bluuebunny/crossref_metadata_2025_split huggingface dataset:
Economical Number Bases
Authors: Phythian J.E. 
Published: January 2007

Throughout this article, all numerals are assumed to be in base ten notation, unless otherwise stated.Under many of the new mathematics programmes currently in use in secondary schools, the topic “Numbers to different bases” is introduced. Indeed, provided such an elementary textbook series has chapters on Sets, Counting to different bases, Symmetry and/or Transformation Geometry, and, possibly, Vectors and Matrices, it is then allowed to write “Modern Mathematics” on its title page almost regardless of the methods employed in the book. However, my topic does not concern the vagaries of modern mathematics textbooks, their content and their methodology, but rather the question of why ten is used as a number base. Undoubtedly many of you already feel that you know, and that the reason is concerned with numbers of fingers and toes. However, one might try to decide more rationally whether ten is a sufficient base to represent the wide range of numbers with which we are normally concerned.
Some Problems in Combinatorics
Authors: Forder H. G. 
Published: January 2007

The following problems are merely different forms of one1. In how many ways can a convex polygon of n + 1 sides be split into triangles by non-intersecting diagonals? We represent such a splitting by a symbol. Take one side of the polygon as base and letter the other n sides in order by a, b, c,…. If a triangle with sides lettered x, y is cut off, denote the diagonal by (xy). If this diagonal and side z form the sides of another triangle of the dissection, denote the third side of that triangle by ((xy)z). Similarly for two diagonals, as the figure illustrates. Finally the symbol for the unlettered base is the symbol for the dissection.
Going one Better in Geometric Dissections
Authors: Lindgren H. 
Published: January 2007

Methods have been described that facilitate the discovery of economical dissections. They are summarized in §§ 1 and 2 that follow.1. Each of the figures to be dissected is made an element of a strip with parallel sides; 1 and 2 show strips formed from a Latin or tau cross and a pentagon. The first is a P-strip (prototype parallelogram), in which all elements are the same way up. The second is a T-strip (prototype trapezium), in which alternate ones are inverted. Points such as A and B in 1 are called congruent, a term copied from Whittaker and Watson's Modern Analysis, p. 430.
Transcendentals galore
Authors: Wilker J. B. 
Published: January 2007

The natural numbers are the elements of the set N = {1,2,3,…}, the integers are the elements of the set Z = {0,± 1,±2,…} and the rational numbers are the elements of the set Q = {p/q:pεZ, qε6 N}. A real number is called algebraic if it is the root of a polynomial equationP(x) = anxn + an−1xn−1 +…+ a1x + a0 = 0
How many times does n go into n ǃ
Authors: MacKinnon Nick 
Published: January 2007

Sometimes nǃ is very divisible by n. For example, 12ǃ is divisible by 125 while 720ǃ is divisible by 720178. On the other hand, if p is prime then pǃ is divisible by p but not by p2.In general it is quite difficult to calculate the maximum exponent m(n) such that nm(n) divides nǃIn this short article I will locate some values of n, for which nǃ is very divisible by n, find a tight upper bound for m(n), and point the reader in the direction of related problems.
It doesn’t work
Authors: Barton Alan 
Published: January 2007

“The total work done by the external forces acting on a rigid body is equal to the change in the kinetic energy of the body.” O.K. ? Well, it all depends on definitions.The work done by a constant force is usually (in nearly all textbooks ?) defined as the product of the magnitude of the force and the displacement of its point of application, this displacement being measured in the direction of the force. Consider then a sheet of paper on which a student has drawn in pencil a straight line which he is now about to erase. He causes the eraser as it moves along to exert a constant force on it, and he exerts another constant force with his other hand to keep the paper still. The desk (supposed smooth) exerts constant normal forces. Of all these forces on the paper the first force does some work, according to the definition, while the others do none. The total work done by them is positive, yet there is no change in kinetic energy of the paper.
Self-descriptive strings
Authors: Mckay Michael D. , Waterman Michael S. 
Published: January 2007

Take a look at the ‘string’ (or finite sequence)6,2,1,0,0,0,1,0,0,0.Count the occurrences of the numbers:Notice that the bottom row is the string we started with! In fact the above string is the unique answer to the popular question (posed, for example, in a recent edition of the Trans World Airlines magazine, The Ambassador, August 1978) to find a string
Jack-in-the-box
Authors: Helfgott A. , Potts R. B. 
Published: January 2007

A few years ago, a well known laundry detergent manufacturer ran a sales-promotion competition in Australia called “Jack-in-the-box”, with the following rules:1.Draw a continuous line through 13 of the numbered squares (see Fig. 1). The numbers in the squares through which the line has been drawn are then added to give a total score. Entries achieving the highest total scores will qualify for one of the prizes.2.The line must not go through any square more than once. It also cannot be drawn diagonally through the corner of any squares_only up and down or across (see the example in Fig. 1, for which the score is 723).3.The line must begin at the square J (for Jack-in-the-box) and may finish in any square. The J square does not count as one of the 13 squares.
Napoleon revisited
Authors: Nelson R. D. 
Published: January 2007

If on the sides of a triangle ABC equilateral triangles are constructed, inwardly and outwardly, and their circumcircles drawn, the 6 circles will in general have 11 points of intersection: A, B, C; 2 points on each of the 3 sides; a point F common to the circumcircles of the outer triangles, and a point N common to those of the inner triangles (Fig. 1).This article uses complex numbers to investigate the figure, and has as its main object the establishment of an extremal property of N.
“ … Assume the string is inextensible and elastic…”
Authors: Roper Tom , Hartley Ron 
Published: January 2007

If the above phrase appeared in an A-level paper the Board responsible would receive many protests: “a contradiction in terms”, “impossible”. But is it? Our attention was drawn to this via this A-level problem from the J.M.B.Three smooth spheres A, B and C, of equal radii and masses m, 2m and am, respectively, lie at rest in a straight line on a smooth horizontal table, with B between A and C. The sphere is connected to A and C by light inelastic strings, which are initially slack. The sphere A is then projected directly away from B with speed u. Find, in terms of a and u, the common velocity of the three spheres when C has been jerked into motion.Find also in terms of a, m and u, the impulse in each string at the instant when C starts to move. Verify that the ratio of these impulses is independent of a.(Further Maths, Paper II, 1988)
Triangles, surds and pell’s equation
Authors: Clarke Robert J. 
Published: January 2007

This article shows a link between Pell’s equation and the right-angled triangles for 60° and 45° via the trigonometric ratios for 15° and the extraction of square roots.It is well known that the trigonometric ratios of 60°, 30° and 45° are easily obtained from the triangles ABC and RST which are shown in Figure 1.
Partitions and the dancing bear
Authors: Mackinnon Nick 
Published: January 2007

A partition of n is a decomposition of n into a sum of positive integers. So the 5 partitions of 4 areThe number of partitions of n is written p(n) and (with the convection that p(0) = 1) the sequence p(0), p(1), p(2), ... begins1, 1, 2, 3, 5, 7, 11, 15,....
Barcodes I
Authors: Pargeter Robert 
Published: January 2007

Some public libraries use a barcode on the date slips in their books which is easily cracked by anyone with a knowledge of binary arithmetic, but those with which we are now so familiar on purchased goods are much more of a puzzle, as there appears to be little correlation between the printed digits and the bars by which they are represented – a little trial will reveal that it is certainly not one-one!
Even with a large number of examples to experiment with, I very much doubt if anyone not in the secret would succeed in solving the problem, which it is the object of this article to elucidate.
Formula funding of schools: some mathematical results
Authors: Fox Michael 
Published: January 2007

Schools run by local authorities have an annual budget which is calculated by formula. The formula used for funding my school is quite easy to understand and its components all seem reasonable, yet it can cause some unexpected problems for an unwary manager.Most of the funding depends on the number of pupils, each being worth an annual amount according to his or her age. If a comprehensive school has fewer than 750 pupils it is regarded as being small, needing extra money to provide an adequate curriculum. This extra is given as a bonus for each pupil; and tapers to zero as the numbers reach 750.
A proof of Eperson's conjecture
Authors: Hirschhorn Michael D. 
Published: January 2007

Eperson's conjecture is that if n ⩾ 3 is odd then 3n2 can be written in at least two ways as a sum of three squares. We shall give a fairly elementary proof of this, from scratch.
Let q be a real or complex number with
Define for n ⩾ 1.
Playing with Pythagoras and geometric arithmetic
Authors: McNeill Charles 
Published: January 2007

I just couldn't see it; that was my difficulty with many mathematical abstractions: if I couldn't visually process a maths concept I would resort to rule, hoping that some day it would make sense.Take the Pythagorean Theorem. It has been around for two millenniums plus, readily understood by all academically exposed to the liberal arts by the time they reach puberty; but me, I knew it, a2 + b2 = c2 and the picture of three little squares huddled around the perimeter of a right triangle, that was no help. Why not three equilateral triangles around the perimeter Of course a2 √3/4 + b2 √3/4 = c2 √3/4 is a bit ungainly, but it would work.
One hundred years on
Authors: Hoare Graham T. Q. 
Published: January 2007

David Hilbert, one of the giants of mathematics, delivered a lecture at the International Congress of Mathematics at Paris in 1900. The first part of the lecture, a preamble to his announcement of the now-famous 23 problems, began with the words:’Who of us would not be glad to lift the veil behind which the future lies hidden; to cast a glance at the next advances of our science and at the secrets of its development during future centuries? What particular goals will mere be toward which the leading mathematical spirits of coming generations will thrive? What new methods and new facts in the wide and rich fields of mathematical thought will the new centuries disclose?
The Church of the Evangelists at Alahan: A Preliminary Report
Authors: Gough Michael 
Published: January 2007

The publication of another article on the monastery complex at Alahan in Isauria so soon after the appearance of Professor P. Verzone's monograph and Professor G. Forsyth's paper on the same monument may seem premature, and to require some explanation. It can, however, be reasonably justified on the differing times and circumstances in which the various articles appeared.In autumn 1955, I published “Some Recent Finds at Alahan (Koja Kalessi)”, an article based on two short visits which I had made to the monastery during 1952 and 1953. This paper coincided with the publication of the Turkish text of Professor Verzone's monograph, compiled after a stay at Alahan in the summer of the same year. Meanwhile, I had previously requested and obtained permission from the Turkish General Directorate of Museums and Antiquities to carry out limited soundings in the monastery complex, in particular in the building designated Chiesa n. 1 by Verzone. These soundings were, in fact, carried out in the interval between Verzone's visit and the publication of his monograph.
Agricultural Productivity and Past Population Potential at Aşvan
Authors: Hillman Gordon 
Published: January 2007

This paper is not a discussion of archaeological evidence for past population levels in our area, nor of likely sequences of change in population through time. Instead, it is a set of estimations of upper levels of population that would have been possible at recent and ancient agricultural settlements in the Aşvan region, assuming certain combinations of territory, land management systems and levels of productivity. This contrasts, therefore, with the approach more frequently adopted in estimating past population levels which uses settlement size and structural remains.The points in time at which these hypothetical situations (with their corresponding population levels) were likely actually to have existed in the Aşvan region are not considered in detail here. We may be in a position to fix time correlates in some cases once we have more data on local erosion and sedimentation history and once we have assembled all data arising from the site materials, in particular the data from the very large quantities of plant and animal remains.
Modern Agricultural Technology in Aşvan
Authors: Williams David 
Published: January 2007

The reason for the drawing and recording of agricultural tools in the Aşvan bölgesi is partly to study the objects themselves, but mainly to examine the relationship between the tools and the activities for which they were designed and to consider various other features of man/environment interaction which they represent. The significance of agricultural tools in terms of human activities is such that their study forms a necessary component of the baseline situation under study in the Aşvan project (see earlier papers in this volume). This significance holds both for the present situation and also can be extrapolated into the archaeological past.The agricultural tools, as recorded, range in type from the more generalized to highly specialized. The specialized may be used in only one activity, but these individual activities can only exist as part of an established agricultural system; any archaeological evidence of the corresponding tools forms ideal evidence for the past agricultural systems. For example, ploughs and threshing sleds are for ploughing and threshing only, but both activities need draught animals; threshing relates to cereal agriculture, and so on. Less specialized tool types may reflect less closely inter-connected activities; reaping knives for example, represent reaping of all kinds of crops, weeding, clearing of fallow land and cutting of scrub for fodder or firewood; any interpretation of reaping knives in archaeological context must allow for this diversity of usage.
R.E.C.A.M. Notes and Studies No. 1: Inscriptions of Ancyra
Authors: Mitchell Stephen 
Published: January 2007

Even a hurried glance at the walls of the Byzantine citadel, or a rapid inspection of the material collected by the Ankara Archaeological Museum at the depot in the Roman baths is enough to show that Ankara contains a richer collection of Greek and Latin inscriptions than almost any other city of the Anatolian plateau. A long sequence of epigraphic publications stretches back to 1555 when the companions of Augier Ghiselin de Busbecq, ambassador to the court of Suleiman the Magnificent, made the first copy of theRes Gestae, inscribed on the walls of the temple of Rome and Augustus. Since then a succession of travellers and epigraphists has added to the total of known inscriptions, and even if none of their discoveries can rank beside the record which the first emperor published of his life and actions, many of them are of considerable importance both for the history of Ancyra itself and in the wider context of the Roman Empire and the Byzantine world.However, any general study of these inscriptions and their historical implications has been hampered by the fact that they are scattered in a wide range of publications, many of them difficult to obtain. This situation has been partially remedied by Professor E. Bosch'sQuellen zur Geschichte der Stadt Ankara im Altertum, completed in its essentials by 1945, but only published after the author's death by the TTK press in Ankara in 1967. This contains a large proportion of the source material relevant to the city's history from its earliest appearance in the classical sources to the age of Constantine, accompanied by a commentary in German. However, despite its usefulness, the book has not fulfilled the need for a fullcorpusof the city's inscriptions.
An Athena Parthenos from Cilicia
Authors: Williams Hector 
Published: January 2007

In the winter of 1974 farmers working in their fields near the village of Selimiye about fifteen kilometres south-east of Ceyhan uncovered a small round limestone altar bearing an image in relief of the goddess Athena (Pl. XVII a). The form and attributes of the figure—left hand on shield, left leg slightly bent, Nike on right hand, aegis on breast—clearly indicate that the relief owes much to Pheidias' great chryselephantine statue in Athens. It may thus be added to a considerable number of representations dating back to Hellenistic times that show the interest in Pheidias' masterpiece in southeastern Asia Minor. In itself it is important as an addition to the handful of reliefs depicting one of the most famous monuments of antiquity.The altar joins a number of other similar monuments, mostly funerary in nature, of varying dimensions in the Adana regional museum. Its height is 0·64 m., its diameter at the base 0·38 m. It consists of a flat round base supporting a series of mouldings (torus, cyma reversa, fillet—Fig. 1a), a central drum divided unequally into a lower and a slightly projecting upper section, a further series of mouldings (fillet, ovolo—Fig. 1b) above which rises a biconical rim with flattened edge, a short continuation of the drum and finally a capping moulding (much mutilated in our specimen). The top is slightly convex with a shallow, rough depression in the middle 0·011 m. deep and 0·11 m. in diameter. Except for the relief and surrounding area the whole stone is dressed down with a claw chisel. There is some entasis apparent in the central portion of the drum.
Remarks about some Assyrian Reliefs
Authors: Porada E. 
Published: January 2007

To offer Richard Barnett remarks about Assyrian reliefs is a matter of self-indulgence. I wanted to have the reaction of this scholar most likely to be interested in my ideas about the meaning of the two principal scenes of the Black Obelisk of Shalmaneser III (858–24 B.C.); the role of the ziggurat in Assyria, on which I will touch only slightly; and a fragment from the reliefs of Sennacherib (704–681 B.C.). I have had to appeal for his aid for the classification of the latter since he is preparing the publication of the collected reliefs from the palace of Sennacherib with the help of Erica Bleibtreu.Each of the two scenes at the top of Shalmaneser's obelisk, Plate I, a—b, shows a foreign prince kneeling before the Assyrian king with hands and beard touching the ground in the posture of the greatest humility. The lower scene is often reproduced alone because the foreign ruler is Jehu of Israel, whose biblical association is of interest to the general public. The similarity of the two scenes, is unique and invites a search into its meaning. Fortunately, the identity of both foreign rulers is indicated in the inscription above the scenes.
“Louez-le sur la Harpe et la Lyre”
Authors: Spycket Agnès 
Published: January 2007

Ce verset du Psaume 150 s'applique bien à Richard D. Barnett, car durant sa féconde direction du Department of Western Asiatic Antiquities, il a fait restaurer, entre autres objets des tombes royales d'Ur, la harpe de Pu-abi et la lyre en argent. Ces réflexions sur les harpes et les lyres mésopotamiennes m'ont donc été suggérées par son article paru en 1969 dansIraq XXXI: “New Facts about Musical Instruments from Ur” (pp. 96–103).Il faut bien souligner que sans les instruments des tombes d'Ur, “royalement” exhumés par Sir Leonard Woolley, notre matériel de base serait uniquement iconographique, ce qui n'est certes pas négligeable; mais les représentations d'instruments sur les reliefs et les cylindres-sceaux ne nous renseignent pas comme les objets eux-mêmes; par contre elles permettent de préciser la position du musicien par rapport à l'instrument – debout ou assise –, suivant la taille de la lyre et de la harpe. Les femmes dominent dans les tombes d'Ur: les quatre lyres du “Puits de la mort” étaient jouées par quatre femmes au moment de l'holocauste.
The Dream of Kurigalzu and the Tablet of Sins
Authors: Finkel Irving L. 
Published: January 2007

A rather choice cuneiform fragment from the British Museum forms the subject of the present note, viz. BM 47749 = 81-11-3, 454, here copied as Fig. 1. The composition may be conveniently classed in the “historical-literary” genre, or more specifically, in the “historical epic” genre, although at present no more than one-quarter of the original tablet is available. It is with much pleasure that I dedicate this study to the distinguished sometime Keeper of the Department of Western Asiatic Antiquities who is the recipient of this celebratory volume, and who for so many years had the resources of the British Museum tablet collections under his care.The small group of historical epics discussed by A. K. Grayson includes three Late Babylonian copies of texts from Babylon describing events under second millennium kings, two of which are concerned with Kassite kings; a Kurigalzu (probably Kurigalzu II), and Adad-šuma-uṣur. The present Late Babylonian text, BM 47749, is likewise concerned with one of the kings named Kurigalzu, but differs from the published manuscripts in having one, rather than two, columns per side.
qlqlt' tubkinnu, Refuse Tips and Treasure Trove
Authors: Greenfield Jonas C. , Shaffer Aaron 
Published: January 2007

The Tell Fekherye inscriptions contained more than one surprise for both the Assyriologist and the Aramaist. In this article we will deal with Aramaicqlqlt' which was previously known from texts in various Aramaic dialects from the first millennium C.E. and also withtubkinnuits equivalent in the Akkadian text. Richard Barnett, to whom this article is dedicated, has opened one of the great treasure troves to the scholarly world – the Western Asiatic collections of the British Museum. We take this occasion to also comment on treasure trove in the ancient world.The wordqlqlt'occurs in the Tell Fekherye inscription in 1. 22 of the Aramaic text:wmn qlqlt' llqṭw 'nšwh š‘rn klw“may his people scavenge barley to eat from the rubbish dump(s)”. The nounqlqlt' in this form occurs in various Targumic texts. Thus in 1 Sam 2:8 (= Ps 113:7)mē'ašpōt yārīm 'ebyōn“He lifts up the needy from the refuse heap” is translatedmiqqilqilātā/mĕrīm/yerīm hĕšīkā. Theša‘ar ha-ḥarsītof Jer. 19:2 is translatedtĕra‘ qilqiltā“dung gate” and the enigmaticśēfātayimof Ps 68:14 was interpreted as a plural of 'ašpā“dung heap, refuse dump” and translatedqilqilātā.The same translation was offered for 'ašpātōtof Lam 4:5.