bluuebunny/crossref_metadata_2025 huggingface dataset:
Seeing induction at work
Authors: Anderson Johnston
Published: January 2007

For many sixth-formers and undergraduates, the method of proof-by-induction seems to resemble nothing so much as a confidence trick. They appear to have little or no appreciation of the logical foundation of the method; frequently, they have been given a mysterious recipe which might just as easily be “eye of newt and toe of frog”. They slavishly follow the rules given and so it is little wonder that they are confused when, having been cajoled incessantly not to beg the question, they are now seemingly allowed to assume the answer. However, it is not my intention in this article to present yet another justification for the principle of mathematical induction, important as that might be; in any case, perfectly good articles on the subject have already appeared in the Gazette [1,2].
Connected means
Authors: Russell George
Published: January 2007

In recent years the continuous connection between various means has been well-established, but will still be new to many Gazette readers. The double interest in publishing this article is that it is by a sixth-former, showing some of the stunning calculus possible at an elementary level.

VWB
Varying the approach to A-level mathematics
Authors: French Doug
Published: January 2007

Much debate about A-level mathematics centres on organisational, assessment and content issues, whilst another major focus of interest concerns the role of the microcomputer in the sixth form classroom. Many of these issues have been discussed at length in a recent article in the Gazette by Bibby [1], but he does also seek to draw attention to the rather limited success there has been in directing attention to the importance of “process” as well as “content” in A-level mathematics.
Calculus at A-level and its understanding
Authors: Maher Philip
Published: January 2007

It is my contention that in the teaching of calculus at A level we have, all too often, been producing an understanding of calculus—and, implicitly, a view of mathematics—that is distorted and unrealistic. I am glad of the chance to air these criticisms in this contribution to the debate about the future of sixth form mathematics. (In this article, “sixth form” is synonymous with A level, whether studied at school or college.) Nevertheless, as I maintain later, the changes now being wrought in sixth form mathematics generally may well prove beneficial.
Some recent discoveries in elementary geometry
Authors: Scott Paul
Published: January 2007

I have always disagreed with government ministers who assert that it is a good idea to separate teaching from research at the universities. For I believe that with mathematics, research and good teaching go hand in hand. And if we interpret ‘research’ in its widest terms of questioning, discovery, involvement, etc, then I believe that the same holds true at the school level. Mathematics needs to be taught as a vibrant, living subject which challenges the intellect and the imagination, not as a dusty collection of historical facts. Further, asking questions is just as much fun as answering them!
What do you do about 4πr2?
Authors: Mackinnon Nick
Published: January 2007

The mensuration formulae for curved objects ought to be one of the highlights of everyone’s elementary mathematical education. I get my pupils at 13 and they've already been taught that the area of a circle is πr2. It is very upsetting to find that they usually have seen no sort of justification of this result, so they don’t think of it as surprising when π, which was introduced in the circumference formula, mysteriously pops up again in the area formula.

This year I thought I would put some effort into justifying the surface area formula for the sphere. I don’t claim that what follows is very original, and of course the main idea goes back to Archimedes, but I hope this article will save readers a bit of work at least.
Factors in recurrence relations
Authors: Nash Chris
Published: January 2007

Suppose we are given a sequence of numbers defined by a linear recurrence relation with constant coefficients, for example the Fibonacci numbers which are defined by:
π in my eye
Authors: Quadling Douglas
Published: January 2007

When students first meet Simpson’s rule, we look for simple applications to show them what it can do. I don’t imagine I am the only teacher who has suggested using it to find a numerical value for π - which up until then they have always had to take on trust.
A new approach to solving the cubic: Cardan’s solution revealed
Authors: Nickalls R.W.D.
Published: January 2007

The cubic holds a double fascination, since not only is it interesting in its own right, but its solution is also the key to solving quartics. This article describes five fundamental parameters of the cubic (δ, λ, h, xN, and yN), and shows how they lead to a significant modification of the standard method of solving a cubic, generally known as Cardan’s solution.
Bracelets
Authors: Green Paul , Liebeck Pamela
Published: January 2007

Our original source for this investigation was an Open University video on Secondary classroom practice (OU video no. PM644). Since then, however, we have seen the problem mentioned in [1], [2] and [3]. The investigation as presented to pupils is as follows:

Choose two integers between 0 and 9 (not both 0) and write them down. As an example, we shall choose 0 and 2. Write down their sum, doing the addition modulo 10. Then write down the sum of the last two numbers in the sequence, again doing the addition modulo 10. Repeat this process. Our example gives the sequence
What does “mean” mean?
Authors: Machale Desmond
Published: January 2007

In many situations we are faced with two numbers 0 ˂ a ≤ b as values of some variable and we are forced to produce a compromise value which in some way is intermediate between a and b. Such a compromise value can be termed an average or a mean of a and b and we would expect it to lie between a and b, with equality if and only if a = b. There are many different kinds of mean in elementary mathematics (see, for example, “Connected means” in the June 1988 Gazette). Perhaps the following three are the best known and the most important.
An intuitive approach to calculus
Authors: Smith John D.
Published: January 2007

“A derivative is a linear transformation which approximates a function near to a point.” I heard this definition for the first time in 1964, in a lecture at Oxford on the calculus of several variables (the lecturer was D.A. Edwards). The words came as a revelation, and from then on I had a new conception of differential calculus. At school, I thought that I knew about calculus because I could write out proofs of differentiation ‘from first principles’. I enjoyed going through the hoops and proving that δy/δ tends to a limit, but somehow the idea of differentiation never became ‘part of me’.
A deplorable fallacy – and a minor fault
Authors: Hilton Peter , Pedersen Jean
Published: January 2007

In three earlier articles we drew attention to an astonishing error which appears in several texts in the United States, even some of otherwise very high quality. The error relates to a fallacious procedure for the calculation of the Euler characteristic of a polyhedron, producing, in particular, the extraordinary statement that the Euler characteristic of a torus is 2.
Gregory of Saint Vincent: a pioneer of the calculus
Authors: Meskens Ad
Published: January 2007

In MacKinnon‘s article he makes mention of Gregory of St Vincent‘s method of squaring the circle, giving the impression that this method involved ruler and compass, an impression that is reinforced by the title and extravagant frontispiece of the book. In this article I intend to correct this impression by describing St Vincent‘s method, which used a kind of integration method, to calculate, among other things, the area of the circle.
Sieving with sums
Authors: Robertson Jack M. , Webb William A.
Published: January 2007

A number of deep theorems and unsolved problems ask questions about the relationship of the additive and multiplicative structure of the natural numbers. The famous four squares theorem of Lagrange says that if we form all possible sums of four squares we get the entire sequence of nonnegative integers. Goldbach’s conjecture states that if all possible sums of two odd primes are formed we get every even integer greater than 4.

The depth and difficulty of such problems stand in surprising contrast to the similar question: “Which numbers are not generated when all possible sums of two or more consecutive natural numbers are formed?” The answer is all powers of 2 and the proof is accessible to anyone who can sum arithmetic sequences. This result is an excellent discovery exercise for students, particularly appropriate for teacher training courses.
Squaring the circle:Transcendence, Logarithmic Forms and Diophantine Analysis
Authors: Baker A.
Published: January 2007

The evolution of transcendence into a fertile theory with numerous and widespread applications has been an especially exciting development of modern mathematics. The subject was originated by Liouville, Hermite and Lindemann during the last century. Liouville showed that there is a limit to the precision by which an algebraic number, not itself rational, can be approximated by rationals and thereby gave the first examples of transcendental numbers; in fact it suffices to take any non-terminating decimal with sufficiently long blocks of zeros or any continued fraction in which the partial quotients increase sufficiently rapidly.
A century of textbooks
Authors: Quadling Douglas
Published: January 2007

In 1952 I was invited, with teachers of mathematics from many other schools, to a reception hosted by the Cambridge University Press. The guest of honour was A. W. Siddons, and the purpose was to celebrate the fiftieth anniversary of the initiation of Godfrey and Siddons’ first book: Elementary Geometry. There can be few authors who survive to enjoy such an occasion; fewer still whose book remains in print and continues to sell well after fifty years. But this was a book which marked a turning-point in the teaching of mathematics, and set a standard for mathematical education which remains relevant as we approach the end of the century.
Problems to sharpen the young
Authors: Hadley John , Singmaster David
Published: January 2007

An annotated translation of Propositiones ad acuendos juvenes, the oldest mathematical problem collection in Latin, attributed to Alcuin of York

In researching the history of recreational mathematics, one finds that the Propositiones ad acuendos juvenes of Alcuin of York is frequently cited as the earliest problem collection in Latin. The text contains 56 problems, including 7 major types of problem which appear for the first time, and 2 major types which appear for me first time in the West. By any standard such a collection is of major historical interest, so it is surprising that a critical edition was not prepared until Folkerts' edition of 1978, and yet more surprising that no English translation has ever been produced.
Clarifying conditional calculations with ‘Jolly Roger’
Authors: Johnson Roger W.
Published: January 2007

The dice game ‘Jolly Roger’ may be played with 5 regular dice or 5 special
‘Jolly Roger’ dice. A ‘Jolly Roger die is a regular die in which the 1 spot is
replaced by a skull and crossbones (i.e. replaced by a ‘Jolly Roger’). Play cycles
through the players 5 times so that each player has 5 turns in the game. Each turn
consists of 3 rolls of the 5 dice. On a particular roll of the 5 dice a player
(pirate) can score points (capture
cargo) only when some ‘Jolly Rogers’ appear face up. According to
Koplow Games (1993):

“For each ‘Jolly Roger’ that appears on a roll of the dice, the player
can capture one other die and score its points. If three ‘Jolly Rogers’ are
rolled, then only the points on the remaining two dice can be scored. If
five ‘Jolly Rogers’ are rolled, no points are scored, as the pirate fleet
has scared away all cargo ships.”
Determinants of block matrices
Authors: Silvester John R.
Published: January 2007

Let us first consider the 2 x 2 matrices

and

Their sum and product are given by

Here the entries a, b, c, d, e, f, g, h can come from a field, such as the real numbers, or more generally from a ring, commutative or not.
A simple energy-conserving model exhibiting elastic restitution
Authors: Bridges Richard
Published: January 2007

From the date of my own A level studies (many moons ago!) I have been dissatisfied with the presentation of the law of elastic restitution. The title Newton’s ‘Experimental’ Law implies that it is a purely empirical phenomenon, yet if there is a wide range of conditions in which it is approximately valid (and it isn’t worth using at all if this isn’t true), then there must be some reason for it. Equally unsatisfactorily, the law implies loss of energy in most circumstances. Even in my school days I could see that the usual argument about conversion into heat, sound etc didn’t really hold water, as this process couldn’t conceivably be instantaneous. A recent article by O’Connor [1] stimulated me to crystallise my thoughts on the subject [2], and I was later able to develop a simple and plausible mechanical model exhibiting restitution, which also conserved energy [3]. My presentation in [3] was mainly focussed on the physical consequences of the model, and solution of the differential equations involved was numerical. Yet, in the simplest case, the model is amenable to fairly elegant exact analytical techniques, which it is the aim of this paper to present. Apart from the interest of the model, the methods used are a nice illustration of the role of normal modes in the solution of simultaneous linear differential equations—a topic approachable by A level students of Further Maths, or by first-year undergraduates.
Farey rabbits
Authors: Arcavi Abraham , Bruckheimer Maxim
Published: January 2007

The Farey sequence of order n(Fn) is the sequence of all reduced fractions between 0 and 1, whose denominator does not exceed n, arranged in increasing order of magnitude.

For example, F6 is .

The Fibonacci sequence is the sequence for which u1 = 1, u2 = 1 and un = un-1 + un-2,namely, 1, 1, 2, 3, 5, 8, 13, … , un

At first sight, there is little connection between Farey’s fractions and Fibonacci’s integers. The purpose of this note is to show and explore such a connection and hence derive some properties of the Fibonacci sequence directly from previously proved properties of the Farey sequences. The former properties are well-known, but their rather unusual derivation from Farey properties may have some interest.
Greek Potters at Al Mina?
Authors: Boardman John
Published: January 2007

The subject of this paper is a small group of cups found by Sir Leonard Woolley in his excavations at Al Mina (now in the Turkish Hatay). It has been hitherto ignored because, with some reason, the vases were believed neither to be Greek imports nor the products of Cypriot or North Syrian potters. I hope to demonstrate that they could be the work of Greek potters established at Al Mina towards the end of the 8th century B.C. by discussing their apparent relationship to contemporary Greek, Cypriot and North Syrian work. Most of the cups and fragments are in Oxford, and there are fragments in the London Institute of Archaeology and the Museum of Classical Archaeology in Cambridge which I have seen. Nos.1–23in Fig. 1 and Plates XXIV–XXV illustrate the shapes and all the types of decoration met in the group.

All are two-handled cups, the Greek geometricskyphos. The shape, with decoration of this type, is most common in Euboeo-Cycladic vases of the second half of the 8th century, and a considerable number of theseskyphoiwere carried to Al Mina by the Greeks. It was rarely imitated in Cyprus, as we shall see, and is not at home further east.
New Urartian Inscriptions from Adilcevaz
Authors: Hulin P.
Published: January 2007

Adilcevaz lies on the north shore of lake Van, almost due south of the summit of Süphan Dağ (14,547 ft.). At its west end substantial remains of a lofty wall of later than Urartian times run down from below the Ahlat road to the shore of the lake (and actually into the lake, of which the relative level has evidently risen since the construction of the wall). It was on a largely concealed face (at right-angles to the line of the wall) of a stone block in this wall that it was reported that cuneiform writing could be seen.

Accordingly, in September, 1956, the writer inspected the wall, accompanied by his wife, who located the block some fifteen metres below the road in a short secondary wall-surface of dressed blocks, with hard rubble filling behind, parallel with the line of, and running inland from the broken end of a further wall projecting three or four metres in the Adılcevaz direction from, the main wall. The cuneiform writing proved to be visible as a result of the absence, close to the surface, of mortar between the inscribed block and the one lake-ward of it in the same course; and on poking away more mortar between the two blocks and up to the under surface of a third, larger, block, forming part of the next higher, and uppermost surviving, course, it was found that this under surface also bore cuneiform signs.
Anazarbus
Authors: Gough Michael
Published: January 2007

The site of the Cilician city known during the period of the Roman Empire as Caesarea, Caesarea by Anazarbus, or Anazarbus, is some 28 km. south of Kozan in the Turkish province of Seyhan. The place still retains its name as Anavarza, a hamlet built just outside the walls of the ancient city.

The choice of Anazarbus as a subject for research may seem to require some explanation. It was never one of the great cities of antiquity; indeed it is not yet certain that it even existed before the 1st century B.C. It never received more than scant notice from ancient authorities, while modern travellers, hampered by bad communications, a difficult climate, and a lawless population, were unable to spend more than a day or two at the site and consequently could not give more than a general idea of its monuments.

In 1949, as Scholar of the British Institute of Archaeology at Ankara, I had decided to study the Classical architecture of Cilicia, and at the same time to collect information on the many mediaeval castles in the district.
Assyrian Objects from Room M.2
Authors: Barnett Richard
Published: January 2007

The group of small objects from the priestess' room at Sultantepe is of much interest, firstly because they are well dated, secondly because they show signs of mostly originating from some not too distant market. Whereas the source of the alabastra may well be North Syria, it is perhaps not too bold to see in the fayence objects the products of a local factory, perhaps Harran itself.
Beycesultan Excavations: Fourth Preliminary Report, 1957
Authors: Lloyd Seton , Mellaart James
Published: January 2007

Short Reports on the Institute's excavations at Beycesultan, dealing with discoveries in the seasons of 1954, 1955 and 1956 have already been published in this journal (vols. V–VII). In the third of these reports, a break in continuity was occasioned by our temporary concentration on a single isolated discovery; and accordingly, before resuming the more general account, a short recapitulation of our operational sequence may be desirable.

In the final weeks of the 1955 season, a sounding was made in Area “A” on the western summit (see site-plan, Fig. 1), which revealed the presence in this part of the mound of a large public building of the Middle Bronze Age, corresponding in time to the “Burnt Palace” already partly excavated on the eastern summit (Level V). Some preliminary investigations were also made of three occupation levels (VI, VII and VIII) lying directly beneath this building (see Anatolian Studies VI). In 1956 an extension of this sounding was made in the form of a 5-metre trench more than 40 metres long, running out approximately eastwards towards the flank of the mound (Trench “S”). After passing through the already well established sequence of later occupations, further foundations of the Middle Bronze Age were here encountered and it became clear that the building discovered in Area “A” formed part of an administrative complex, perhaps covering the whole of the western summit, and surrounded by its own substantial enclosure wall.
Eastern Anatolia in the Chalcolithic and Early Bronze Age
Authors: Burney C. A.
Published: January 2007

The pottery described in this article was collected during a survey of ancient sites in eastern Turkey carried out in the summer of 1956. More than 150 Chalcolithic, Bronze Age and Iron Age sites were recorded: only the Chalcolithic and Early Bronze Age pottery is discussed here, the later periods being reserved for a future article. A considerable quantity of potsherds was collected, so that only a selection of the more significant examples has been illustrated. The zone covered by this survey is best described as eastern Anatolia within the mountains, excluding both the Pontic region and the south-eastern provinces of Turkey, bordering on Syria and Iraq: it is the narrowest part of the great natural bridge between Asia and Europe that has given Anatolia its long and varied history. The survey covered the greater part of the provinces of Sivas, Malatya, Elazığ, Muş, Bitlis and Van. Sites near Adıyaman, also visited, are not dealt with here. The plain of Iğdır, north of Mount Ararat, was partially explored in 1957, and yielded important material, but the plain of Karaköse proved to have few sites, and those with little surface pottery. The sherds here described are supplemented by intact vessels from Ernis, on the north-eastern shore of Lake Van, now in Van Museum.
An Honorific Inscription from Pisidian Antioch
Authors: Levick Barbara
Published: January 2007

One of the few inscribed stones which still remain on the hilly site of Pisidian Antioch is a large and impressive block, 0·564 m. by 1·091 m. by 0·475 m., with an inscription cut in elegant letters into the face which now lies uppermost. This stone has probably been moved only a few yards from its original position, for otherwise it would have been taken to the neighbouring town of Yalvaç for building purposes. Such a stone, perhaps originally the basis of a statue, would have been set up in a prominent place in the colony, probably in or near the main square, the Tiberia Platea, and its present position is not far from that square. It is surprising that so fresh-looking a stone should have escaped the notice both of the inhabitants of Yalvaç, and, apparently, of epigraphists. It has, however, been somewhat defaced, and the hole in the centre of the inscription indicates that it has been used for something other than its original purpose: see Plate XXXV(b).
Urartian Stones in the Van Museum
Authors: Hulin P.
Published: January 2007

Professor F. W. König published in 1956 a note listing and describing the stones lying in the Van Museum, as far as he was able to do so from photographs of them taken in 1954 by Professor H. Gamerith and placed at his disposal. Professor König's note included two sketches, based on the photographs, of the stones as they lay; and he gave to each stone in the sketches a number by which he referred to it in his list.

Visits to the Van Museum made in the course of journeys in eastern Turkey undertaken by the writer in September 1956 (accompanied and assisted by his wife) and in September 1957 (alone) have made possible the following amplified account of the Urartian stones in the museum. The numbers assigned to the stones in König's sketches are used as a means of reference; information already available in König's note or in his Handbuch is not repeated, except that identifications made by him from the photographs are repeated (in parenthesis) to make the list complete; numbers not occurring in the series relate to stones which could not be seen to bear any Urartian inscription.
Excavations at Can Hasan, 1966: Sixth Preliminary Report
Authors: French D. H.
Published: January 2007

The sixth season of excavations at Can Hasan took place between 28th August and 30th September. Additional work on storing and arranging the non-registered materials from the excavations continued until 12 th October. All materials other than the registered objects from the 1961 to the 1966 seasons are now stored in the depot at Can Hasan. These are the sherds, animal bones, heavy stone objects, the samples of stone, clay and other materials. They are stored by year and by category in locked storerooms in the dig house. In addition to the house bekçi there is now a full-time official bekçi for the Hüyük and for other hüyüks in the neighbourhood.

In the 1966 excavations Messrs. D. C. Biernoff, S. Payne and J. N. Postgate were field assistants; Mrs. Payne took charge of the work in the house, assisted by Mr. C. Slack and the Misses M. Bell, C. Prater, and T. Harrington-Smith. In addition Mrs. Payne had charge of the pottery; Mr. Payne of the obsidian, Miss Harrington-Smith of registration and Mr. Slack and Miss Bell of conservation and pottery mending. Bay Bedri Yalman from the Konya Museum represented the Turkish Government.
The Chipped Stone Industry of Çatal Hüyük
Authors: Bialor Perry A.
Published: January 2007

The analysis of the chipped stone industry of Çatal Hüyük East presented here is based on a collection of 1,377 pieces, of which only 366 are waste flakes. The collection represents the complete assemblage of chipped stone recovered during six weeks' excavation (17th May to 29th June, 1961) by Mr. James Mellaart at which the author assisted. All stone was saved. The area excavated covers approximately two-thirds of an acre, in which nearly forty houses from the various levels were uncovered. The considerable number of chipped stone implements which we collected from the surface of the mound during our first two days at the site (the presence of which along with an Early Neolithic pottery was initially responsible for Mr. Mellaart's special interest in the site) is not presented here. Except for the pleasure of presenting some beautiful examples of pressure flaked projectile points it would not alter the facts as garnered from the excavated material.
The Early Minoan Occupation of Knossos: A Note on some new Evidence.
Authors: Evans John
Published: January 2007

Following their discovery of the “Burnt Palace” at Beycesultan in the mid 1950's, Seton Lloyd and James Mellaart drew attention to a number of features of its architecture which seemed to indicate links with the palace architecture of Minoan Crete, and discussed the possible significance of these similarities (Lloyd and Mellaart, 1956 118–123, 1965 61, 62). Whatever this may be in terms of relationships between the two areas in the second millennium B.C., however, it seems clear that they cannot throw any light on the first appearance of palaces in Crete. The problems of the origin and development of the Cretan Bronze Age palaces are complex, and though they have been much discussed since the first excavations in the early years of the century, a major obstacle to progress has always been the lack of precise evidence, or even of any evidence at all, for the early stages of the process. As they stand, most of the palaces are the product of a series of rebuildings and remodellings over a long period, and it is not always clear just what they were like when first erected. Most frustrating of all, however, is the lack of evidence bearing on the question of whether they were preceded, during the Early Bronze Age, by buildings which were in any respect analogous in form and function.

It has long been clear that the sites of some of the major Middle and Late Minoan palaces were occupied during the Early Minoan period, but at Phaistos and Knossos at any rate extensive clearing and levelling in preparation for the erection of the Middle Minoan palaces has obliterated practically all traces of the Early Minoan buildings. At Phaistos Branigan has hinted that the fragments of walls found by Pernier (1935, pl. VI) on the highest point of the hill might have belonged to a building of some consequence, possibly similar to the Early Minoan II mansion known as the House on the Hill at Vasiliki (Branigan 1970, p. 41). Branigan thinks that in addition to the rooms mentioned by Pernier, there may be traces of a corridor similar to that in the Vasiliki building. Only the bottom two courses of the walls survive, so that it is difficult to say much about their construction, though it seems to be poorer than that of the walls of some Early Minoan private houses later found by Levi on another part of the site.
More Addenda from Toprak Kale.
Authors: Barnett R. D.
Published: January 2007

Over twenty years have passed since the present writer first drew attention to the remarkable but completely forgotten archaeological discoveries made at the Urartian site of Toprak Kale, discoveries made in 1880 by Rassam and his associates, Dr. Raynolds and Captain Clayton, acting for the British Museum. I also summarised the results of the work in 1898 at the same site done by Lehmann (afterwards Lehmann-Haupt) and Belck; these finds are now all well-known. Since then, modern museum conservation work and study has resulted in several new achievements, such as in a fresh publication of the candelabrum at Hamburg Museum, the discovery and publication by Professor G. R. Meyer of a small silver pectoral at Berlin with a presentation scene and á detailed study by him also of the large bronze figure of a “eunuch” in the same museum. Professor Meyer also mentions a fine bronze palmette forming part of a wall panel of bronze plate made up of 17 fragments, also part of a bronze model building similar to that in the British Museum. Lastly, a brief preliminary report of the fruitful excavations of Professors Afif Erzen and Emin Bilgiç, in 1959–61, has been published. One of their most notable finds was another shield similar to those found by Rassam and Lehmann-Haupt with concentric friezes of lions and bulls and a dedicatory inscription of Rusas III.
Waqf and Patronage in Seljuk Anatolia: the Epigraphic Evidence
Authors: Rogers J. M.
Published: January 2007

L. A. Mayer's Islamic Architects and their Works, a provisional list of individuals associated with the erection of Muslim buildings, has justly become a standard handbook of Muslim architectural practice. However, this varied as much as in the West, from Byzantium through the Middle Ages to the Renaissance. There are differences of basic vocabulary: the ustādh (master builder or master craftsman) of Seljuk Anatolia is unknown in the Maghrib; differences of status, suggested by the frequency of “signatures” in Seljuk Anatolia and their rarity in Mamlūk Syria and Egypt; or even differences of organization, particularly the Ottoman khāṣṣa mi‘mārlari, a corps of architect-engineers whose rôle in the 16th century has been briefly described by Şerafettin Turan but whose existence in Seljuk Anatolia is highly dubious. The present article is an attempt to use the Seljuk foundation inscriptions of Anatolia, which have not hitherto been exploited as a source, to illuminate Seljuk practice, despite the obvious difficulty of generalizing from the very inadequate evidence.
A Lydian Funerary Banquet
Authors: Ramage Nancy Hirschland
Published: January 2007

The funerary banquet, a frequent theme in ancient sculpture and painting, has been thoroughly studied in recent years. The addition to the corpus of a newly discovered grave stele from Sardis (Pl. XIIIa) is of particular interest because it is a demonstrably local piece of work, with a Lydian inscription carved above a figured relief.

The piece was found in the summer of 1977 by villagers and was reportedly discovered in the east bank of the Pactolus river bed, to the south of the area “Pactolus Cliff”. The slab, which is of local whitish marble, tapers slightly toward the top. Its height is 0·41 m., its width at the bottom is 0·30 m., and its approximate original width at the top was 0·26 m. There is no border at the edge of the stone, but a small ledge protrudes at the bottom of the relief stone. The back has been left rough and unfinished.
Archaische Bauglieder aus Kyzikos
Authors: Koenigs Wolf
Published: January 2007

Bereits F. W. Hasluck fand bei seinem survey über Kyzikos in den Jahren 1902–1906 drei archaische Kapitellfragmente, die zeigen, dass der Ort auch in diesem Bereich eigenständige Leistungen hervorgebracht hat, und deren Marmormaterial einen gewissen Reichtum der Stadt schon in früher Zeit im Vergleich etwa zu Larisa und Neandria zum Ausdruck brachte.

Die beiden leider verschollenen Fragmente eines kleinen ionischen Kapitells mit wenigen breiten, konvexen Volutengängen, ein fachem Rundstab und schalenförmigem Auge, gehörten wegen des geringen Echinusdurchmessers (36 cm.) wohl zu einer Votivsäule.
A Hittite Cylinder Seal in the Yale Babylonian Collection
Authors: Beckman Gary
Published: January 2007

Recently Professor Harald Ingholt generously donated to the Yale Babylonian Collection a Hittite cylinder seal from the empire period, which has received the inventory number YBC 16575. The piece, which is of copper and measures 24·5 × 11 mm., is in excellent condition and shows little sign of wear – see Plate XX and Figure 1. According to Professor Ingholt, he purchased the seal in the 1930s in the bazaar of Beirut, a city which lies outside of the area controlled by the Hittite empire at the greatest extent of its expansion, but which at the time of the acquisition of the seal was linked by daily train service to Adana in Cilicia, the rail line running through the heart of what had once been the southern domains of the Hittites.
Some Assyrians at Sippar in the Old Babylonian Period
Authors: Walker Christopher
Published: January 2007

The trade in tin, textiles, and silver between Ashur and its trading colony Kanesh is by now well known from the partly published archives from Kanesh. While the textiles involved were primarily produced in Ashur itself, a small proportion of them were imported from Babylonia, being described in the texts as “Akkadian textiles”. This link in the trading chain is still scarcely documented in the absence of the trading archives which must be presumed to have existed at Ashur, and probably at Sippar. The Babylonians themselves were actively involved in the trade, as is shown by the well-known but still inadequately published letter VAT 9249, referring to the absence of the Akkadians and their textiles from Ashur because of a revolt in their country.

From its geographical position the city of Sippar must have occupied a focal position in trading relations between Babylonia and the kingdoms to the north and north-west. It naturally figures in the Old Babylonian itinerary from Larsa to Emar. Some years ago W. F. Leemans summarised the evidence for trading relations between Sippar and Assyria and the Middle Euphrates and for Sippar's involvement in the trade in tin in the reverse direction from Ashur to Babylonia.
Nerik and its “Weather-God”
Authors: Macqueen J. G.
Published: January 2007

Hittite geography and Hittite religion have for many years been among Oliver Gurney's principal interests. It therefore gives me the greatest pleasure that this small contribution in his honour deals with both these subjects, especially since the text with which it is mainly concerned is one which I first studied many years ago under his supervision. Like so many others, I owe him a debt of gratitude which can never be adequately repaid.

For many years now it has been clear that in any attempt to locate the site of Nerik the most important fact to be kept in mind is that the town was for a long period in the hands of the Gasga-peoples. Their capture of it was allegedly in the reign of Hantilis, and it was calculated that five hundred years passed before it was recovered by Hattusilis III. More probably however it fell into enemy hands in the reign of Arnuwandas I and his queen Asmunikkal, shortly after 1450 B.C. But whatever the exact details may be, it has to be accepted that any town subjected to an extended period of Gasgan occupation must have been situated to the north of Hattusas, in the direction of the area known in Classical times as Pontus. More recently there has been further evidence pointing to a similar conclusion.
Terracotta Spacer Pins in Lycian Bath Buildings
Authors: Farrington A. , Coulton J. J.
Published: January 2007

A puzzling feature of a number of Lycian bath buildings is the array of holes cut in their walls at intervals of about 0·5 × 0·5 m. In size they are often about 0·12 × 0·12 m. × 0·06 m. deep, and so too large for the normal iron spikes which hold marble veneers or other wall facings in place. A chance find made during the course of the survey of Balboura in 1986 provides an explanation for these holes; they were to take spool-headed terracotta spacer pins which in turn held a series of large flat tiles with a space behind for the circulation of hot air from the hypocaust (Fig. 4), so providing the same effect as the better knowntubuliandtegulae mammatae.
The Hieroglyphic Luwian Rock-Inscription of Malpınar
Authors: Kalaç M. , Hawkins J. D.
Published: January 2007

A notable new rock-inscription has been discovered in the vilayet of Adıyaman, which shows clear links with the Neo-Hittite dynasty of Kummuh already known from the BOYBEYPINARI blocks and the fragments from the productive site of Ancoz. The site of the new inscription adjacent to the village of Malpınar was discovered by Mustafa Kalaç, together with his students Selahattin Aksu (komiser) and Hüseyin Sayıcı, in September 1979 during a survey conducted by the Lower Euphrates Project of the Middle East Technical University. The discovery was reported by M. Kalaç to the Xth Turkish Congress of History held in Ankara, 22–6 September 1986. Hawkins had the opportunity to visit the inscription in October 1986 and August 1987. Travelling from Adıyaman to Akpınar (22 km. as the crow flies), past Kuyulu (alias Turuş, 9 km.), one reaches Malpınar on the east bank of the Göksu Çayı (8 km.). See Fig. 1. The Göksu, flowing south, joins the Euphrates near Gümüşkaya, some 35 km. downstream from Samsat.
The Inscriptions from the so-called “Library” at Cremna
Authors: Horsley G. H. R.
Published: January 2007

In July 1985, the opportunity was afforded to participate in a Surface Survey at the Roman Colony of Cremna in Pisidia. Coincidentally, 1985 marked the centenary of the visit there by the first traveller to publish a still useful site plan.

One building only has been excavated at Cremna (Pl. VII, a). As a result of the discovery by local villagers of several statues during illegal digging at the site, a team led by Professor Jale İnan of the University of Istanbul fully cleared this building in a short season during 1970. Professor İnan has provided an admirable preliminary report of the building and of the ten statues, and Professor Bean undertook publication of the inscriptions found in the building, mostly statue bases and mostly in Greek. Bean had to work from copies, squeezes and photographs: some improvements to his versions are offered below. Because his publication of these texts appeared while SEG was in abeyance, they were picked up only by J. and L. Robert in Bulletin épigraphique. So although there is no inscription here of outstanding individual importance it seemed worthwhile to republish them all here in a more accurate form and with more detailed information. There are three texts not published by Bean (nos. 3, 4 and 9 below). Fuller texts than those given by him have been provided in two cases (nos. 7 and 8 below).
Muş in the Early Bronze Age
Authors: Rothman Mitchell S. , Kozbe Gülriz
Published: January 2007

In 1991 a crew of American, Canadian, and Turkish researchers began a new and comprehensive survey in the Muş Province of Eastern Turkey. The goal of the survey was to study the evolution of settlement and landuse in a marginal zone at the intersection of four great culture areas of the Middle East: Central Anatolia, Western Iran, the Transcaucasus, and Mesopotamia.

This area of Eastern Turkey had been visited previously by I. K. Kökten in 1940s (1947) and Charles Burney in 1950s (1958). Given the large area these surveyors covered and their limited means of transportation, and given the newly excavated material coming from north of the great Taurus mountain massif and from Van (e.g., Sagona 1994, Sagonaet al1992, Çilingiroğlu 1987, 1988), a more comprehensive effort appeared warranted. The first season was six weeks in duration. During that time we re-visited 17 of the sites found by Kökten and Burney, and located 11 new sites. A second season was launched in 1993 with the aim of covering areas not surveyed previously (see Figure 1), mostly in the northern foothills and higher elevations near Hamurpet Lake. Unfortunately, conditions did not permit us to do a second season, nor is a season in the very near future likely. We, therefore, will be publishing the results we have already arrived at, aware that our sample is not complete.
The Pisidian Survey 1995: Panemoteichos and Ören Tepe
Authors: Aydal Sabri , Mitchell Stephen , Robinson Thurstan , Vandeput Lutgarde
Published: January 2007

The site of the southern Pisidian city of Panemoteichos was located by a fortunate discovery in 1993. Excavations to lay the foundations of a new mosque at Boğazköy, a village close to the southern boundary of Burdur vilayet one kilometre east of the Burdur-Antalya highway, exposed a quantity of cut limestone blocks and two Greek inscriptions, one a dedication to the emperor Septimius Severus, the other a mid 3rd century A.D. statue base in honour of C. Iulius Sempronius Visellius, who had served in the Roman army and risen to become high-priest of the emperors in his local community, which the text named as ὁ δῆμοs ὁ Πανεμοτειχειτῶν. Four fragments of the statue itself, including the head, were also recovered. The find thus resolved a long-standing problem of Pisidian topography. Panemoteichos was located at the north-east edge of the highland valley (ancient Greekaulôn), which begins at the narrow pass traversed by the modern highway (theboğazof Boğazköy) and extends to the Çubuk boğaz to the south (see map, Fig. 1). At the same time a rapid reconnaissance of the hill east of the village revealed fortifications and numerous other remains of an ancient settlement (Pl. XVIIa).
Un Tombeau de Famille d'Ancyre de Galatie et la Question de TETPI.ΟΣΚΟΝ
Authors: Kubińska Jadwiga
Published: January 2007

Le monument de marbre blanc avec l'inscription a été découvert par Monsieur D. H. French, directeur du British Institute of Archaeology at Ankara, dans le village de Buğduz (région d'Ankara) en octobre 1973. La photo de la pierre et la copie du texte ont été faites par lui (Pl. XXXIV).

Le monument a été sûrement déplacé de son lieu d'origine et un jour remployé dans la fontaine où l'a vu French et où il semble être resté jusqu'à présent.

L'inscription a été publiée par S. Mitchell qui a seulement défini la pierre portant l'épitaphe comme autel de marbre blanc cassé en deux morceaux a) et b) et en a donné les dimensions:

a) haut. 0,93 m; larg. 0,61 m;

b) haut. 1,47 m; larg. 0,62 m; épaiss. 0,33 m.

La hauteur de la pierre est donc considérable, de 2,20 m. Pour cette raison sa définition comme autel nous semble douteuse. L'éditeur n'a pas publié de photo qui aurait permis de se faire une opinion propre sur ce monument.
Victors in the Meleagria and the Balbouran Élite
Authors: Milner N. P.
Published: January 2007

A sizeable part of the epigraphic record of the North Lycian city of Balboura concerns the erection of statues honouring athletics victors of the Antoninia Meleagria, a “musical” festival founded A.D. 158–161 by the local notable Meleager, the subject of J. J. Coulton, N. P. Milner, A. T. Reyes, “Balboura Survey: Onesimos and Meleager Part II”, AS XXXIX (1989) 41–60. In this paper the whole series of 12 Meleagria bases is published, five for the first time, together with other inscriptions demonstrating the victors' membership of the leading families of Balboura, with one possible exception (Inscr. 11). The Meleagria bases are presented in chronological order, and are referred to by the same numbers as the inscriptions they carry. The tops and front elevations of the better-preserved ones are shown on Fig. 2.
Excavations at Büyüktepe Höyük, 1990: First Preliminary Report
Authors: Sagona Antonio , Pemberton Elizabeth , McPhee Ian
Published: January 2007

A new inquiry into the archaeology of north-eastern Anatolia was initiated in the summer of 1990 at Büyüktepe Höyük, alternatively called İkiztepe. Located about 1·8 km. north of the village of Çiftetaş, in the mountain-girdled Bayburt plain, some 1500 m. above the level of the Black Sea, the site comprises layers of human occupation stretched across two distinct natural hills joined by a saddle (Figs 1–3). Orientated along a northwest–southeast axis, Büyüktepe rises impressively some 20 m. above the floor of the Beşpınar valley. In a direct line from Bayburt, Büyüktepe is only 30 km. to the southwest, although, if one follows the Bayburt to Demirözü road, the distance is increased to about 35 km. From the village of Çiftetaş, a track leads to Büyüktepe and bifurcates roughly 350 m. from its southern end. One branch skirts its eastern base on its way to Çayıryolu; the other runs toward the spurs of Baltakaya Tepesi which were also settled in antiquity.
Archaeological Evidence for the Achaemenid Period in Eastern Turkey
Authors: Summers G. D.
Published: January 2007

The aim of this paper is to highlight the evidence for Achaemenid settlement in eastern Turkey and to publish the sherds from two sites, Altıntepe (Cimin Tepe I, CAB Site 112) and Cimin Tepe II (CAB Site 113) collected by C. A. Burney during his survey in 1955 and now housed in the British Institute of Archaeology at Ankara. An Achaemenid date for Altıntepe level II has often been proposed (e.g. Burney and Lang 1971, 158–9; Forbes 1983, 59) and the site is often now included in studies of the Achaemenid Empire without comment (e.g. Tuplin 1987, 201 n. 118 and map I p. 241; Cook 1983, 198), but the large amount of evidence for extensive and wealthy Achaemenid settlement at the closely related sites of Altıntepe and Cimin Tepe II has not been considered in detail.

Three recent papers concerned with the administration of the Achaemenid Empire in general (Tuplin 1987) and Achaemenid garrisons (Tuplin 1987 B and 1988) have highlighted the sparsity of sites in eastern Anatolia which are known to have been occupied in the Persian period. For the preceding era of the Median Empire, which stretched as far westwards as the Halys river (the modern Kızılırmak), archaeological evidence has been so thin that the very existence of a Median Empire has been seriously, if not convincingly, questioned (SancisiWeerdenburg 1988).
New Insights in Balkan–Anatolian Connections in the Late Chalcolithic: Old Evidence from the Turkish Black Sea Littoral
Authors: Thissen Laurens
Published: January 2007

The Northern Anatolian region under consideration here, the Bafra plain with its main site of Ikiztepe, and the Samsun area with Dündartepe, should be seen as a contact zone between Central Anatolia, the Balkans and the Eastern Aegean. Several items of material culture from Northern Anatolia can be linked with Southeast Europe, the islands off the coast of Western Turkey and Central Anatolia. These connections were established at least by the end of the fifth millennium B.C. Strong similarities in pottery and metal finds from North and Central Anatolian sites with the Cernavoda cultures in Romania indicate that close linkage did in fact continue into the third millennium B.C., thus giving proof of a long tradition. Here, only a small segment of this huge time-span,viz., the last quarter of the fourth millennium, equated with the last stretch of the Late Chalcolithic period, is my concern.