bluuebunny/crossref_metadata_2025 huggingface dataset:
Pirandello and the Nature of Man
Authors: Heffner Hubert C.
Published: January 2007

The students and critics of Pirandello are almost unanimous in their assertions that a chief, if not the chief, contribution of his dramatic works lies in his reevaluation of the nature of man and his reassessment of conceptions of reality. Joseph Wood Krutch, for example, in his Messenger Lectures delivered at Cornell University in October of 1952 and later published under the title “Modernism” in the Modern Drama,: places Pirandello among the chief four or five modern dramatists and among the foremost contributors to modernism chiefly because his plays are centrally concerned with the “dissolution of the ego” and hence sets Pirandello centrally in that main stream of modern thought about the nature of man represented likewise by the novels of Proust and James Joyce, among others.
Lorca: The Puppets and The Artist
Authors: Oliver William I.
Published: January 2007

It is quite natural for us to wonder why a great poet such as Lorca should devote so much energy and interest to a form of drama which in English-speaking countries is limited almost exclusively to the amusement of children. The reasons are several but simple. In Spain, as in other Mediterranean countries, puppet theatre is still a popular form of drama. That is to say, it is performed at fairs, festivals, and even in its own well established theatres—and performed for a general audience. And this holds true for both the major puppet traditions in the Spanish theatre: the violent Punch and Judy-like drama in which plot, theme, even logic are sacrificed to the brouhaha, as well as the more complex, romantic, musical, and somewhat narrative genre. In the romantic genre one finds three general approaches to the action.
Male and Female in August Strindberg
Authors: Brustein Robert
Published: January 2007

To all appearances, August Strindberg would seem to be the most revolutionary spirit in the theatre of revolt. Actually, that distinction must go to Ibsen, but Strindberg is certainly the most restless and experimental. Perpetually dissatisfied, perpetually reaching after shifting truths, he seems like a latter-day Faust with the unconscious as his laboratory—seeking the miracle of transmutation in the crucible of his tormented intellect. The metaphor is precise, for transmutation—the conversion of existing material into something higher—is the goal of all his activity, whether he works in science, turning base metals into gold, or religious philosophy, turning matter into spirit, or in drama, turning literature into music. His entire career, in fact, is a search for the philosopher's stone of ultimate truth through the testing of varied commitments.
The Failure of English Realism
Authors: Douglas Reid
Published: January 2007

Great acclamation for realism in the theatre tends to be cyclical. While the form itself may always be with us, every so often it becomes fashionable again, especially in England, and is praised a little more than it deserves. Recently it has been the playwrights who work in the idiom of the Royal Court and Joan Littlewood's Theatre Workshop who have been given rather more critical notice than their achievements warrant. Both the Royal Court and Miss Littlewood have followed, in their preoccupation with working-class life, all similar fashions before them. Real life always seems to live in a particularly unfashionable district. This can be an occasional welcome change from too much costumed romanticism; but apparent verisimilitude in speech or setting does not insure a genuine and perceptive authenticity.
The New English Realism
Authors: Trilling Ossia
Published: January 2007

Ever since John Osborne dropped his dramatic H-bomb on the complacent British middle-class theatregoer in April 1956 in the shape of Look Back in Anger, critics and public alike have been looking to London for a steady flow of new plays of revolt, plays that would be leavened with the yeast of a new social criticism and rooted in the new post-war realism. This new realism is, to my mind, best described as a compound of two elements. The first represents an involuntary and instinctive resistance to the irksome class structure of British society and the other, in one form or another, the universal dilemma which has split the world down the middle in an age of threatening nuclear destruction and exacerbated the rivalries inherent in class, in nation, or in industrial or commercial power. The technological complexities of our new era are hardly touched on in the new drama.
Soviet Theatre: 2 Views
Authors: Glenny Michael , Kinsolving William Lee
Published: January 2007

Although the Soviet theatre is gigantic in extent and past achievements, its exact lineaments are often hard to discern from the West. Because of a distance which is linguistic, cultural, and political as well as geographical, balanced news does not filter through to us with any regularity; for many the Russian theatre is still summed up by one man—Stanislavski. Others are impressed by the Soviet system of permanent theatre companies but are unaware of their disadvantages and the pressures to which they are subject. Except on a few festival occasions, such as Edinburgh, London's “World Theatre Season,” or Aix-en-Provence, the theatre is not a very exportable commodity, and on the rare tours by Soviet theatre companies outside Eastern Europe, critical reaction has usually differed sharply.
Transactional Analysis and Acting
Authors: Wagner Arthur
Published: January 2007

Late in Robert Lowell's Benito Cereno, Captain Amasa Delano interrupts a conversation with his bosun, Perkins, to say, “I seem to have been dreaming … I dreamed someone was trying to kill me.” Delano never leaves the stage, there is no time for him to actually fall asleep and dream, and yet the statement is certainly not descriptive of a daydream. During rehearsals of my production at Tulane we attempted to justify the moment as best we could. There was a long pause before the line while Perkins checked the approach of their own ship to the San Domingo. William Wolak, playing Delano, did the most he could with the moment, but was never really comfortable in it. I knew he was uncomfortable, but could not offer a satisfactory solution.
Theatre and Performance: The Cherry Orchard and Henry V
Authors: Melnick Burton
Published: January 2007

Experience as it is represented on stage—“represent” understood as the simple action —can be divided into performance, productive work, statecraft, and personal relations; theoretically, any one of these can serve as a subject for theatrical representation. In practice, however, some kinds of experience appear on stage more frequently than others. Productive work is rarely represented in theatre. Even in plays like John Gabriel Borkman or The Cherry Orchard, where the productive mentality is an important theme, we rarely see the producer actually working. Performance is shown on stage more often than productive work, but still rather infrequently. When it does occur—in a play within a play, in a marriage or funeral scene, in a boxing match—it is usually an isolated scene, and is rarely the subject of an entire play. The most common subjects for theatrical representation are without doubt statecraft and personal relations.
Dionysus and the Cultured Policeman
Authors: Anderson Michael
Published: January 2007

Recently Richard Schechner has attacked critics of the drama for relying so heavily on the views of the Cambridge school of comparative anthropology, at a time when their evidence for the ritual origins of Greek drama is viewed skeptically by most classical scholars [Approaches to Theory/Criticism, T32]. Whether right or not, he states, “origin theories, I think, are irrelevant to studying theatre,” and in place of a fruitless search for the origins of drama, he puts forward a critical approach of his own. The subject is an important one. But it seems to me that Schechner's discussion of the ritual question rests on a narrow, possibly a too academic, approach and misses its significance, while his own system of analysis is likely to lead us further from a sensitive appreciation of the drama than the theories it is intended to supersede.
Firmin Gemier and Shakespeare-for-Everybody
Authors: Pentzell Raymond
Published: January 2007

Neglect alone would be sufficient excuse for writing about Firmin Gémier. Remembered hazily as the creator of the role of King Ubu and as the founder of France's Théâtre National Populaire, Gémier remains for most of us only a name. There are reasons for this. The history of French theatre in the twentieth century lends itself easily to schematic ideas of “progress,” and Gémier refuses to fall in line. Our “march-of-theatre” allows Antoine to pass a torch to Lugné-Poe, followed by Copeau, the Cartel de Quatre, Barrault, Vilar.
The Plays of John Whiting
Authors: Trussler Simon
Published: January 2007

Only recently has the new drama begun to catch up with John Whiting, who if he were alive would now be almost fifty. He was out of sympathy with the social commitment of the early days. Whiting was not one of the cultural knight-errants who crusaded for working-class culture and against the bomb; rather, he belonged instinctively to the older tradition of the intellectual elite, writing difficult plays for a discriminating audience—an audience with which he never truly made contact, and which perhaps had long ceased to exist.

Yet his lifelong preoccupations with the nature of violence and of personal responsibility foreshadowed the concern of a younger generation of dramatists with issues more elemental than the kitchen sink.
Euclid and his Successors: Some Confusion and a Way Out
Authors: Goodwill G.
Published: January 2007

Many of us who learned Euclid in our schooldays, feel that something substantial has been lost in the training in precise expression and logical statement that it gave. Even those mathematical teachers who would admit no such thing, must admit, if their experience is anything like my own, that many of their colleagues, particularly science teachers, have deplored the loss of what was at least a standard of reference for logical form.
Partial Fractions Associated with Quadratic Factors
Authors: Neville E. H.
Published: January 2007

The determination of the group of partial fractions corresponding to the powers of a linear factor x+b in the denominator of a rational function f (x)/{(x+b)nφ(x)} is one of the comparatively rare algebraic problems whose theoretical solutions are feasible in practice. The numerator of (x+b)n−r is the coefficient of yr in the expansion of f(−b+y)/φ(−b+y), and the calculation of the group of numerators is effected by means of two Horner transformations followed by one division, which can of course be arranged synthetically; no operation need be taken further than the term in yn−1, whatever the degrees of f(x) and φ(x).
How is e to be Introduced into our Teaching?
Authors: Katz J.
Published: January 2007

As soon as the Calculus had descended from its academic heights and had been persuaded to frequent the schoolroom, there was bound to be trouble about e.
The Use of Tangential Coordinates
Authors: Hudson R. W. H. T.
Published: January 2007

There are two reasons why the use of tangential coordinates should be introduced at an earlier stage than is customary into the teaching of analytical geometry and placed on a somewhat different footing. The educational advantages of encouraging the student to follow out a course of reasoning with the help of only a few symbols instead of grinding out hard examples by long meaningless algebra should not require much pressing, although they do not seem to be sufficiently recognised in this country; and on the other hand many theories receive their most appropriate expression in tangentials chiefly owing to the fact that the absolute has a less specialised form in tangential than in point coordinates, being (in two dimensions) the product of two distinct factors in the former and a perfect square in the latter.
Some Notes on Certain Theorems in Higher Trigonometry
Authors: Hardy G. H.
Published: January 2007

I Admire the ingenuity of the method by which Prof. Nanson establishes the expansions of sin x and cos x as power series in x. But I must confess that his attempt to ‘simplify’ the ‘accepted accurate’ proofs of these expansions seems to me a fundamentally mistaken one. Nor can I admit that the result is at all satisfactory ‘from the elementary didactic point of view.’ His proof is to my mind essentially an artificial verification, and altogether unnatural, in the sense that it has no place in any natural and logical way of developing the ideas which lead to the result. I speak with diffidence as one who has had far less experience of teaching than Prof. Nanson. But I am convinced that my criticism is a fair one: and I think that many of the proofs usually given, in English text-books, of many of the theorems of ‘Higher Trigonometry,’ are open to fair criticism on similar grounds, when (as is too seldom the case) they are not to be condemned for ‘hopeless complexity’ or utter lack of force.
On Practical Mathematics in Schools
Authors: Steggall J.E.A.
Published: January 2007

When, with the other members, I received a request from the Secretary, it seemed only fair to him that I should express my willingness to do whatever might be in my power towards the provision of a subject for discussion ; and therefore, with an earnest wish that he would if possible ignore my suggestions, I proposed the rather well worn subject of this paper. To my dismay he did not ignore the suggestions, and in consequence you will have to listen to the trite observations of one who, sufficiently remote from great centres of education, and in great measure precluded from intimate contact with modern methods, is nevertheless sufficiently interested in them to form theories, or rather opinions, of his own. Those to whom the element of novelty may be absent in the points that I proceed to consider will, I trust, extend a charitable reception on the great moral principle of the Western States that the pianist who does his best is not to be shot.

In the ordinary course of lecturing to students who come stamped with the approval of some of the entrance examination Boards, and their name is legion, I find that, especially when they have had a more or less practical course, very great difficulties arise on account of their weak grasp of mathematical reasoning.
The Teaching of Geometey in Schools. A Report Prepared for the Mathematical Association
Authors: Durell C. V.
Published: January 2007

There is little doubt that many teachers are seriously bewildered by this Report. It is not an easy document to read and frequently it is difficult to ascertain the precise nature and application of its recommendations. It suffers from attempting to cover too much ground: the reader is confused by the double purpose it tries to serve, (i) instruction on the axiomatic basis of geometry for teachers who have made no special study of the logical foundations of the subject, (ii) pronouncements on practical procedure in teaching and geometrical method.
The Eccentric Circle of Boscovich
Authors: Langley E. M.
Published: January 2007

Consideration of the special case in which the centre of the eccentric circle lies on the straight line whose points of intersection with the conic are required.

In what follows it will be convenient to abandon the system of lettering adopted by Boscovich which we have hitherto followed, and as far as possible to use that common to modern text books.
The Combinatory Method in Analysis Situs
Authors: Newman M.H.A.
Published: January 2007

Analysis Situs, or Topology, is the investigation of those properties of surfaces and spaces which are unaltered by deformation, that is, by bending and stretching without tearing. For example, a circular disc with a hole in it can be stretched so that its boundary circuits have any of a great variety of forms, but the number of circuits (two) remains unaltered—it is a topological invariant. The fundamental problem of topology (at present unsolved) is to determine necessary and sufficient conditions that a given surface or space A should be deformable into a given surface or space B.
Reform of Mathematical Teaching in Germany. (Continued.)
Authors: Price E A
Published: January 2007

AT the beginning of this century we find that there was a lively movement on foot to insist on the application of mathematics to actual problems occurring in daily life—a reaction from that purely formal mathematical teaching which for half a century had treated the subject-matter as of secondary importance so long as the logical training was achieved. This reaction became apparent amongst schoolmasters, especially in the meetings of the Forderungsverein, and it was even asserted by the extremists that Mathematics was nothing more than the handmaid of Science.
Some Incidental Writings by de Morgan
Authors: T. S. D.
Published: January 2007

“The constant reference to this barleycorn measure (which is seldom, if ever, omitted) induced me to try what it really would make. There is some difference between the breadths of barleycorns. A certain statement of Thevenot (cited in the History of Astronomy, Lib. Usef. Kn.) makes the breadths of 144 grains of oriental barley give 1½ French feet; at which rate 64 would only give 8 53 inches English. A sample from a London shop gave me (when the largest grains were picked out) 33 to just more than five inches. Some other samples, procured from two different parts of England as the finest which could be got, gave 33 to 5 inches, 33 to 5.1 inches, and 33 to 5.1 inches. The average of these is 9.8 inches to 64 grain-breadths : a result which coincides more nearly than could have been expected with the following determinations.
Approximations to n√1+x where n is an integer and 0<x<1
Authors: Child J.M.
Published: January 2007

If we seek approximations to in the form

of such a nature that the fraction gives, on performing the division, an infinite series whose first 2r+1 terms are identical with the first 2r+1 terms of the Binomial Expansion for we shall obtain 2r equations of the form
The Conic through Five Given Points
Authors: Dixon A. C.
Published: January 2007

The following discussion may be of interest on account of the way in which it leads to the axial and focal properties.

I. Let the locus of a point P such that A(CDEP) = B(CDEP), where A, B, C, D, E are fixed points, be called the conic (AB, CDE). Then it is clear that permuting A, B or C, D, E does not affect the conic, and that the conic passes through C, D, E, and also through A, B. (Give BP the four positions BC, BD, BE, BA and then give AP the position AB.)
Avoiding Symbolic Methods in the Solution of Differential Equations
Authors: Barnard R. J A.
Published: January 2007

The discussion on symbolic operators in differential equations in recent numbers of the Gazette shows the need of a different method of attacking the linear equation of the second order with constant coefficients, which is the case most wanted in practice. It seems a pity that no method is given in the English books except the symbolic one, in which pass students get lost owing to their not understanding exactly what they can or cannot do with the operators. And is this to be wondered at when a theorem which gives erroneous results if not interpreted in a particular way has stood in Forsyth’s Treatise for forty years?
On a Continued Fraction of Stieltjes
Authors: Phillips E. G.
Published: January 2007

1. One of the two curious self-reciprocal formulae stated by Rama-nujan,

where

of which I have recently given a proof, can be established by using a result proved by Stieltjes that, if x > 0, m ≥ 0, 0≤a≤ 1,

The proof only requires the above result in the case in which m = 1, a = 0. While seeking an extension of the result (1. 1), I have obtained an expression for the continued fraction (1. 3) in the form of an infinite series.
The Circle in Homogeneous Coordinates
Authors: Gibbins N. M.
Published: January 2007

1. It is necessary to challenge Mr. F H. V Gulasekharam’s Note 1448 (May, 1940) in which he claims to give simpler methods than usual for dealing with the circle

S ≡ (Σlx)(Σx) − Σa2yz = 0.

Objection must be taken at the very beginning where he says “Suppose the circle cuts the sides of the triangle of reference ABC at D1D2” The arguments of §§ 1 and 2 are sound when these points are real, but it is asking too much of a young student to expect him to understand what is meant by the ratios D1C/BD1 and D2C/BD2 when D1 and D2 are imaginary Moreover the writer considers that the arguments of §§ 3 and 4 are not simple but very difficult.
Infinity in Plane Geometry
Authors: Neville E. H.
Published: January 2007

It has been suggested that a sketch, limited to the real plane, of the theory of homogeneous coordinates and points at infinity which is developed for complex space in my Prolegomena to Analytical Geometry, would be of interest to teachers who without wanting to go deeply into the matter are humanly discontented with the crude treatment that makes of infinity “the place where things happen that don’t”.
Dashboard Mathematics
Authors: Elliott T. C. J.
Published: January 2007

On the dashboard of a car we have a collection of direct-reading instruments, such as voltmeters, clocks, etc. The great simplification of practical physics which has been brought about by the ever-growing use of direct-reading instruments has unfortunately not been accompanied by an equal simplification of mathematical teaching. Schoolmasters ignore the dashboard, and base their teaching on Greek mathematics, for, though they profess to build on those foundations which are familiar to their pupils, they show a strange partiality for the familiar knowledge of two thousand years ago.
Note on Cartesian Geometry
Authors: Milne J. J.
Published: January 2007

When it is said that Descartes was the inventor of analytical geometry, the impression is often given that by Cartesian Geometry is simply meant a system in which the position of a point is determined by means of its coordinates referred to two fixed straight lines, either at right angles or oblique. A little consideration shows us that it is not correct to say that this system was invented by Descartes, as we find that Apollonius, Bk. V, Prop. 52, gives the values of the coordinates of the centre of curvature of a point on a conic referred to two rectangular axes. It will no doubt interest the readers of the Mathematical Gazette to know what is was that Descartes invented, and what led him to it.
Napier’s Method as a Basis for the Theory of Logarithms
Authors: Fletcher W. C.
Published: January 2007

The customary school method of dealing with logarithms (i.e. the initial definition : if ax=N then …) has one great defect : it gives no lead whatever towards the higher theory of logarithms, nor even towards methods for calculating them. “How shall we introduce our sixth form girls to the theory?” a mistress recently asked; “it seems to come like a bolt from the blue.” Klein has some true and forcible things to say on the subject [Elementar Mathematik vom höheren Standpunkte aus, (3 ed. 1924) I, p. 155 et seq.] from among which a sentence or two may be quoted.
Conics and Cubics
Authors: Forder H. G
Published: January 2007

I am sorry that Professor Watson (this volume, p. 261) has been so puzzled by the last sentence in a recent note of mine “Query! What is the envelope of the principal axes of conics touching any four lines? ” By “Query ” I did not mean that I was delivering a seventeenth-century challenge to the learned world, but that I should be interested to see a really elementary investigation, provided it was short, though I was disinclined to seek one myself. For from a slightly higher standpoint the question is very simple. Consider the envelope of lines perpendicular to their conjugates with respect to all conics of a pencil of conic envelopes touching four lines.
Rotation and Strain
Authors: Browne H. F
Published: January 2007

The following method of introducing the ideas of rotation and strain into the study of Elasticity depends upon the identity

m · n grad u=n · (m grad u + m × curl u).....(1)

and upon the fact that if the straight line PQ undergoes a small rotation ω about an axis through P, the displacement of Q is

Consider first of all a rigid body which undergoes a small displacement. Let the point P of the body move to P′. We shall represent PP′ by u and regard u as typical of a vector field extending throughout the space originally occupied by the body. Let Q be a point near to P and represent by m.
Additive Prime Number Theory
Authors: Mirsky L.
Published: January 2007

The scope of the additive prime number theory is evident from its name. In this part of the theory of numbers we are concerned with the representation of integers as sums of primes; and here the central problem consists in the proof (or possibly refutation) of a celebrated conjecture made by Goldbach in 1742 to the effect that every even integer ≥4 can be represented as the sum of 2 primes. The truth of this conjecture is still unsettled; but though progress in this field has been slow, attempts to deal with the problem have led to a whole series of striking results.
A Comedy of Errors
Authors: Watson G. N.
Published: January 2007

The following question came near to being set in a recent examination: The area of a triangle is calculated from the formula

where 2s = a + b + c. It is known that the measurements of the sides are correct to within 1 per cent. Find the greatest possible percentage error in the area.
Reciprocal Nomograms
Authors: Gregg C. V.
Published: January 2007

The reciprocal nomogram described in Note 2108 (February, 1950) for the solution of 1/R=1/R1 + 1/R2 is a particular case of a more general property.
Euler’s Equation and (p, r) Coordinates
Authors: Bullen K. E.
Published: January 2007

1. In a seismological context, it was recently noticed that the use of (p, r) coordinates in a variation problem where polar coordinates had previously been used presented some unusual features. The method followed is one of some generality, and the purpose of the present note is to illustrate it in a suitable elementary problem: “A heavy uniform inelastic string has its ends fastened to two assigned points on the surface of a smooth right circular cone fixed with its axis vertical and vertex O uppermost, and rests in equilibrium on the surface of the cone. Prove that if this surface is developed into a plane, the curve on which the string lay is given by the form p (a + br) = 1.”
On the Behaviour of the Roots of an Algebraic Equation as the Coefficients Vary
Authors: Jaeger J. C.
Published: January 2007

There are many methods of solving algebraic equations whose coefficients are real and have given numerical values. In practice it very often happens that the coefficients are not given numerically, but are expressed in terms of certain parameters, and that what is wanted is not the roots of the equation for special values of the parameters, but an indication of the way in which the roots behave as these parameters vary between certain limits. For example, if the equation is the period equation of a mechanical or electrical system, we may wish to know how its roots vary as certain components of the system are changed, not merely the values of the roots for definite values of the components. The method sketched below has been found very useful for studying cubics from this point of view and applies quite well to quartics. It also provides interesting elementary examples in the theory of equations.
On the Intersections of a Central Conic and its Principal Hyperbolas
Authors: Rajagopal C. T.
Published: January 2007

Let an ellipse or a hyperbola be given by the equation

Then, following Vaidyanathaswamy [8, p. 124], we shall refer to a hyperbola H having its asymptotes parallel to the principal axes of S as a principal hyperbola of S. H is thus given by an equation of the type

and it is uniquely determined when we know three of its intersections with S. It is one of the purposes of this article to bring together some of the elementary properties of H which have been ignored, quite unjustifiably, by most of the textbooks on conic sections produced after Casey's Analytical Geometry [2]. Another purpose which it is hoped the article will serve is that of bringing within easy reach of students, who have had only a preliminary course in geometries of two and three dimensions, some of Vaidyanathaswamy's investigations into the concurrency of normals to a central conic [6].
Gulliver in the Land without One, Two, Three
Authors: Menger Karl
Published: January 2007

About the year 1700, in the course of heretofore unrecorded travels, Gulliver met islanders who used a rather odd arithmetical vocabulary They counted.
Some Interesting Sets of Circles
Authors: Child J. M.
Published: January 2007

The “curious” property noted by Mr. A. P. Rollett (Note 1261 in the Mathematical Gazette for December 1937), with regard to the centres of circles touching one another and inscribed in the space between two given circles, leads to an interesting general theorem on all such sets of circles.

Given any two circles, and a set of circles touching one another and the two given circles, then, if r1r2, r3 are the radii of three successive circles of the set, of which r2 is known, r1 and r3 are the roots of a quadratic equation of which the coefficients are simple functions of r2 and the radii of the given circles.
The Product of Two Series
Authors: Siddons A.W.
Published: January 2007

The followitlg is a useful introduction to the proof of the theorem about the product of two series.

(1) Let Ur =u1 + u2 + .. +ur

and Vr = v1 + v2 + ... + vr

be two convergent series of real positive terms, and let Ur → U, Vr→V as r→∞.
Sign, and Elementary Vector ideas, in Plane Analytical Geometry and Trigonometry.
Authors: Picken D. K.
Published: January 2007

Plane Analytical Geometry, and elementary Trigonometry, are the beginnings of the systematic application of mathematical analysis to Geometry, i.e. of systematic expression in terms of “number”—which is essentially “real” number.

Complete application of the generality of the algebra (within the restriction to real number) is, of course, the power of the method; and, in particular, sign of the (real) numbers is significant throughout.
“The Teaching of Mechanics in Schools” and Other Reports
Authors: Combridge J. T.
Published: January 2007

It is the duty of the Teaching Committee to keep under review Reports published by the Association, and accordingly members of this committee were asked last May to answer the following questions :

(a) Do you consider that the Mechanics Report is sufficiently in need of revision or rewriting for a sub-committee to be appointed now for this purpose, or do you consider that any other Report needs revision more urgently?

(b) Which parts of the Mechanics Report do you think are most in need of rewriting?

(c) Are there any topics not included in the Mechanics Report which you consider should be put into a new report?
A Lattice-Diagram for the Propositional Calculus
Authors: Evenden John
Published: January 2007

Boolean class algebra is a special case of lattice theory and it is well known that the propositional calculus is Boolean. It is also well known that there are sixteen and only sixteen truth functionally distinct relationships between two elementary propositions in the pronositional calculus.
Boole’s Method for Solving Boolean Equations
Authors: Hooley John
Published: January 2007

George Boole gave (in his books, listed under [1] and [2] in the references at the end of this article) a method for solving any equation in his algebra. This part of his work is now largely ignored in the many modern books on boolean algebra which are making their appearance (I can think of several reasons why). Nevertheless, the method can be adapted to conform with our standards of rigour.
On the Inversion Property of the Mobius’ μ-Function II
Authors: Satyanarayana U. V.
Published: January 2007

In a recent paper, under the same title, I proved that inversion of certain functional relations is the characteristic property of the Mobius’ μ-function, by establishing the:

THEOREM I′: f(n), g(n) and μ*(n) (possibly depending on f) are three arithmetical functions with
The Teaching of Statistics in Schools
Authors: Conway Freda
Published: January 2007

The inclusion of statistics in the school curriculum is generally advocated for two reasons. All citizens need to develop “the habit of disciplined thinking about ordinary affairs in terms of quantities” and many scientists need to learn techniques essential to their special studies. Perhaps a third reason should be added; statistics can be regarded as part of the training of mathematicians.
The 9th International Mathematical Olympiad, Cetinje, Yugoslavia, July 3rd-13th,
1967
Authors: Routledge N. A.
Published: January 2007

In Spring 1963 the first National Mathematical Contest here was organized by Mr. F. R.
Watson (now of the Dept. of Education, Keele University). The papers were those of the
Mathematical Society of America and Society of Actuaries (past papers are published in the two
“Contest Problem Books” (Random House)). About 1000 people, aged 14-18, took part. There were
no prizes, only the interest, for teacher and pupil, of submitting to an American test in
which even those of modest talent can put up a satisfactory performance.
Square Flexagons
Authors: Chapman P. B.
Published: January 2007

The flexagon was defined by Mr R. F. Wheeler (M. G. 1958, p.1) as a strip of equilateral triangles which can be folded in various ways into a hexagon to exhibit different colour combinations. Can this idea be generalised? Suppose a plane figure to consist of m regular n-gons, with a common vertex, which can be folded together in pairs.
A General Quadrille Solution
Authors: Philpott Wade E.
Published: January 2007

The problem of arranging dominoes with like numbers in groups of four was proposed by Édouard Lucas. Although Lucas published only symmetrical solutions for the double-six set, generalizations of the problem have led to some interesting results. For the double-six set, it has been shown there are hundreds of shapes meeting the requirement that like numbers appear in groups of four.
Early Nineteenth Century Mathematics
Authors: More W
Published: January 2007

I have in my possession a school exercise book written by John Stewart between January 1801 and 29th June 1802, while he was a pupil at Dundee Academy, later to become the present High School of Dundee. The book runs to 140 pages covering very much the same course as that outlined by T M. Flett in the Gazette of Feb., 1961. Rules are in the identical words repeated by Edward Winder 25 years later
Public Opinion Polls in Schools
Authors: Smithers Graham S.
Published: January 2007

The purpose of this article is to describe how we arranged a Gallup Poll for the North Norfolk Constituency some three weeks before the General Election. At the time of writing, the latter result is not known (and so this has been added later). The constituency itself is some 55,648 electors strong and, at the last General Election, Labour won the seat with a majority of approximately 700 in a straight fight with the Conservatives. It is therefore a highly marginal seat (although it has been Labour held for many years) and the result promised to be of some interest.
Getting it Taped I
Authors: Cundy H. M.
Published: January 2007

The field of tape-recorders is ripe for some form of standardization. Except that speeds are supposed to be standardized (though a tape recorded on one model of a well-known make plays a semitone sharp on a newer model of the same make) most other things seem to be totally variable. This particular article was inspired by the frustration arising from the fact that some counters count the turns of the run-off spool, while others count the turns of the take-up spool. (Some counters only count every other turn; we shall ignore this wholly unnecessary complication.) The question is: how does one convert a reading from one type of counter to that from the other? This produces an unexpected graph in the form of a circular arc—a rarity which perhaps justifies a note.
Uses of Sylow Theory
Authors: Malone Joseph J.
Published: January 2007

One approach to investigating the structure of a group is to examine the family of subgroups of the group. In particular, one often looks for normal subgroups and considers things such as direct products and composition series. However, fruitful investigation usually involves establishing that certain subgroups do, in fact, exist. Hence it is important to find conditions which will guarantee the existence of subgroups. This note indicates the usefulness of one such set of conditions—the Sylow theorems for finite groups.
Computer Building Blocks
Authors: Grimsditch D. S.
Published: January 2007

It has been my pleasure lately to be involved in the organizing and teaching of elementary computer techniques in a college of further education. Whilst the courses were not intended to give tuition in the electronic side of computing it was felt, nevertheless, that some simple explanation of logic circuits and their adaptability to binary adders would not only be an advantage to the students but, if supported by practical classes, would create some considerable interest.
Rotating the Fifteen Puzzle
Authors: Davies A. L.
Published: January 2007

The Fifteen puzzle is well known. In its original form it consists of a shallow square box that can just hold sixteen small squares. Squares, numbered 1 to 15, are placed in any order in the box, leaving the sixteenth position empty (e.g. Fig. 1). The problem is to slide the squares, without lifting them out, until the numbers are in their natural order (Fig. 2).
How Many Triangles?
Authors: Gerrish F.
Published: January 2007

A selection process used by some compilers of big-prize competitions is to present a triangle (usually equilateral) divided into (say) nine congruent sub triangles by the lines joining corresponding trisection points of the sides, and to ask how many triangles there are in the figure. It is amusing to obtain the general result when each side of the original triangle A is divided into n equal parts and pairs of dividing points are joined by parallels to the sides in all possible ways.
Two Remarks on a Note by Mordell
Authors: Smithies F.
Published: January 2007

1. L. J. Mordell has shown very simply (Math. Gaz. Lii (1968), p. 135) that the minimum value of the definite integral
The Generalized Vandermonde Determinant
Authors: Goodstein R. L.
Published: January 2007

Let xi, i = 1, 2, ... , n, be the roots of the polynomial equation

1. xn = p1xn−1 + p2xn−2 + . . . + pn;

we first determine the value of the generalized Vandermonde determinant
What Can be Taught in the Sixth Form?
Authors: Jones T.A.
Published: January 2007

To design a sixth form mathematics course suitable for grammar schools one must keep in mind the nature of secondary school education. In earlier days, grammar schools gave a specialized academic training to a small number of boys, whereas nowadays, with a much larger population, such schools are expected to train boys as useful citizens in a more complex social and economic world, giving them a breadth of knowledge and a depth of understanding.
Speedway tournaments
Authors: Fletcher T. J.
Published: January 2007

I like an active Saturday afternoon, so it comes about that I often end up watching sport on television. The other day it was speedway racing. I gradually became aware that I was watching 16 riders riding four at a time in a complicated arrangement of heats, the object of which was to ensure that each rider rode against every other rider exactly once. Naturally (?) there were 20 heats; but the question arises as to what numbers of riders may be arranged into a tournament, given the firm speedway requirement that four riders are to be on the track at a time, and the requirement that each meets each just once. It is also a problem to arrange the riders into heats suitably.
Dividing an angle into equal parts
Authors: Buckley Stephen , MacHale Desmond
Published: January 2007

The problem of finding a geometric construction in a finite number of steps to trisect an arbitrary angle using straightedge and compasses alone is a very old one, originally proposed by the mathematicians of ancient Greece. It was only with modern algebraic techniques in the nineteenth century that it was shown conclusively that no such construction can exist. This fact has in no way deterred a legion of crank angle-trisectors from presenting their alleged solutions to the problem! However some angles (even non-constructible ones) can be trisected: we’ll see later, for example, that given an angle π/7 it can be trisected. We can also consider the more general problem:

For which natural numbers n > 2 does there exist a geometric construction in a finite number of steps to divide an arbitrary angle into n equal parts, using straightedge and compasses alone?
(1) Archimedes and balances
Authors: Tobias Ruth K.
Published: January 2007

If asked to give the origins of the calculus, most pupils who know anything about the subject would answer that Newton and Leibniz invented the calculus in the seventeenth century. It is interesting then to be able to demonstrate the method by which Archimedes found the volume of various solid objects in the third century B.C.
Some thoughts on the educational system and mathematics teaching
Authors: Kerr E.
Published: January 2007

1.1 It might be supposed that I had chosen the title of this address to fit in with the great national debate on education which has taken place since the Prime Minister’s speech at Ruskin College in October last. However, this is not so (and thus this is not a trendy genuflexion to these recent events). It is entirely fortuitous that the theme does enable me to make references to the debate and to some of the issues raised by it. Before and at the Conference last year I kept wondering what approach I should take in this address. I knew that I wished to choose a theme which fitted in with my personal and recent experiences.
A contribution to mathematical evangelism
Authors: Baylis John
Published: January 2007

1. Presumably all readers of this journal, and certainly all contributors to it do mathematics because they enjoy it. Have you ever stopped to think what a wonderful but strange gift it is, this ability to enjoy mathematics? Outsiders are not, I claim, capable of sharing or appreciating this enjoyment, but the reasons are not easy to find, as we see when we try out a few possibilities. The language is technical—yes, but so is that of art, music, atomic physics and computing, and these subjects suffer from no shortage of enthusiastic followers whose technical knowledge is virtually nil. The subject is hard, and to become a participant requires dedication, even sacrifice; true, but true also of the other examples. Mathematicians are all slightly over the edge of the sanity/insanity divide, a common view but isn’t the same said of mountaineers and marathon runners while we watch their exploits with baited breath?
A useful group and an uninteresting operation
Authors: Haines Chris
Published: January 2007

I am continually surprised by the mathematical structure which surfaces in unexpected situations, and even more so when arranging a tenth birthday party for my elder son. The invasion of the home by some eight rather energetic boys on a cold February afternoon was viewed with some trepidation. The instinct of self preservation was uppermost in the search for activities which would allow the afternoon to pass with the minimum of discomfort and the maximum enjoyment. A family friend is very good at organising team games at parties, but with a space problem (our house does not have a large living room as so many modern houses have these days) it was important to split the children up for their activities, but yet devise a programme which was coherent.
A plane introduction to surfaces
Authors: Firby P. A. , Gardiner C. F.
Published: January 2007

1. Introduction

Since Poincaré introduced algebraic or geometric topology in a series of papers during the years 1895-1901, the subject has grown rapidly to become one of the major branches of mathematics with ramifications in many other branches. However, apart from some recreational level ‘rubber-sheet’ geometry, very few students, even at first degree level, meet algebraic topology.
61.4 Basic topological concepts without intimidation
Authors: Meyers Leroy F.
Published: January 2007

The usual basic topological concepts, as seen by students for the first time in a course such as analysis, often seem unintuitive. The following procedure may be more digestible.

Virtually everyone can recognise a boundary point of a set A in a space X. It is merely a point of X all of whose neighbourhoods contain both a point belonging to A and a point not belonging to A. The boundary bA of A consists of the boundary points of A.
A polyhedral series or two
Authors: Goodwin P.
Published: January 2007

About four years ago after consulting my copy of Cundy and Rollett [1] and then leaving it on my desk, I noticed that it had fallen open at a diagram of an approximation to Von Koch’s ‘snowflake’ curve. Interest in such curves has increased of late but for most mathematics students they make a fleeting appearance in the analysis course as examples of closed, continuous curves of infinite length and differentiable nowhere.
A variation on the Steiner-Lehmus theme
Authors: Parry C. F.
Published: January 2007

A famous problem in euclidean geometry, associated with the names of J. Steiner (1796-1867) and D. C. Lehmus (1780-1863), is to show that a triangle is isosceles when two internal bisectors are equal. Although the converse is obvious, a direct proof of the statement is far from simple. A large number of demonstrations have been devised, some valid and some spurious, and a considerable literature exists on the subject.
A set of inequalities
Authors: Ward A. J. B.
Published: January 2007

It is my purpose to establish a set of inequalities between symmetric homogeneous polynomials in several real variables. That may sound a bit grand, but the simplest example of such an inequality is the familiar

A more complicated inequality of the same general type is the inequality

Again increasing the degree of complexity we have the pair of inequalities
Identifying points of inflection
Authors: Ball A. A.
Published: January 2007

We start with a geometric definition:

A point of inflection is a point of a smooth curve at which the tangent not only touches the curve but also crosses it.

Fig. 1 illustrates the definition and shows a curve, its point of inflection and the inflectional tangent (i.e. the tangent at the point of inflection) which crosses the curve. We can see that the point of inflection occurs where the curve stops bending to the left and starts bending to the right. This leads to a more descriptive definition of a point of inflection as a point where the direction of bending of a smooth curve changes sense.
(1) Meriden and Allendale—where is the hub?
Authors: Cundy H. Martyn
Published: January 2007

To all who live south of Watford, London is doubtless the hub of the solar system, as Boston State House was to Oliver Wendell Holmes. Asked for greater precision, they might opt for 10 Downing Street, Charing Cross, or Threadneedle Street according to taste. Most people I have asked “where is the centre of Britain?” plump for Meriden, but that answer would not commend itself to the inhabitants of Scourie. And if you should chance to be in Allendale Town on New Year’s Eve (assuming you can find the way to it), you will be in no doubt that this is where it’s at, and you have reached the roistering heart of Britain. But to give a more reasoned and accurate answer is an investigation well within the scope of a school class equipped with an O.S. map and a micro- or mini-computer.