bluuebunny/crossref_metadata_2025_split huggingface dataset:
Theatre in Eastern Europe
Authors: Popkin Henry 
Published: January 2007

Right now, the East European theatre is the most exciting in the world. (When I say East Europe, I refer to the Soviet Union, Poland, Czechoslovakia, Hungary, Rumania, Bulgaria, East Germany, and Yugoslavia.) This theatre is not necessarily the most accomplished, although that is a defensible claim. I mean that theatrical creativity is blooming there, and that, in the theatre, encouragements and incitements outweigh efforts to keep creative people in check.The most important single element is the existence of a cheap, subsidized theatre that has mass appeal. Of course, subsidies encourage the continued popularity of a great deal of junk, but they protect quality as well, and sometimes theatre of the highest standards is popular, too. If subsidy is one secret, the other is the relative absence of competition. Television is generally confined to a single channel and only to certain hours of the day.
Arden's Unsteady Ground
Authors: Gilman Richard 
Published: January 2007

“An object of art is artistic only insofar as it is not real,” Ortega y Gasset once wrote, and meant something much broader than an attack upon naturalism. Until we are able to think of drama, for all its physical contingencies and aesthetic impurities, as existing in a different realm from the “real”—the way we are mostly able to think of poetry, painting, music—we will go on disputing over everything that is peripheral and secondary in the work of a playwright like Arden, in the effort to establish its “validity,” unconscious that this validity has already been established by the play's own internal processes and conquests.There is something dispiriting about Arden's own vacillations between apology and peevish resentment. The prefaces to his plays are full of protests against his critics, but also of weakly enunciated and what can only be called supererogatory statements of his dramatic intentions.
The Uses of Film in the New Theatre
Authors: Kirby Michael 
Published: January 2007

The film experience is not necessarily a single rectangle of light and shadow that flickers at one end of a darkened room. Call this “movies” or “cinema”—that archetypal dream world in which the spectator, seated in a near-foetal position, attempts to ignore the physical space, the other spectators, the projector's shifting beam, to concentrate on the images and the sounds that accompany them. Of course, the movies are a film experience—and a theatre experience—but the use of motion pictures is not so limited, and theatre is just beginning to realize the possibilities inherent in film.For many years, motion pictures have been used as elements in staged drama—epic and “total” theatre, the “living newspaper,” etc. In 1941, Robert Edmund Jones foresaw “in the simultaneous use of the living actor and the talking picture…a wholly new theatrical art, whose possibilities are as infinite as those of speech itself.”
The Calculus as an Item in School Mathematics
Authors: Jackson C. S. 
Published: January 2007

A bold induction by simple enumeration has been made. The graph when plotted confirms it. Let elementary algebra justify it. A little later the algebra will come first.Just when to introduce the synlbol Δ is of course a question of knowing the class.How the differences give the slope of certain chords will be evident. How far at this stage to allow the question of the tangent to arise is a question of tact.
On Binal Fractions
Authors: Cunningham Allan 
Published: January 2007

Binal Fractions. The reciprocals (1/N) of any number (N) will be termed Binal Fractions, or shortly Binals, when expressed in the binary scale. The notation used is similar to that of ordinary decimals. Thus (see table at end):1°. A point is used to mark the beginning of the fraction.2°. The binal (1/N) consists of a certain sequence of ciphers and units (the only digits used) to the right of the point; partly non-recurrent and partly recurrent.
Notes on Elementary Dynamics. II
Authors: Muirhead R. F. 
Published: January 2007

In problems where more than two bodies are simultaneously in collision, the rules usually stated in the text books are not, in general, sufficient for their solution. It has been suggested to me that I should continue the subject of Collision by a discussion of the method required in such cases.In what follows I confine myself to the case of smooth spheres impinging on one another, or on fixed bodies, so that rotations do not fall to be considered.
On Approximations and Reductions
Authors: Lodge A. 
Published: January 2007

1.It may not be generally known how much more rapidly such operations as multiplying or dividing by π, or reducing metres to yards, etc. can be effected by the methods of “Practice” than by direct multiplication and division.2.For example, the commonly used approximation for the value of π, though an excellent first approximation, is only true to three significant figures; but (i) is true to five significant figures, and thus yields a second approximation by a correction of the first. The value (ii) which is slightly higher, may be used as a useful check.
Fractional Calculus
Authors: Fabian W. 
Published: January 2007

We continue here our work on fractional integration and differentiation of functions of a real variable which we began in a previous paper. All quantities in the present paper are real.We define a λth integral, or a (−λ)th differential coefficient, of f(x) over an interval (a, x)bywhere D stands for and γ is the least integer greater than or equal to zero such that λ + γ>0, f(x) is bounded on the path of integration, and is continuous on this path except possibly for a finite number of ordinary discontinuities.
Remainders in Interpolation and Quadrature Formulae
Authors: Daniell P. J. 
Published: January 2007

The determination of the errors involved in interpolation or quadrature formulae often involves complicated reasoning. There are many cases, however, where the remainder can be obtained very easily. These cases belong to the class which we call simplex.In general a formula will be expressible in the formL(f) =∑rArf(xr) + ∑sBsf'(xs)+ ∑tCtf''(xt) +… ......(1)to a finite number of terms and it is assumed throughout that f(x) possesses derivatives as far as the remainder may require.
The Conjugate Hyperbola and the Involutory Ellipse
Authors: Freeman J. B. 
Published: January 2007

N.B.—In what follows we consider the conic as the projection of the circle and assume only its descriptive (including cross-ratio) properties as known.1. A circle, centre g1 is cut by a secant line at ww′. Any line cpp′ through c, the pole of ww′, cuts the circle at p and again at p′. The lines wp and w′p′ intersect at d. The locus of d for the variable secant line through c is a hyperbola touching the given circle at ww′ (If w′p and wp′ meet at d′, the locus of d′ is the same hyperbola.)
Formulae for Numerical Integration
Authors: Bickley W. G. 
Published: January 2007

Numerical integration, including the numerical integration of differential equations, is becoming increasingly necessary in technical applications. For such purposes, when a very high order of accuracy is not required, formulae which use successive values of the function to be integrated are more convenient than those using differences. Individual authors have given formulae of this type from time to time but a systematic list is not known to the present writer, and would seem to be of service.The present list gives formulae of four types : (I) formulae for evaluating definite integrals ; (II) formulae for forward integration ; (III) formulae for integrating over a subrange ; and (IV) formulae involving values of both the function and its integral. The leading term in the error series is given. Finally, some comments are made upon the formulae and their uses.
The Teaching of “Applied” Mathematics
Authors: Buxton A. 
Published: January 2007

Attention has been recently drawn to the rapid mathematisation of science during the past half-century and the contributions to educational technique which are being made by teachers of mathematics in technical colleges.The kind of mathematics with which they deal may be called “Applied” Mathematics, although it is far different from what is ordinarily termed applied mathematics. It may be said to include certain portions of pure mathematics, practical mathematics, theoretical mechanics and, in rare cases, such practical mechanics as is considered necessary to illustrate the theory—whereas, in fact, it should cover all applications of mathematics to the various fields of knowledge.
Elementary Inequalities
Authors: Brown T. Arnold 
Published: January 2007

The article by Mrs. Linfoot on the “Teaching of Elementary Inequalities” published in the issue of the Mathematical Gazette for July, 1940, raises a matter of considerable interest and importance.It is unhappily the case that the elementary treatment of inequalities remains a weak point in English mathematical teaching. While no Higher School Certificate examination paper in Algebra would be considered complete without the inclusion of questions on identities and equations, yet direct questions on inequalities and in equations occur comparatively rarely and, indeed, even when such questions are included in University Entrance Scholarship examinations, they tend to be ignored by the majority of candidates.
Results of Relativity without the Theory of Tensors
Authors: Kearney R. A. M. 
Published: January 2007

The Special Theory of Relativity leads to the following conclusions :
(i)The three dimensions of space and one of time constitute an isotropic fourfold, in which there is no unique time-direction, just as there is no unique space direction.(ii)Specifying the velocity of a body is equivalent to specifying its “ time-direction”, that is, the direction of its path through space-time (its “ world-line ”).(iii) If the units of distance and time are taken to correspond with each other, so that the velocity of light is unity, then the lines in our diagram (L'OL, M'OM, and lines parallel to these) which represent the paths of light pulses (Robb's “ optical lines ”) are at right angles for light going in opposite directions, and in this case the time direction (T'OT) of a particle and its corresponding space-direction (X'OX) are equally inclined to the optical line (L'OL) between them, so that setting a particle in motion involves “ rotating ” its time-direction and its space-direction through equal angles (T1OT2, X1OX2 towards the optical line which goes in the direction of motion of the particle.
Determinant Expansions
Authors: Milne-Thomson L. M. 
Published: January 2007

A Set of numbers aij (called elements) arranged in a rectangular array of m rows and n columns constitutes a matrix of orders m × n. For example, of the arraysthe first is a matrix of two rows and three columns, i.e. of orders 2 × 3, the second is a square matrix of orders 3 × 3.From a square matrix of orders n × n we can form a determinant of order n. Thus from the above square matrix we can form the determinant of order 3
Motion of a Body Whose Mass is Changing
Authors: Ramsey A. S. 
Published: January 2007

In Routh’s Elementary Rigid Dynamics (Sixth edition, 1897, § 300) a section is given to the application of the principle of linear momentum to determine the gradual changes produced by alterations of mass, with examples; but I cannot recall that any modern textbook explicitly points out that the formulaeM dV/dt = F .....(1)and d(MV)/dt = F, .....(2)which serve to determine the motion of a body of constant mass, are not necessarily true when the mass is changing.
Pansymmetrical Pencils
Authors: Peek B.M. 
Published: January 2007

In Fig. 1, AA1A2A3 … is a rectangular hyperbola, whose asymptotes are OT, OT', and whose vertex is A. We make the following construction

At A1, a point on the hyperbola, a tangent is drawn, cutting OA at P The tangent at A is drawn, cutting OA1 at P1. Let the other tangent from P1 touch the hyperbola at A2. Produce PA1 to cut OA2 at P2. Let the other tangent from P2 touch the hyperbola at A3, and let P1A2 produced cut OA3 at P3.
Consider this process to be continued indefinitely and to be repeated on the other side of the axis OA, A′1 being the point of contact of the other tangent from P We obtain a pencil of rays OA
n
, OA′
n
which gradually lie closer together, becoming infinite in number as the asymptotes, which are the ultimate rays of the pencil, are approached. The system is obviously symmetrical about OA, and I shall show that this pencil has further remarkable properties, which I have named “pansymmetry” These properties can be stated thus

If a tangent to the hyperbola at the point An be produced both ways, it will be symmetrically divided by all the rays of the pencil, the p th section on the one side of An being equal to the p th section on the other side.
A Descriptive Proof of a Theorem for Conic Sections
Authors: Lyons R. J. 
Published: January 2007

1 To prove that a line meeting one given conic in points harmonic to its intersections with another given conic, touches a conic.2. Lemma I. Let two conies intersect in P, Q, R, S as shown in Fig. 1.Let UV, FG be a pair of common tangents intersecting in T, and let the tangents at P to the two conies cut UF, VG in the points M, N respectively. Then M, N, T are collinearFor: QR, PS, FU, GV all meet in a point X, and the range MFUX is related to the pencil P(PFUS), which is related to F(PFUS), which is related to PQ′XS, where Q′ is the intersection of SP and FG Similarly, NGVX is related to PQ′XS. Hence MFUX and NGVX are related, and thus MN passes through T
Mathematics in the Schools
Authors: Hickling A. N. 
Published: January 2007

The teaching of mathematics has been brought to so high a pitch of excellence by the eminent teachers of the past century that it may be thought there is little scope for improvement in their methods.Since the radical revision of our geometry text-books towards the end of the nineteenth century, when modern methods first superseded the age-old system of Euclid, we find no fundamental change of doctrine until we come to consider the place of trigonometry and of the calculus in present-day curricula.
Conic-Tracing in Line Coordinates
Authors: Johnson S. P. 
Published: January 2007

Consider x : y : 1 = t2 - 2t : t : t2 - t - 1. ........................ ( i) The curve meets the line lx +my + n = 0 in points given byl(t2 -2t) +mt +n(t2 -t-1) =0.For any given Z, m, n there are two values of t. Hence the curve meets any line in two points and is therefore a conic. For a given l, m, n the values of t are the roots of the equation t2 (l +n) + t(m -2l -n) -n =0.
Sums of Powers of Reciprocals
Authors: Lodge A. 
Published: January 2007

Formulae are established below forfor both odd and even integer values of r(r>1), and x≥0; also forthis series reducing to when x is an integerIn 1920 I established the formula, a most useful one,where γ is Euler’s constant0·57721 56649 01532 86060 6,and in 1920 gave a simpler proof with extension to higher powers of x(x + 1) with formulae for Σ2n+1, but not for Σ2n.
Numerical Equations with Complex Coefficients
Authors: Neville E. H. 
Published: January 2007

In response to Dr. Lidstone’s letter in the May number of the Gazette, I have solved the equationz
2−(2+i)z + (4+3i)=0,a quadratic equation with complex coefficients chosen at random, by a process, or rather a succession of processes, of complete generality.
Curves of Constant Diameter
Authors: Kearsley M. J. 
Published: January 2007

The literature dealing with curves of constant diameter is not very extensive, and the following notes may be of general interest.If the distance between parallel tangents to any curve is constant, whatever their common direction, then the curve is a corve of constant diameter. Thus, if p (ψ) is the perpendicular distance from the origin to the tangent to the curve, where ψ is the angle the tangent makes with the positive x-axis, and D(ψ) is the diameter of the curve, that is, the distance between parallel tangents, then
On the Marking of Chess-Players
Authors: Good I.J. 
Published: January 2007

The purpose of this note is to suggest a system of marking chess-players that is both simple to apply and based on a theoretical background. The non-mathematical reader will not need to understand the formulae, but is recommended to read all the words.In the British Chess Federation Year Book, 1953–4, pages 39–42, there is an article entitled “ A grading system for British players ”. It describes a system that it admits to be open to some objections. At first sight the system looks reasonable and is fairly simple to apply, though of course any system requires a fair amount of calculation if it is to be applied to hundreds of players. An objection to the system, mentioned in the article, is that it is always profitable to play an opponent whose mark exceeds one's own by more than 500 points, unless the system is modified in an inelegant manner. The publication of the article is stimulating to further thought and the system to be described here is one of the results. It is not open to an objection of the above form.
On the Three-Cusped Hypocycloid
Authors: Hadamard J. 
Published: January 2007

I have had a recent opportunity to recall an early article (1884) which I wrote on the three-cusped hypocycloid. My starting point was the property that the asymptotes of any pencil of equilateral hyperbolas envelop such a hypocycloid. I proved this analytically in the aforesaid article ; perhaps there is some interest in finding geometrical reasons for it.Principles on pencils of conies are well known. According to these principles :(1) The polars of any point a with respect to the various conies of the pencil are concurrent at one and the same point a, which we shall call the corresponding point of a.(2) If a describes a straight line D, then a. describes a certain conic C.(3) This conic C is also the locus of the poles of D with respect to the conies of the pencil, a consequence being:(4) If m, a point of C, is the pole of D with respect to one of the conies H of the pencil and a a point of D with the corresponding point α, then the polar line of a with respect to H is mα.
Planes of Circular Section of a Cone
Authors: Robinson R. T. 
Published: January 2007

If BPC, DPE are circular sections of the cone vertex A, a sphere can be drawn containing these two sections, and the cone will touch the sphere at the points P, P1 where the line of intersection of the two planes meets the sphere. Thus AP2 = AD AB. Taking BPC as the base of the cone, if AC is the least and AB the greatest of the generating lines drawn from A to the base, ABC will be a principal section of the cone and the planes of circular ection of the cone are perpendicular to the plane ABC. If AF is perpendicular to DE and AH perpendicular to BC,AP2 = AF AH sin B sin C;That is, AP2 is the product of the perpendiculars drawn from P to the planes hrough the vertex A parallel to the planes of circular section, divided by in B sin C.
Geometric Representation of Analytic Functions
Authors: Vermes P. 
Published: January 2007

The study of the function of a real variable is aided by the " graph " of the function. Whenever difficult analytical notions are considered, such as continuity, turning points, etc., a study of the graph enables the student to get a general view of the problem.No such help appears to be available in teaching the theory of functions of the complex variable. A " graph " of f(x + iy) = u + iv would require a fourdimensional space. Nevertheless some representation of an analytic function seems necessary if the student is not to be discouraged by the abstract nature of the idea.
Some Exercises in Laplace Transform Integrals
Authors: Williams John 
Published: January 2007

If 𝜙(t) is a given function of the real variable t then the integral (in which p is constant) if convergent, is defined to be the Laplace transform of 𝜙(t). The use of the integral in determining the solutions of certain types of differential equations is now well known; see, for example, Carslaw and Jaeger, Operational methods in applied mathematics (Oxford University Press).
The Cissoid of Diocles
Authors: McCarthy J. P. 
Published: January 2007

The polar equation of the parabola y2=8ax, referred to the origin of coordinates as pole isr sin2θ = 8a cos θor Inverting with the pole as centre of inversion and 4a as the radius of inversion we find that the equation to the inverse curve isor r cos θ = 2a sin2θor r = 2a sin θ tan θ.
On the Multiplication of Complex Numbers
Authors: Newing R.A. 
Published: January 2007

In the development of the theory of complex numbers, it is important to give a definition of them dependent only upon real numbers. In the usual algebraic treatments the product is postulated in the formor obtained from a matrix representation. The object of the present note is to show by elementary methods that the assumption that the multiplication of complex numbers is distributive, associative, and such that the vanishing of a product implies the vanishing of at least one factor, is sufficient to define the product. This is indeed merely a special case of results well known in the theory of linear algebras.
Free Variable Axioms for Groups
Authors: Goodstein R. L. 
Published: January 2007

The growing importance of the elements of group theory in sixth form teaching has been recognised by a number of recent publications, but a very simple presentation of the theory of groups by means of free variable axioms which was introduced by Lorenzen more than twenty-five years ago, and which is particularly well suited for elementary teaching, does not appear to be as well known as it deserves to be.Lorenzen defines a group in terms of divisionx/y, instead of multiplication, a device which obviates the need to postulate the existence of a neutral element and an inverse.
Junior and School Mathematical Societies
Authors: Sherlock Alan 
Published: January 2007

In the Gazette (176) for May, 1925, Miss J. M. Brown wrote a delightful article on “ Mathematical Clubs ” in Schools. It is interesting today to recall some of the ideas mentioned.“ The obvious function of a Mathematical Club is to stimulate the interest which may have been aroused in the classroom, or if possible to awaken an interest hitherto dormant.”The History of Mathematics was considered a starting point but was not found to be a very suitable topic for arousing enthusiasm. Mention is made of graph work (there was no Cundy and Rollett, Mathematical Models, in those days)—and of interest shown in Flatland (Dr. Abbott).
Non-Convex Pentahedra
Authors: Norgate M. 
Published: January 2007

Three straight lines are needed to enclose a finite region of a plane, a two-dimensional space. The polygon formed is a triangle. Different types of triangle are described by adjectives; scalene, isosceles, equilateral and acute angled, right angled, obtuse angled. All the triangles have a property in common: they are all convex.Four lines form a quadrilateral. The convex examples are well known. There are two further types: those which are “re-entrant” having an interior angle greater than 180 degrees, a reflex angle; those in which a pair of opposite sides cross within the quadrilateral, a “crossed” quadrilateral.