll be a mathematician’. My grandmother, who worked as a dressmaker, often allowed my sister and me to use her razor sharp scissors on the strips of leftover tracing paper. This paper is inspired by a notebook that I kept in grade school when I ‘studied’ paper dolls, and the figures are based on dolls found pressed between the pages.