bluuebunny/crossref_metadata_2025_split huggingface dataset:
Countless Simson line configurations
Authors: Bradley C. J. , Bradley J. T. 
Published: January 2007

The Simson line property is normally associated with points on the circumcircle of a triangle. It is embodied by the following theorem.Given any triangle ABC and a point P in the plane of the triangle, if perpendiculars from P on to the sides BC, CA, AB meet those sides at L, M, N respectively then L, M, N are collinear if and only if P lies on the circumcircle of triangle ABC. The line LMN is then known as the Simson line of P.
Dungeons, dragons and dice
Authors: McLean K. Robin 
Published: January 2007

My younger son has become interested in the game “dungeons and dragons”. He is intrigued by the shapes of the dice that are used to play the game and by the number of faces they have. Besides the standard cubical die with its 6 faces, there are the other regular solids with 4,8,12 and 20 faces. There is also a die with 10 faces, each in the form of a kite, and my informant points out longingly that our local games shop has a die with 100 faces. “Could you have one with an odd number of faces?” he asks.His innocent question led me to think about many mathematical aspects of dice. This article answers his question, examines the geometry of dice (highlighting some unnamed solids which deserve to be better known to model-makers), considers surprising aspects of the mechanics of tossing dice and describes sets of unusual dice whose probabilities offer scope for many games which can trap the unwary gambler.
Sums on Channel 4’s “Countdown”
Authors: Glasbey C. A. 
Published: January 2007

As part of a daily game-show on Channel 4
television, contestants on
Countdown have to
combine up to six numbers to produce a specified
(but randomly chosen) three-digit result. For
example, a few weeks ago they were given the
numbers 4, 5, 7, 8, 9 and 10. By use of addition,
subtraction, multiplication and division (provided
that the result is an integer) they had to use
each number at most once to obtain the number 526.
And they have only 30 seconds in which to do it!
One possible solution turned out to be
(7 x 9 + 4) x 8 - 10 = 526.
Newton's teaser
Authors: Mackinnon Nick 
Published: January 2007

This article looks at some of the history of “Leibniz's series”and at Newton's riposte in a letter to Leibniz, the Epistola Posterior:On the way we shall take in Gregory's well known contribution to the problem, and Newton's own description of how he discovered the binomial theorem using a method that has considerable appeal in classrooms today. For light relief Newton's apples will make an entrance. I have tried to track down as many copies of the original manuscripts as possible, as these have a great motivating effect on students. Knowledgeable readers will realise that this article is really an extended review of three magnificent sources, The Mathematical Papers of Isaac Newton, edited by D.T. Whiteside, Leibniz in Paris 1672-1676, by J.E. Hofmann, and The Correspondence of Isaac Newton edited by H.W. Turnbull. My interest in the history of mathematics stems from a conversation with Professor Whiteside at the MA conference at Leicester in 1990, during which it became clear to me that despite having read and digested the works of Bell, Kline and Boyer, I knew nothing of the history of the calculus I was supposed to be teaching.
A gemstone in matrix algebra
Authors: Crilly Tony 
Published: January 2007

The history of mathematics is an abundant field for making surprising discoveries. Some luck is necessary, but whereas the literary tradition has been extensively explored by scholars, finding a nugget in the history of mathematics is not so difficult as turning up a new fragment by Jane Austen, or a lost piece by Mozart. In my case I struck lucky in the theory of matrices.As is well known, the theory of matrices arose during the 1850s – a useful benchmark is the publication of Arthur Cayley's celebrated memoir of 1858, A memoir on the theory of matrices, a paper which generations of mathematicians have taken as signalling the beginning of matrix theory. Even today the opening paragraphs serve as a useful introduction to the subject.
The concept of integration: a fundamental approach
Authors: Hobbs David , Relf Simon 
Published: January 2007

According to Richard Courant and Herbert Robbins writing more than fifty years ago in their classic book What is Mathematics? (which is still in print)‘... today the calculus can be taught without a trace of mystery.’Sadly for many students entering university with A level Mathematics, and for some leaving university with a degree in Mathematics, this is not so. As was noted by John Smith, for some students there appears to be little understanding of the principles.
Generalising ‘Sums of cubes equal to squares of sums’
Authors: Mason John 
Published: January 2007

David Pagni drew attention to a result which is ascribed by Dickson [2, p.
286] to Liouville (1857), that the sum of the cubes of the number of divisors of
each of the divisors of an integer, is equal to the square of their sum. For
example, the divisors of 6 are 1, 2, 3, and 6, which have 1, 2, 2, and 4 divisors
respectively, and
Pagni observed, as have others, including Mason et
al. [4, p. 179], that the reason Liouville’s result works is
because the numbers generated are element-by-element products of sequences of the
form {1, 2, ..., t}, which are well known to have the
sum of their cubes equal to the square of their sum.
Vector products
Authors: Gerrish F. 
Published: January 2007

In his thought-provoking Note 82.45 (November 1998) about products of vectors, Bob Ardler asks (p. 454) “Why does dot thrive in n dimensions, but cross only in 3?” and (p. 456) “Which, if any, generalisations of the cross product have been pursued?”
Both of these matters have been treated fairly recently in several journals, including the Gazette, but the subject was first discussed and completely settled in 1942 by B. Eckmann in [1] (see especially pp. 338-339); cf. also [2].
The factorial function: Stirling’s formula
Authors: Fowler David 
Published: January 2007

How big is n!? For example, to pluck a number out of thin air, what is the order of magnitude of 272! ?This is the third note of a series on the factorial. The two previous notes [1] and [2] dealt with the factorial function x! while here we only consider n! when n is an integer, but its main results also apply to non-integer arguments. This note is longer and more elaborate than the previous ones, but the principal result is in the opening section. Only aficionados need go any further.
The Site of Derbe; A New Inscription
Authors: Ballance M. 
Published: January 2007

The question of the site of Derbe has for many years exercised the ingenuity of those who have studied the topography of ancient Lycaonia.As long ago as 1824 Leake wrote that “of the cities, which the journey of St. Paul has made so interesting to us, the site of one only (Iconium) is yet certainly known. Perga, Antioch of Pisidia, Lystra, and Derbe, remain to be discovered”.Leake's own conjecture as to the site of Perga was confirmed within thirty years; Antioch was fixed beyond reasonable doubt by Arundell in 1833; and fifty-two years later Sterrett confirmed Leake's suggestion that Lystra lay at Hatunsaray.The following dedication by the council and people of Derbe, found by the writer in 1956 at Kerti Hüyük, twenty-two kilometres north-north-east of Karaman, provides an answer to the last of Leake's problems and shows that his own location of Derbe at Maden Şehir, based though it was on the slenderest of evidence, was probably closer to the truth than any of those proposed by his successors in the field.
Preliminary Report on a Survey of Pre-classical Remains in Southern Turkey
Authors: Mellaart James 
Published: January 2007

During the Autumn of 1951 and from April to November, 1952, a survey of pre-classical remains in still mostly unknown areas of Southern Turkey was undertaken with the grant of a scholarship from the British Institute of Archaeology at Ankara (for the session 1951–2). A renewal of this scholarship in 1953 will make the continuation and completion of the survey possible in 1953–4.A vast amount of new material, some of which is of great importance for Anatolian prehistory, having been collected, it was considered advisable to write a preliminary report dealing with the pottery in order to make preliminary results immediately available rather than postpone it until the end of the survey. Hence the sketchy nature of this report which deals with pottery groups only, and the unavoidable omission of the description of the sites, size, period and distribution maps and general conclusions.
Ursu and Ḫaššum
Authors: Smith Sidney 
Published: January 2007

Professor Garstang, Whose excavations and geographical studies have so notably increased sources of information about, and our knowledge of, eastern Cilicia in early times, will have watched with interest, and perhaps with amusement, the way in which, in modern studies of texts, locations proposed for Ursu have jumped about over a considerable area, in which physical features might be expected to restrict the possibilities. As the story of Ursu in the second millennium ends just before that of Qizzuwadana begins, so far as our present information goes, it may not be inappropriate to dedicate a brief account of the development of evidence about, and the changes of opinion concerning, the situation of the city and the land to the friend who has often discussed Qizzuwadana with me during the last thirty years; the course taken is not without its lessons for criticism, which should be a form of intellectual discipline.The reason for believing that Ursu was a city in the mountainous region Ibla was an inscription of GU.DE.A, that for identifying Ibla with part of the Amanus was based on texts concerning Naram-Sin. The argument seemed simple and logical enough for Peter Jensen to identify Ursu with Arsuz, by which, probably, he understood no more than a location on the coastal strip west of the Bailan Pass.
Beycesultan, 1959: Sixth Preliminary Report
Authors: Lloyd Seton 
Published: January 2007

A final season of excavating at Beycesultan was arranged in the autumn of 1959 and lasted from 15th September to 28th October. The work was once more in charge of the Director, who was accompanied by Mrs. Seton Lloyd and a staff consisting of Mr. Martin Harrison (Institute Scholar for 1958–59) and Mrs. Harrison, Mr. Harry Smith of Christ's College, Cambridge, Miss Carol Cruikshank, Mr. Michael Brett as architect and Bay Osman Aksoy as Turkish Government representative. The Assistant Director and Miss Clare Goff also took part in the excavations during the second half of the season.It had been decided on this occasion to concentrate the entire resources of the expedition on the continued clearance of the Middle Bronze Age palace on the eastern summit of the mound, partly excavated in the seasons of 1954 and 1955, in the hope of recovering as much of the plan as possible before the excavations finally closed down. This was accomplished with considerable success. Two large new areas of the building were cleared and a point reached where any further extension would have met with serious practical difficulties.
The Overland Route across Anatolia in the Eighth and Seventh Centuries B.C.
Authors: Birmingham J. M. 
Published: January 2007

An overland route by which oriental merchandise and ideas were transmitted to the Ionian Greeks via the Anatolian plateau and the river valley routes of the west was long ago posited by Hogarth, and supported by Karo, Barnett and others, although there was little evidence from central Anatolia to confirm it. More recently this route was virtually discounted in favour of a sea route from N. Syria, especially Carchemish, through the port of Al Mina, to Greece and Etruria, via Cyprus, Rhodes and Crete, discussed by Sidney Smith, Humphrey Payne, Mrs. Maxwell-Hyslop and others, which is assumed to have been at its height in the earlier eighth century; and Barnett has also shown the importance of a third route, from Azerbaijan to Trebizond and west via the Black Sea, for which the main evidence, a tomb group from the Caucasus, is probably later seventh century.It is clear that the second of these three routes carried the bulk of Oriental trade to Greece and the west. Undoubtedly the most important Orientalizing influences on Greece, as shown by Payne, were those from the Cypro-Levantine cultural province, and there is ample evidence of the exchange of pottery, terracottas and ornamental bronzes of Cypriot and Phoenician production between the Syrian coast, Cyprus, Rhodes, Samos, Miletus, Chios, Delos and the west.
Excavations at Çatal Hüyük, 1965, Fourth Preliminary Report
Authors: Mellaart James 
Published: January 2007

A fourth season of excavation at Çatal Hüyük took place between 18th July and 25th September 1965 under the auspices of the British Institute of Archaeology at Ankara with Professor O. R. Gurney as director administratively responsible to the Turkish Authorities. The excavation staff were Mr. and Mrs. James Mellaart, Miss Pamela Pratt and Miss Priscilla Berridge as conservators, Miss Raymonde Enderlé Ludovici (artist), Mr. and Mrs. N. Alcock (surveyor), Mr. Ian Todd, Mlle Anne Timonier and Mr. J. Jurriaanse as field assistants. Bayan Nemika Altan and Bay Mehmet Turgut, both from the Ankara Archaeological Museum, were our official Turkish Representatives.The excavation was sponsored by the British Academy, the Universities of Edinburgh and London, The Royal Ontario Museum, Canada, the Wenner-Gren Foundation for Anthropological Research, the Bollingen Foundation, both in New York, the Australian Institute of Archaeology, the British Institute of Archaeology at Ankara and the German Archaeological Institute in Berlin. BP Aegean Ltd. in Istanbul once again supported the expedition with survey equipment and transport.
The Chipped Stone Industry of Avla Dağ
Authors: Todd Ian A. , Pasquare Giorgio 
Published: January 2007

The mountain Avla Dağ lies c. 245 km. SE. of Ankara, c. 8 km. SSE. of Ürgüp on the east side of the Damsa Çay valley, in the vilayet of Nevşehir.Obsidian implements were first found on this site by Dr. Giorgio Pasquare of the Maden Tetkik ve Arama Enstitüsü, Ankara, during the course of a geological survey of the Ürgüp area in 1963–4. A considerable quantity of obsidian implements and flakes was collected at the time, and subsequent visits to the area by the authors have resulted in further additions to this collection.The geological section of this paper was written by Dr. G. Pasquare, and the archaeological section by I. A. Todd.
Prehistoric Sites in the Göksu Valley
Authors: French D. H. 
Published: January 2007

The valley of the river Göksu (the ancient Calycadnus) is not unique as a road through the Taurus mountains. At least one other route was used in antiquity; this was by the Cilician Gates (now the Gülek boğazı). The valley of the Göksu, however, provides the easiest means of access from the coast to the plateau and, conversely, the easiest descent from the plateau to the coast. At the upper end of the route lies the Konya Plain with the sites of Çatal, Can Hasan, Karahüyük-Konya and numerous mounds of the Hittite period; at the lower end, the Plain of Adana and the sites of Mersin and Tarsus.The excavations at Çatal East and West, Can Hasan and Karahüyük-Konya promise to produce an almost complete pottery sequence for the Konya Plain. At certain points in this sequence influence from the south coast has been suggested. Traces of this contact, if it existed, between the two areas might possibily be found in the valley of the Göksu. With this possibility in mind, a re-examination of the Mut area was carried out and, at the same time, an attempt was made to verify the suggested relationship of the Göksu valley to the two “culture-areas”, the Konya Plain and the Plain of Adana, from the Neolithic period until the Iron Age.
Aşvan 1968–72: the Excavations
Authors: French David 
Published: January 2007

The purpose of this long, interim report is fourfold:1. to provide a straightforward preliminary account of results of excavations in the Aşvan region in the years 1968–72;2. to attempt an explanation of how and why the modern studies were carried out;3. to offer a tentative demonstration of the relevance of the modern studies to archaeology (i.e. the excavation of objects and structures);4. to outline, by using concrete examples, the general theory and methods, and thereby to demonstrate the feasibility of a co-ordinated approach.The Keban Project was founded in 1968 under the aegis of the Middle East Technical University and with the co-operation of the Turkish Government. The stated aim of the Project was the rescue of historical materials from the area to be flooded by the Keban Dam, located just below the confluence of the Murat and the upper Euphrates (Fig. 1). The necessity of immediate action had been demonstrated largely through the efforts of the Faculty of Architecture and Restoration. In the area of the flood zone staff and students had carried out feasibility and recording surveys which then made clear both the nature and requirements of a rescue operation. Their results were published in Doomed by the Dam (METU, Ankara 1967). In 1968 a Committee (METU Keban Dam Area Salvage Project Executive Committee) was set up, under the chairmanship of the then Rector of METU, Dr. Kemal Kurdaş, to co-ordinate the efforts of those various teams, both Turkish and foreign, which had accepted the Committee's appeal for joint action in a rescue operation.
Kill-off Patterns in Sheep and Goats: the Mandibles from Aşvan Kale
Authors: Payne Sebastian 
Published: January 2007

Reports on animal bones from archaeological sites often include information about the “kill-off pattern” for each species – i.e. the relative representation of different age-groups in the sample. Osteologists believe that this information can be used as evidence for whether an animal was wild or domesticated, and, if domesticated, about the way in which man managed the animal. In this paper a method is described for recording such data for sheep and goat using mandibles and mandibular teeth; the analysis and interpretation of such data is discussed using excavated samples from Aşvan Kale.When people keep sheep or goats, the age at which the animals are slaughtered depends on a range of factors: on the relative value placed on the different products, on the characteristics of the stock, and on a range of environmental factors – in particular, seasonal variation in the availability of grazing and feed. If meat production is the aim, most of the young males are killed when they reach the optimum point in weight-gain, only a few being kept for breeding.
A Babylonian Architect?.
Authors: Wiseman D. J. 
Published: January 2007

Professor Seton Lloyd's publications and teaching have always been marked by his profound understanding of Mesopotamian architecture. It therefore seems appropriate, in this volume to his honour, to present some hitherto unpublished tablets which may add a little to our knowledge of some aspects of the ancient practice of surveying.
The small tablet BM.38217 (Fig. 1), probably originating from Babylon itself, shows in elevation a six, originally seven, stepped ziggurat with the principal dimensions given, UŠ being used for the length, and SAG (the “short side” of the rectangle as drawn) for the height. The second level is described as “Front (-view) of the dwelling of Anshar” (pa-ni šu-bat an-šár). While this note may well apply to the whole of this unique plan, it is to be observed that the first two storeys have accentuated (and external) markings which must represent the frontal and lateral access. The inner markings are perhaps to show where the ramps or stairway crossed the front of the main building (as in the ziggurat at Ur). The gaps in the base of the third and probably fourth (and higher?) stages may show that a direct frontal stairway to the seventh stage was envisaged. This seems a better explanation than that a five staged ziggurat is shown imposed upon the ground-plan of an adjacent and larger building. The lower stages are certainly not the plan of any two-storied “temple of Anshar” or of a gate-building.
Biliotti's Excavations at Satala
Authors: Mitford T. B. 
Published: January 2007

Alfred Biliotti, British vice-consul at Trebizond, spent nine days at Satala in 1874. He is well known as an enquiring and meticulous observer. The account of his visit, in a consular paper in the British Museum, remains by far the best description of the legionary fortress, and holds several items of particular interest.Biliotti was able to record at leisure structural remains in an altogether better state of preservation than is true today. His 18 ft walls, with traces of ashlar facing, are now reduced to rubble cores visible, except at the north-east and south-east angles, only in eroded sections (Figs. 1, 2). Of the square projecting towers there is now barely a trace. The supposed look-out towers reported on the surrounding mountain tops are known from no other source.His are the only excavations on record in Armenia Minor, and at any point on the limes itself between Trapezus and the rescue work north of the Keban dam.His account is a valuable source for social conditions in the villages during the late Ottoman period. The way of life at Satala depended on techniques that can have changed little since Roman times, and survived virtually unaltered until the introduction of tractors in the later 1960s.
Ptolemy II and Halicarnassus: An Honorary Decree
Authors: Frost Frank J. 
Published: January 2007

This white marble slab was cut into its present shape when the verso was incised for use as a decorative panel. An unknown amount of text is therefore missing on all sides, while a few spots in the middle make for difficult reading because of patches of mortar and some pick marks, notably in the first two lines. I am unable to guess at the original length of line, other than to say that it was considerably longer than what is preserved here.Height, 0·24 m.; width, 0·187 m; thickness, 0·043 m.Height of letters, 0·011–0·014 m.At some time between 1960 and 1964, this inscription was brought to the Castle of St. Peter in Bodrum, which has in recent years doubled as the Bodrum Museum under the wise and careful supervision of Director Halık Elbe. Unfortunately, no one today knows who brought the stone in, or where it had been found, for the Museum fell heir to a vast store of material of archaeological value before any system of cataloguing could be devised.
A Byzantine Well-Deposit from Anemurium (Rough Cilicia)
Authors: Williams Caroline 
Published: January 2007

Excavations at the coastal Cilician city of Anemurium (Eski Anamur) have recently brought to light a significant well-deposit containing pottery, lamps, coins and miscellaneous metal objects. The well appears to have been deliberately filled in on one occasion for reasons that we cannot now ascertain. The homogeneous nature of the deposit is indicated by the fact that joining sherds come indiscriminately from all levels in the deposit. Since all the pieces from any one vessel are generally not present and the majority of sherds are body sherds from amphorae for which there are no necks, handles or bases, it would seem that those charged with the task of filling in the well took whatever was closest to hand for their work and it is quite fortuitous that almost whole vessels came to be included in the deposit.The terminus post quem for the act of filling in the well is provided by two coins of Heraclius belonging to the years A.D. 629–630 and 630–631. The evidence of coins also points to widespread abandonment of the city c. A.D. 660, although the appearance of a few coins belonging to the last decades of the seventh century seems to indicate a limited degree of continued occupation.