bluuebunny/crossref_metadata_2025_split huggingface dataset:
Artaud and Film
Authors: Virmaux Alain 
Published: January 2007

Since his death eighteen years ago, Artaud's fame has steadily increased. Everyone claims him as predecessor; literary magazines and theatre programs propagate his name; he is quoted as having said things which he never said and he is used as a front for the worst eccentricities. After the Rimbaud myth we have the Artaud myth; to expose the hoax we need a new Etiemble.In the meantime, Gallimard's careful publication of Artaud's complete works puts into our hands an objective tool to evaluate texts which have been distorted by faddism. The six volumes published so far have already set straight a number of wrong judgments. Volume III revealed Artaud's creativity in cinema; until then, film historians knew Artaud only as an actor. They barely mentioned the one film he had directly inspired, The Shell and the Clergyman [see p. 173], and dismissed it as unimportant.
The Division of the Circle
Authors: Manzitti Camillo 
Published: January 2007

The possibility of solving the problem of the elementary division of a circumference into equal parts was known to the ancients for the casesn = 2p, n = 3, n = 5, and their products.Gauss in his Disquisitiones Arithmeticae proved the possibility of solving the problem by quadratics, and therefore geometrically with ruler and the compass, for all the prime numbers of the seriesn = 22p + 1.
Note on the Sphero-Conic
Authors: Morley Frank 
Published: January 2007

(i.) A quadric cone is a cone having any conic for base, and a point O on the line perpendicular to the plane of the conic through the focus for vertex.(ii.) A sphero-conic is the curve in which any quadric cone cuts a sphere whose centre is the vertex of the cone.In an introductory course on space-geometry, where only a passing mention of sphero-conics seems possible, I have found it useful to show directly the fundamental property that the sum or difference of the focal distances is constant, instead of following the classical method, which consists in deducing the property by the use of infinitesimals, from the fact that these focal distances make equal angles with the curve; this latter fact being in effect a direct consequence of Desargue’s theorem.
A Certain Dissection Problem
Authors: Brill J. 
Published: January 2007

To cut up an isosceles triangle so that the parts may be put together to form two triangles similar to the original triangle.Let ABC be the triangle, having the angles at B and C equal, and let D be the middle point of the base. Draw a circle, passing through A, having its centre on AD, and cutting AB and AC in E and F. Join DE, cutting the circle in G.
The Equation of Activity in Dynamics, and the Principle of Zero Activity in Statics.
Authors: Hassé H. R. 
Published: January 2007

In spite of the great increase in the last fifteen years in the use of the Calculus in the higher forms of schools, and of its introduction into the Intermediate Examinations of many universities, it has not yet been used as much as it could be in the teaching of elementary Applied Mathematics.It has, of course, long been realised that in the kinematics of the motion of a particle in a straight line we have some of the best examples of the ideas that are the basis of the Calculus, and the notation and machinery of the Calculus is now extensively used in dealing with this part of the subject.
The Teaching of Mathematics in English Public Schools for Boys
Authors: Godfrey C. 
Published: January 2007

In the first place, the present paper refers to conditions prevailing in England only, to the exclusion of Scotland, Ireland and Wales.Secondly, the term " public school" has, in England, a rather special meaning. A public school is generally understood to be an endowed secondary school of fair size, educating boys of the upper and middle classes, independent of state control except in so far as its income is supplemented from public funds. Public schools may be either boarding schools or day schools, but most of them belong to the former category.
On the Approximation to Irrational Numbers By Rationals
Authors: Heath A.C. 
Published: January 2007

The problem of deciding whether a given number is irrational or not is frequently one of some difficulty, as in the proof that π is irrational. Several numbers which are very probably irrational have never been proved so, e.g. y, eπ. However, we have one quite simple test for deciding whether a number is irrational or not when we have the number expressed as a continued fraction, viz. if the continued fraction terminates, the number is rational; if not, irrational. In what follows we assume our irrational number given as a continued fraction :or shortly
The Teaching of Indices and Logarithms
Authors: Dobbs W. J. 
Published: January 2007

I propose to give you in outline the short course on Indices and Logarithms taken at the present time by the Upper Fifth Form at the Holloway County School. Soon I hope it may be attempted by the Lower Fifth Forms, and, later on, perhaps by kind permission of the examining authority, it may be found possible to include it in the work of the Fourth Forms.§ 1. Index Notation.—Let a denote any positive numerical quantity, and n any positive integer. Then “ x a” means “ multiplied n times in succession by a.” “an” alone means “1 x an”, i.e. “unity multiplied n times in succession by a.” The index n tells us the number of multiplications.
Geometry and Relativity
Authors: Piaggio H. T. H. 
Published: January 2007

Thus Euclidean geometry does not hold in the gravitational field even in the first approximation, if we conceive that one and the same rod independent of its position and orientation can serve as the measure of the same extension.This quotation from Einstein is merely one of the many disturbing statements that a teacher of geometry may find in recent books on physics or even in the newspapers. It will not be long before some of our pupils will ask if it is worth while to continue the study of a subject of which the principal results are apparently contradicted by the latest discoveries. The object of the present article is to examine these apparent contradictions. To do this we shall trace the evolution of ideas concerning the nature of geometry and consider their relation to school work. The conclusion will be reached that certain changes in our teaching are desirable. Fortunately these changes will actually make school geometry easier as well as more scientific.
Elliptic Trammels and Fagnano Points
Authors: Harding P. J. 
Published: January 2007

1. Giulio Carlo dei Toschi di Fagnano, Count and Marquis, was an Italian mathematician of the first half of the eighteenth century. He was one of the second generation of the followers of Leibniz, a generation rather pale and unimportant compared either with the first great founders of the Differential Calculus or with the third generation that dated from about the middle of the eighteenth century, of which Lagrange was the leading genius.Several of the men of this second generation are known mainly for some one piece of work. This is particularly the case with Fagnano, who extended the application of the Integral Calculus to the rectification of curves in a way that may be regarded as the first germ from which afterwards sprang the Theory of Elliptic Functions.Experiencing the well known difficulty of rectifying, by elementary integration, many curves whose equations seem, at first sight, easy to deal with, he showed that on some curves two arcs could be found whose difference was rectifiable ; although each separate arc presented the same difficulty as before.
Analysis and Projective Geometry
Authors: Durell C. V. 
Published: January 2007

FEW branches of elementary mathematics have escaped reform in recent years; algebra, trigonometry, elementary geometry, statics, and the calculus have all been transformed to suit the practical needs of the time. But amid all this change, there have been few attempts to alter the methods employed in introducing students to the geometry of the conic. Dr. Filon, in his most interesting treatise on Projective Geometry published in 1909, points out that students learn the same facts about the conic practically three times over, (1) analytically, (2) through a course of what is called “geometrical conies” based on the focus-directrix definition, and (3) protectively ; and his book indicates a method of co-ordinating and uniting the last two systems of approach. Although it is undoubtedly the general custom in this country to start in the first place from the focus definition, it is worth while considering afresh whether this plan is really the most advantageous.It is interesting to note that historically this was not the starting point of the early geometers. It is true that the focus-directrix property was known to Pappus, but so far from being regarded as fundamental, it was actually lost sight of altogether, until attention was called to it by Newton. The geometrical investigations of Apollonius were based on the conception of the conic as the plane section of a cone, the advantages of which plan may be enumerated roughly as follows:
On the Setting Out of Certain Easy Cubics
Authors: Edwards R.W.K. 
Published: January 2007

If we wish to develop a race of geometers, I think we should begin by encouraging the habit of speculation. This we do nowadays by using squared paper for plotting graphs. Here, however, we place ourselves very much in the hands of the printer : and although ideas of geometrical shape are enlarged and systematised, the right angle plays too great a part in whatever knowledge of curves is acquired ; indeed a knowledge of curves is not the professed object in plotting graphs so much as a visualised representation of corresponding changes in related physical quantities.In teaching elementary geometry there lingers an aversion from the use of dividers in pricking out equal distances : for the transference of distances is not recognised in the postulates of Euclid, and Euclid's influence remains.Later on a study of the conics, carried on for a prolonged period, and the application of the theorems of Pascal and Brianchon, must exercise their fascination. Ideas about infinity become clarified : the use of parallels is seen to be necessary, to exercise the right accorded by Euclid's first postulate to join any given point to any other, even if one be at infinity. But the mind inevitably tends to become obsessed with the second-degree idea. Mere straight-edge methods are found to be so potent in the construction of conics that metrical properties are neglected. Primary notions about equal distances interfere with the whole scheme of a projective geometry confined to the conics ; and the bisection of a given finite straight line becomes a search for the harmonic conjugate of the point at infinity in its direction, with regard to its two ends.
Kinetic Energy, Divided into Molar Energy and Available, Internal, or Molecular Energy
Authors: Greenhill G. 
Published: January 2007

The algebraical transformationshould be introduced into dynamical instruction at an early stage, and interpreted as the resolution or rearrangement of the left-hand side, the kinetic energy of two bodies, say railway trucks, of weight W1 and W2 tons, moving on the same line with velocity U1 and U2 feet per second, into (A) and (B) in the right-hand side.
Vectors
Authors: Godfrey C. 
Published: January 2007

Vectors in two dimensions are generally studied in schools; I do not suppose that the study is often pushed into three dimensions. But it is difficult to understand a modern book on electricity without some knowledge of three-dimensional vector notation.The particular point that I wish to bring before you is that the two-dimensional case is often presented in such a way that its relation to the more general case is obscured.
The Principles of Dynamics
Authors: Larden W. 
Published: January 2007

(1)We have, above, assigned an intelligible meaning to this expression if the body be considered as a member of a system. But, taken absolutely, it has no meaning.(2)If our shot, now considered separately, meet directly a target of mass M′ and there be inelastic collision, and if the relative velocity be U, then the velocity u′ of the shot relatively to the c.m. of this new system will be , and the velocity V′ of the target relatively to this c.m. will be .The total internal energy of this system as measured by the heat given out will be , and of this the shot may with some reason be said to contribute the first term, and the target the second, in virtue of its K.E. [see VII., (3) and (4)].
A Case of Three Rotating Lines and the Point “O.” (Continued.)
Authors: Taylor F Glanville 
Published: January 2007

15. Let X1, Y1, Z1 be the second points in which AH, BH, CH meet the circle GHThen GX1 ┴ HX, and hence ║ BC,X1X =⅓AX;tan PX1X= 3 tan PAX = 3 tan θ,i.e. -PX1X= ø.But OX1H = OGH= ø; 0X1P is a straight line.
The Division of the Circle—Concluded
Authors: Manzitti Camillo 
Published: January 2007

To establish the order of the locus we must note that besides the above mentioned n intersections with the circumference, the point D also belongs to the curve, so that the latter cuts the circle in n+1 points. The order of the curve is therefore Let n be even.The ratio is not an integer, so that a complete rotation of the straight line BC must take place before the two generating straight lines can be in their initial mutual position; the line revolving round D will be, after a semi-rotation of BC, parallel to BC in DE, and we may say that all the loci for n = 2p are asymptotic in the direction BC, on account of the initial position of BC and DA.
Conjugate Diameters in Areals
Authors: Gibbins N. M. 
Published: January 2007

Principles. 1. If K be the centre of a conic and P a point not on it, the diameter conjugate to KP is parallel to the polar of P.2. Conjugate diameters form a pencil in involution. Hence if S=0 and S' =0 be the equations of two known pairs of conjugate diameters, the general equation is S + λS' =0.The method then is to find the diameters conjugate to KA, KB, KC, where ABC is the triangle of reference, by means of 1, and then to write down the general equation by means of 2.
A Curious Property of Numbers
Authors: Ayyangar A. A. Krishnaswami 
Published: January 2007

The difference between any number and another formed by reversing its digits has certain interesting properties, which, I believe, have not been explicitly noticed before, and these properties determine the necessary and sufficient conditions that a number may be expressed as such a difference.To begin with, let us take a number having an even number of digits and denote it bywhere ap, bp are the middle digits, b1 the units digit and a1>b1.
Presidential Address to the London Branch of the Mathematical Association
Authors: Greenhill Sir George 
Published: January 2007

WHEN your chairman, Mr. Jackson, asked me to supply a title for the Presidential Address, I could think of no name short enough and suitable for these random remarks, à bâtons rompus for half an hour.Professor Turner gave the Mathematical Association an account of some new methods in calculation, found successful for Halley’s Comet; and Ray Lankester held forth in the afternoon on his perennial subject of the place of Greek in education, about which Turner has given you his say on a previous occasion.I must avow myself at the outset in complete disagreement with their opinion, as in Greek we come to the bedrock of all our knowledge in history, literature, science, and art. Greek is the lighthouse to guide us out of barbarism to the human ideal.
The Proof of the Formula for the Vector Triple Product
Authors: Chapman S. , Milne E. A. 
Published: January 2007

This note relates to the proof of the formula for the vector triple product (or continued vector product)a ∧ (b ∧ c) = (a c) b − (a b)c, .....(1)where the sign ∧ denotes vector multiplication and a dot denotes scalar multiplication.
A Class of Homogeneous Linear Differential Equations of the Second Order
Authors: Underwood F. 
Published: January 2007

1. In a recent paper Mammana considered the equationz″ + pz′ + qz = 0,.....(1)where x is the independent variable and p and q are functions of x, real, finite and continuous in the interval (a, b), and investigated the possibilities of its decomposition into the form(D + α)(D + β)z = 0,.....(2)where D ≡ d/dx and α and β are functions of x.
Triangles with Sides and Medians Commensurable
Authors: Hardingham C. H. 
Published: January 2007

It is economical in the use of symbols to express the sides of a triangle fractionally, by dividing the expressions for a, b, c given in my previous Note (Gazette, XXIII, October, 1939, Note 1398, p. 380) by qy. Thus writing h for x/y and K for p/q, we havea = hk + h − k + 1,b = hk − h + k + 1,c = 2(h + k),and n = hk − 1,where l, m, n are the medians bisecting a, b, c.
Mass and Force in Newtonian Mechanics
Authors: Filon L. N. G. 
Published: January 2007

The considerations which I propose to put before you to-day arose from an attempt, when teaching students, to build up the classical laws of Newtonian Mechanics inductively from laboratory experiments.In this task we are immediately confronted with two fundamental notions, those of mass and force.It will probably be admitted that no definition of a physical quantity can be accepted as adequate unless it implies a criterion leading to an unambiguous measure of the thing defined.
New Geometry for Germany
Authors: Pidduck F. B. , Borel E. , Sadler D. H. 
Published: January 2007

The circle will in future have 400 degrees in Germany, instead of 360, as at present, and the right angle 100, instead of 90. This is ordered in a new decree of the German Minister of the Interior.Degrees will continue to be divided into minutes and seconds, but these will also be arranged on the decimal principle.Several years will be allowed to elapse before the new geometry is made obligatory, especially for use at sea, but it will be taught in the schools next year.—Daily Telegraph and Morning Post, Nov 1, 1937.
The Pillory
Authors: Richardson S. 
Published: January 2007

The following question was set in the University of London Inter mediate B.Sc. Applied Mathematics paper, 1922.“Two masses of 2 lbs. and 3 lbs. are fastened at the ends of a light string of length 2 feet and placed on a smooth horizontal shelf 5 feet above the ground. The 2 1b. mass is placed on the edge of the shelf and the 3 lb. mass one foot away from the edge on a line perpendicular to the edge through the mass of 2 lbs. If the mass is gently pushed over the edge find the time that elapses before the 3 lb. mass strike the ground” (g=32 f.p.s2)
A Difficult Converse
Authors: McCarthy J P. 
Published: January 2007

If the bisectors of the base angles of a triangle are equal, the triangle is isosceles.Several solutions of the problem are given in the Gazette for July 1932, and again in the issue of May 1933. It is stated in the former that the problem was mentioned in the Lady’s and Gentleman’s Diary of 1859 and of 1860. The history of the problem is interesting. It appears that it was first proposed in 1840 by Professor Lehmus of Berlin to Jacob Steiner, who had been Professor of Geometry at Berlin since 1834 and held that post until his death in 1863.
Mathematics: In Search of a Soul
Authors: Bowcock J.E. 
Published: January 2007

As this is to be a purely scientific talk it is best to start from fundamental definitions and concrete propositions.So first the definitions.Mathematics is merely the high-sounding name designated to the efforts of a child in its attempt to count up to ten, which is crystallised in those immortal words, “One little piggy went to market, one little piggy stayed at home. .” If this is not acceptable to some of the unenlightened members, the alternative “addin’ up and takin’ away” may be substituted.
A Problem on Circles
Authors: Reifenberg E. R. 
Published: January 2007

In connection with a general form of the covering principle and the relative differentiation of additive functions Mr. A. S. Besicovitch has proved that given a unit circle C with centre O, then any set of circles satisfying the conditions1. Each circle of the set meets (or touches) C;A. 2. Each circle of the set has radius not less than 1;3. No circle contains O or the center of any other circle of the set, has less than 22 members.
Some Summation Formulae for Binomial Coefficients
Authors: Moorthy T. Narayana 
Published: January 2007

Dr. S. Vajda commences Note 2159 (Math. Gazette, Vol. 34, p. 211) with the following :In his review of H. S. M. Coxeters Regular Polytopes (Math. Gazette Vol. 33, p. 49) Mr. H. Martyn Cundy quotes the formulaand supplies the proof by considering the coefficients of xn in the expansion of
Sign Convention for Bending Moment and Shearing Force
Authors: Chaffer F.T. 
Published: January 2007

If one is concerned merely with the magnitude of the bending moment or the shear, the sign convention to be adopted is of minor importance. When, however, the question of deflection arises, it is essential to obtain the correct sign for the moment and it is therefore desirable to use a convention which not only inspires confidence in obtaining the correct sign but which is also simple to apply.Among many engineers at the present time the hogging moment is taken as the positive moment. There is much to be said for adopting this convention. It fulfils the conditions mentioned above and provides an easy, and, from the students’ point of view, a natural approach to the subject.
An Enquiry about Entry to Mathematics Courses
Authors: Peierls R.E. 
Published: January 2007

In recent years the people concerned with admission of students to undergraduate courses reported that a good deal of difficulty and confusion had arisen from the multiplicity of applications and from students accepting places in several Universities without notifying the Departments concerned, or withdrawing at the last minute from a place already accepted. In this way places were often kept for applicants who did not turn up in the end and vacancies were left for which suitable candidates would have been available earlier.In the discussion of this problem various remedies had been suggested, including a deposit to be paid either at the time of application or at the time when a place was offered, but it was felt that this would not be a complete remedy and in addition might, in some cases, cause hardship.
How they Learnt, 1600-1850
Authors: Robson A. 
Published: January 2007

On some previous occasions when we have had schoolmaster presidents they have told us about the events of the early years of our Association.Canon Wilson, who addressed us about twenty-five years ago, was an original member; he taught mathematics not far from here, at Rugby. Mr. Siddons told us of the beginning of mathematics in some well-known schools in the nineteenth century; he was himself a pupil of another of our original members, Rawdon Levett, who taught for thirty-four years at King Edward’s School in this city. Levett was our first secretary, and when he retired the president attributed to him a full share of the credit for our initial successes. He was a schoolmaster of genius: one of the greatest teachers of his time. It is natural that we should think of him this year when we are meeting in Birmingham. Two years ago, Mr. Bushell, the son of another original member, told us about the last century of school mathematics.
Some Results in the Theory of Mass Systems: A Study in “Calculus-Dodging”
Authors: Finucan H. M. 
Published: January 2007

1. Let the rod be of length l, line density d, mass M = ld. If I is its moment of inertia about one end, then from the theory of dimensionswhere C is dimensionless, i.e. a constant, independent of M and l.