Showing papers in "The Mathematical Gazette in 1993"
TL;DR: The cubic holds a double fascination, since not only is it interesting in its own right, but its solution is also the key to solving quartics as mentioned in this paper, which is also known as Cardan's solution.
Abstract: The cubic holds a double fascination, since not only is it interesting in its own right, but its solution is also the key to solving quartics. This article describes five fundamental parameters of the cubic (δ, λ, h, xN , and yN ), and shows how they lead to a significant modification of the standard method of solving a cubic, generally known as Cardan’s solution.
343 citations
309 citations
TL;DR: This article is in fact prepared as a Mathematica “notebook”, and an extensive library of supporting software “packages” has been developed, and several books about using it are now available.
Abstract: Mathematica is a computer software system for symbolic manipulation and numerical computation; it has excellent graphics, a high-level, mathematically-oriented programming language and, very importantly, it takes seriously the need for work to be interactive, properly presented and communicated. This article is in fact prepared as a Mathematica “notebook”. An extensive library of supporting software “packages” has been developed, and several books about using it are now available.
152 citations
TL;DR: The game of self-knowledge in the game of snakes and ladders was introduced by Harish Johari in Leela as discussed by the authors, a serious commentary and religious interpretation of the board game Leela.
Abstract: “There is really only one Game, the Game in which each of us is a player acting out his role. The Game is Leela, the universal play of cosmic energy.” Thus begins Harish Johari in Leela: the game of selfknowledge, a serious commentary and religious interpretation of the Hindu board game Leela. Leela is essentially the game Snakes and Ladders, which in the U.S. is the popular children’s game of snakes and ladders, England’s famous indoor sport,” for 50o in 1943 by the Milton Bradley Company of Springfield, Massachusetts. This game is really a 101 state absorbing Markov chain, which is amenable to mathematical as well as moral analysis. In what follows we investigate only the mathematical side of this diversion, specifically the expected playing time.
33 citations
31 citations
29 citations
TL;DR: This book discusses children as mathematicians, whole school approaches practicalities and ways forward, and what makes successful problem solving the use of standard notation.
Abstract: Introduction - children as mathematicians a new approach to maths what makes successful problem solving the use of standard notation childrens' graphical representations childrens' own mathematical representations what does it mean to work investigatively? the power of childrens' own intuitive methods teachers' stories - nursery children explore maths young children plan a picnic reception write about their maths a simple starting point explode a number children working with numbers a maths advisory support teacher how many tablets can we buy? children build a natural area and pond Jenny, a primary school teacher do they really know how to do it? schemes Tariq gets lost I'll do it my way real "real" problem solving thinking algebraically does "maths with reason" work? whole school approaches practicalities and ways forward starting off.
18 citations
17 citations
15 citations
TL;DR: The bicentenary of George Green's birth will be marked by the dedication of a plaque in Westminster Abbey as discussed by the authors, which will be in proximity to those commemorating Newton, Kelvin, Faraday and Clerk Maxwell.
Abstract: These past two years have seen the bicentenaries of Michael Faraday, Charles Babbage and John Frederick Herschel. A fourth contemporary, who deserves to rank with these, is George Green, the bicentenary of whose birth will be marked by the dedication of a plaque in Westminster Abbey. His memorial will be in proximity to those commemorating Newton, Kelvin, Faraday and Clerk Maxwell. Those to the Herschels (William and John) and Stokes are close by. Green’s memorial designates him “Mathematician and Physicist”. Most mathematicians will know of Green’s theorem and Green’s functions; physicists find his papers seminal to the study of, for example, solid state physics and elasticity and, since the mid-twentieth century, Green’s functions have become an indispensable technique for those working in nuclear physics.
13 citations
Journal Article•
TL;DR: Coleridge, Christabel as mentioned in this paper wrote: "They had been friends in youth; But whispering tongues can poison truth; And constancy lies in realms above; and life is thorny; and youth is vain; And to be wroth with one we love I Doth work like madness in the brain."
Abstract: Alas! They had been friends in youth; But whispering tongues can poison truth; And constancy lies in realms above; and life is thorny; and youth is vain; And to be wroth with one we love I Doth work like madness in the brain. Coleridge, Christabel.
TL;DR: The eminent physicist, Peter Guthrie Tait, having constructed mathematical models of the flight of a golf-ball and having carried out an extensive series of experiments to evaluate their parameters, specified the maximum distance a golf ball could be made to carry by the most accomplished golfer as mentioned in this paper.
Abstract: The eminent physicist, Peter Guthrie Tait, having constructed mathematical models of the flight of a golf-ball and having carried out an extensive series of experiments to evaluate their parameters, specified the maximum distance a golf ball could be made to carry by the most accomplished golfer. He was then upstaged by his son who hit a monumental drive which pitched even further. The golfing press of the day - what there was of it - was happy to run the story and scientists themselves seemed to enjoy the joke at Tait’s expense. Macfarlane, for example, related the anecdote in the following terms in a lecture delivered just eight months after Tait’s death: “He […] communicated his results to the Royal Society of Edinburgh and there stated definitely the longest distance to which a golf ball could possibly be driven […] but the champion golfer upset his father's calculations […] by driving a ball five yards further.”
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TL;DR: In this paper, it was shown that our intuitive estimate of the probability of a coincidence occuring becomes increasingly inaccurate the more "outlandish" the coincidence seems to be, and that the root cause of this disparity between expectation and reality is due to the fact that our intuition becomes increasingly unreliable.
Abstract: Coincidences are a source of amusement and occasional unease in our lives. They often appear to defy the laws of probability – even to demand a supernatural “explanation”. Probability theory reveals the root cause of this disparity between expectation and reality. As I shall show, it stems from the fact that our intuitive estimate of the probability of a coincidence occuring becomes increasingly inaccurate the more “outlandish” the coincidence seems to be.