bluuebunny/crossref_metadata_2025 huggingface dataset:
Approximate integration by best fit
Authors: Kumar Kuldeep
Published: January 2007

In order to obtain the area of a curve by the method of the integral calculus the following two conditions should hold:

(a) the equation of the curve must be known,

(b) the function representing the equation of the curve must be integrable.
A further helping of π
Authors: Fox L. , Hayes Linda
Published: January 2007

In the June 1974 edition of the Mathematical Gazette Dr. C. W. Puritz gave an interesting description of a school-room exercise on the calculation of π and some associated numerical error analysis. This note suggests some further relevant material which his pupils might also find interesting and instructive.
Infinite exponentials
Authors: Rippon P. J.
Published: January 2007

1. Introduction

A question of the following type recently appeared in a mathematics contest for high school students in the U.S.A.
Old curves in a new setting
Authors: Haines C. R.
Published: January 2007

Apart from the conic sections, many well known curves have physical and geometrical applications which are readily understood by sixth formers and undergraduates. The catenary, cycloid, spirals, involutes, evolutes and many others appear in courses in civil engineering and control mechanisms, and frequently in A level calculus questions.
Groups of linear transformations
Authors: Burn R. P.
Published: January 2007

“Groups are important because they arise from structures as systems of automorphisms of those structures . . . Group tables and group diagrams are devices to make groups explicit or to visualise them, but they are utterly inefficient tools to introduce groups or to prove that some system is a group ... Are there valid arguments to teach a school group theory, different from the genuine one? I would doubt it.” H. FREUDENTHAL: Address to the ICME congress at Exeter, 1972, on What groups mean in mathematics, and what they should mean in mathematical education.
Patch-determined tilings
Authors: Grünbaum B. , Shephard G. C.
Published: January 2007

A tiling of the plane is a family of sets, called tiles, that cover the plane without gaps or overlaps. Usually we are concerned with tilings whose tiles are of a small number of different shapes; familiar examples are the regular and uniform tilings (see, for example, [1]).

Although the mathematical theory of tiling is very old, it still contains a rich supply of interesting and challenging problems. The purpose of this article is to describe some of these. In many cases the mathematical aspect is enhanced by the aesthetic appeal of the resulting tilings.
Binomial Expansions as a Source of Rapidly Convergent Series
Authors: Colegrave Robert
Published: January 2007

The widespread availability of electronic computers has widened the domain of possible investigations at all levels in mathematics, in the classroom no less than in advanced research. For instance, provided convergence is not exceptionally slow, series may be summed quite accurately and very quickly using a pocket calculator. This enables us to check theoretical work like the evaluation of certain integrals which can be expressed as series.
Cyclic polygons and related questions
Authors: Macnab D. S.
Published: January 2007

This is the story of a problem that began in an innocent way and in the course of time spread out in unexpected directions involving some interesting side-issues. It all began with the following problem which I constructed for the Mathematical Challenge competition run by the Scottish Mathematical Council.
What they don’t teach you about integration at school
Authors: Fitt A. D.
Published: January 2007

As a mathematician involved in teaching students whose abilities range from barely numerate to MSc level, I am frequently concerned by the lack of basic understanding exhibited by pupils regarding the subject of integration. Invariably the most practical way of introducing the subject of integration is by thinking of it as “anti-differentiation”, so that the problem is to pick a function which “when differentiated will give what you first thought of”. This of course may be allied to the idea of the area under a curve to give the student a conceptual feel for the subject. Usually when simple rules for the integration of powers, trigonometric functions, exponentials, logarithms and so on have been mastered, the next step is to introduce the standard methods for proceeding.
Bye-bye Bourbaki Paradigm shifts in mathematics
Authors: Stewart Ian
Published: January 2007

Thomas Kuhn made his reputation by pointing out that science is not just a steady series of rational developments, but is subject to paradigm shifts – revolutions in which the entire point of view changes. A less flattering word for the process is ‘fashion’. But what is fashion other than a paradigm shift in a rather trivial area of human activity? It is often thought that mathematics is immune to paradigm shifts. After all, mathematics consists of perfect truths, proven by impeccable logic. Doesn't it? Well, no, not really – but even if it did, that wouldn't prevent paradigm shifts. Paradigm shifts are not about the internal logic; they are about the external viewpoint. They are about seeing the same facts in a new light, incorporating them into a new framework.
A Quartic with a thousand roots
Authors: Mills John , Tall David , Wardle Michael
Published: January 2007

In a first year university course on programming and numerical methods (in BBC BASIC), it was decided to give the students the quartic equation:

x4 + 2·88x3 − 19·23x2 − 36·11x + 91·56 = 0

to solve numerically. One root of this equation is an integer—to help the students get started—but a second root is close to the first to make it more interesting. Initially we did not realise quite how interesting this would prove to be.
The folding box problem
Authors: Lord Nick
Published: January 2007

A standard introductory calculus problem is to calculate the size of small squares that have to be removed from (say) a unit square of metal so that the resulting net folds into a tray of maximum volume. With notation as in the figure, this requires that be maximised which occurs when x = 2/3 giving a maximum volume of 2/27. (Surprisingly, this conclusion may also be reached without using calculus via the inequality of arithmetic and geometric means:

with equality if and only if or x = 2/3.)
Gauss’s counterexample
Authors: Hall Bob
Published: January 2007

In an article by Nick MacKinnon in the December 1990 Gazette on Sophie Germain, some interesting mathematical questions were left unanswered, and I was inspired to have a go at following them up.

In correspondence with Gauss, Germain had made a conjecture which MacKinnon refined to the following statement

Conjecture. Let q be an odd prime, and a, b be coprime. If aq + bq can be represented by the form x2 + qy2, then so can a + b.
The addition formula for sine: A compilation of methods
Authors: Colwell Derek , Gillett Jack
Published: January 2007

Over the years we have come across many different methods of proving the sine function addition formula

and we have long felt it could be both interesting and useful to gather together in one article a list of methods to illustrate how different ideas from geometry, algebra and calculus may be used to prove it.
Calculating probabilities for Premium Bonds winnings
Authors: Hopkins David
Published: January 2007

A correspondent raised a question concerning Premium Bonds. (See page 459 of the November 1992 Gazette.) He had held 10,000 bonds for 2 years without winning a single prize and wondered how likely this was. In this note, I will describe a simple method for calculating the probabilities of winning. I will also look at the effects of some recent changes in the Premium Bond rules.
Symmetrical paths on a calculator
Authors: Bainbridge A. F. , Binding P. A.
Published: January 2007

The first author discovered the property below while playing with his pocket calculator, and the second author then tried to find out what was behind this property. We enjoyed this voyage of discovery and thought that you might like to share it with us.

Actually, a calculator is not essential, but you will need a square array like

in front of you. If your calculator looks different, that is no problem: all standard keyboards will work just as well.
The traveller’s problem
Authors: Robin Anthony C.
Published: January 2007

There are n 1 places in the world which I should like to visit. If I take the shortest possible route to visit all of these places, starting and finishing at home, what is the greatest possible distance I need to travel?

In this article we are going to look at the above problem, namely that of finding the maximin circuit length for n points (n 1 and home).
Say it with numbers
Authors: Crilly Tony
Published: January 2007

The notion of Morse code is familiar to many school pupils through interests outside of mathematics and computer studies. How can this knowledge be related to algebraic coding theory? The difficulty is that mainstream algebraic coding theory deals with block codes—in which the codewords are of uniform length. Morse code has codewords of variable length in which short codewords are used to represent common characters and longer ones for representing characters which occur less frequently (like. for E as opposed to —..—for X).
The Archimedean honeycomb duals
Authors: Inchbald Guy
Published: January 2007

The first part of this article covers some well-known ground in preparation for the second part on the Archimedean honeycomb duals. Mathematically speaking some of this second part is, so far as I know, no more than conjecture: I do not myself know of a proper systematic approach to such honeycombs.

As far as possible I have used names for the polyhedra from standard references (e.g. [1]). But references vary, and I have not found all of them described. In such cases I have tried to choose names which are appropriate and technically correct.
The variation in the length of daylight
Authors: Ling J. F.
Published: January 2007

It is a well-known fact that the number of hours of daylight varies with the time of year, except at points on the equator. It is sometimes thought that at latitudes between the Arctic and Antarctic circles the variation takes the form of a sine curve. However there is no theoretical basis for this idea, although it is true that a sine curve may give quite a good approximation.
The Steiner point
Authors: MacKinnon Nick
Published: January 2007

The Steiner point S of a triangle ABC is such that the total distance SA + SB + SC is as small as possible. The nice fact about S is that the angles ASB, BSC and CSA are all 120°. I mentioned this casually in a lesson with 5Ma recently, and they decided we would try to prove it. It became clear quite quickly that we would have to invent a bit of partial differentiation, but nothing too advanced.
Walking and running
Authors: Alexander R. McNeill
Published: January 2007

The human body is a complicated machine whose movements involve many different joints, operated by a great many muscles. For that reason it is easy to get bogged down in detail when thinking about walking and running from a mathematical point of view.

Any position of the human body (or of any other jointed mechanism) can be described by giving the angles of joints. The number of angles needed for an unambiguous description is the number of degrees of freedom of the mechanism. For example, the position of a hinge joint is described by just one angle: a hinge allows only one degree of freedom. The human knee is a hinge. The ankle, however, allows rotation about two axes – you can tilt your foot toes up or toes down, and you can also rock it sideways so that the sole faces inwards towards the other foot – so it gives two degrees of freedom. The hip is a ball and socket joint allowing rotation about any axis through the centre of the ball, but any position can be described by just three angles (measured, for example, in three planes at right angles to each other), so it allows three degrees of freedom. In total, there are six degrees of freedom in each leg, making twelve in all, and suggesting that we need twelve equations of motion to describe walking. If we took account of the flexibility of the foot and the movements of the arms, we would need more.
The geometry of the discriminant of a polynomial
Authors: Nickalls R. W. D. , Dye R. H.
Published: January 2007

Everyone knows that the condition for the quadratic to have two equal roots, i.e. to have a repeated root, is that its discriminant should be zero. We should remark, at the outset, that we are concerned only with ordinary polynomials whose coefficients are complex numbers. Indeed, little is lost if a reader assumes that all our polynomials are real, i.e. have real numbers for all their coefficients, though their complex roots must be considered as well as their real ones.
A conservation theorem for colliding snooker balls
Authors: Mackie A. G.
Published: January 2007

In the elementary theory of collisions of two small particles, it is a well-known result that the momentum of the system as a whole is the same after impact as before. This is because the impulses on the two particles are taken to be equal and opposite, thereby implying zero total impulse on the system. It is not obvious that the same will be true after rolling snooker balls collide because, apart from the impulsive forces due to the impact, frictional forces also act on the balls. These are caused by the friction of the table when the balls are in a temporary sliding phase immediately following the impact.
The Portrait of Fra Luca Pacioli
Authors: Mackinnon Nick
Published: January 2007

There have been many attempts to understand the portrait of the mathematician Luca Pacioli which now hangs in the Museo di Capodimonte, Naples (Plate 1), and which will be familiar to users of the Pacioli 2000 accountancy software. However none of these attempts by art historians engages with the mathematics of the picture, which the artist has gone to such trouble to detail. While to a connoisseur the painting might be thought wooden and peripheral to the history of art, I believe that the artist has recorded the most important meeting of the Renaissance.
Choice of programming language for schools—(2)
Authors: Johnson Ken
Published: January 2007

I would like to offer the following contribution to the discussion on the Choice of programming language for schools which will (I hope) ensue following F. R. Watson's and David Tali's article in the December 1987 Gazette. (lam happy to consider other points of view for publication: Ed.) As the authors observe, if the schools do not have a policy of their own, they may well have one they don't like foisted onto them.
A theorem about running round a triangle
and two applications
Authors: Austin Keith
Published: January 2007

Diana runs from
A to
B with speed
u and then from
B to
C with speed
v. Eric runs from
A to
C with speed
w. They start together
and finish together.

If we now draw three lines from a point
O, with
OP parallel to
AB and of length
u,
OQ parallel to
BC and of length
v and
OR parallel to
AC and of length
w, then we find
P,
Q and
R are
collinear.

It is not difficult to construct a proof
of the theorem so that is left as an exercise for
the reader.
Heads you lose, tails I win
Authors: Bradley C. J.
Published: January 2007

The array shown in the diagram, where each
integer appearing shows the number of routes to
that point, assuming there is a North-South wall
that cannot be crossed, but otherwise constructed
using the same one-step, no back-tracking rules as
in the production of Pascal’s triangle, may be
used as the starting point of an interesting
investigation, provided one’s pupils know a bit
about combinations, the binomial theorem and
discrete probability distributions.
What is the matter with negative
r?
Authors: Quadling Douglas
Published: January 2007

Soon after the publication of the new
edition of the SMP booklet Formulae
for advanced mathematics with statistical
tables, I received a letter from a
colleague objecting to the statement that

“If the origin is taken at a focus of the
conic,…, then the equation of the conic has the
form

where e is the
eccentricity …”
In praise of geometry
Authors: Pargeter A. Robert
Published: January 2007

My first contribution to the Mathematical Gazette appeared over half a century ago in October 1943 (why does ‘half a century’ sound more impressive than ‘fifty years’?) so the editor thinks I ought to contribute to the centenary issue. Looking back over the time I have spent studying and teaching mathematics, of all the changes that have taken place the one I most regret is the eclipse of geometry. As readers should know, the Association was originally founded as the ‘Association for the Improvement of Geometrical Teaching’ (in 1871), as in those days the only geometrical textbook in use was Euclid’s Elements. Splendid a job as Euclid did some 2300 years ago in bringing together and systematising the mathematical knowledge of his time (not all geometry, as some of his Books are really disguised algebra), it was never intended for the instruction of the young (although I suppose it was the world’s longest running best-seller!), and was doubtless little understood except by the ablest pupils.
Once upon a time
Authors: Gardiner Tony
Published: January 2007

Seeking to placate the furies of the present we demean the past…. The evasions…the self-denials and the arbitrary re-structurings of historical remembrance which guilt forces upon us are usually spurious.

(George Steiner. In Bluebeard's Castle).

Teaching mathematics has never been easy. There is no reason to imagine that it ever will be. Yet it is still worth asking whether there might not be relatively simple ways of improving our teaching of particular topics and of particular groups of pupils. History of mathematics has much to offer on both counts, and can enrich ordinary teaching in many ways and on many levels. But it also has its problems and its pitfalls. This article focuses on two issues: the temptation to enlist the support of ‘history’ when trying to change social attitudes; and the uncritical way in which intelligent students respond to such pseudohistory.
The mathematics of flat green bowling
Authors: Williams Harold
Published: January 2007

Being aware of John Branfield’s request and having enjoyed Tom Roper’s response may I offer a contribution to the problem of describing the curve on which the bowls move? The important first thing is to decide upon a model of the system which is hopefully sound, and closely approximates the truth. It must also be amenable to mathematical analysis.
Early-Christian Epitaphs from Phrygia
Authors: Calder W. M.
Published: January 2007

The earliest Christians of Phrygia were the nameless converts made by Paul the Apostle when he preached to a congregation of Jews and “Godfearing” gentiles (the latter being Greek or Greco-Phrygian incolae or cives of the colonia and Greek-speaking members of Roman colonial families in the synagogue at Colonia Caesareia Antiocheia in A.D. 49; and before Paul's death the Christian mission to Phrygia had been launched from bases both in the east (Iconium and Antioch) and in the west (Laodicea, Hierapolis and Colossae). Between the middle of the first and the end of the second century, five generations of Phrygian Christians (as Paul expressed it on the same occasion) “fell on sleep and were laid unto their fathers”—in surface family sepulchres along the roads outside the cities and in country graveyards throughout all the hellenised districts of Phrygia. During this period the strong conservatism of Phrygian sepulchral custom, reinforced by the prudence in the face of persecution or proscription held to be enjoined by Scripture (had not Jesus himself withdrawn into Gethsemane?), precluded the open display on tombstones—in all ages the consecrated tokens of sorrow and of hope—of any trace of the Christian profession.
Notes and Inscriptions from Pisidia, Part 1
Authors: Bean G. E.
Published: January 2007

The region discussed in the present article lies on the Phrygian border of Pisidia, just beyond the eastern boundary of the province of Asia, and in the north-west corner of the enlarged province of Pamphylia as reconstituted by Vespasian; previously it belonged to the huge and straggling province of Galatia. It coincides approximately with the Milyas as defined by Strabo 631, and nowadays with the eastern half of the vilâyet of Burdur. First visited by Lucas in 1714, then by Arundell in 1833 and Schönborn in 1842, this region was, towards the end of last century, the scene of considerable activity on the part of scholar-explorers.
Hattian Mythology and Hittite Monarchy
Authors: Macqueen J. G.
Published: January 2007

The ritual text published by H. Otten as K.U.B. XXXVI 89 + 88 is of great interest both for its linguistic and lexicographical difficulties and for the religious importance of the myth which it contains. This myth is concerned with the Weather-god of Nerik, and although the state of the tablet is too poor for a complete reconstruction to be made, the mutilated fragment that remains bears a striking resemblance to the well-known Telipinus-myth. It begins (obv. 12) with the withdrawal of the Weather-god in anger.
Assyrian Contracts from Sultantepe
Authors: Finkelstein J. J.
Published: January 2007

The four tablets published here were found in room C II, on the western side of the Assyrian acropolis at Sultantepe, during the excavations of the British Institute and the Turkish Department of Antiquities in 1951. Two of these are more or less complete, while two are only fragmentary. It is only in these last two, however, that the dates are preserved; S.U. 51/43 being dated in the eponym of Sharru-nūri, 674 B.C., and S.U. 51/43A in the eponym of Mannu-zīrni, 684 B.C. S.U. 51/36 may have had an eponym date at the end of the first line of the left edge, but that part is now lost. S.U. 51/44, contrary to the usual practice with legal documents, is undated.

There is no clear indication from the Sultantepe tablets concerning the name of the site in Assyrian times. Although the city of Ḫuzir(i)na is mentioned in line 36 of 51/36 and in a number of colophons on the literary tablets from Sultantepe, it has already been pointed out by Gurney that Sultantepe, situated about fifteen miles north of Harran, could not be identical with the city of Ḫuzirina, familiar from the Assyrian royal annals, which was situated at a distance of not more than one day's march to the west of Nasibina (Nisibis); in other words, some 130 miles to the east of Sultantepe.
Keftiu and Karamania (Asia Minor)
Authors: Wainwright G. A.
Published: January 2007

In this article it is argued once more that the Egyptian Keftiu was situated in Cilicia Tracheia, and not in Crete as has generally been supposed. For this there has already been adduced evidence drawn from many sources, and here still more, mainly cultural and historical, is added to the sum total. Some of this new evidence shows that certain features of the culture with which it deals are at home in Cilicia Tracheia and its neighbourhood, and that they have continued to exist there from ancient times right up to the present day. The thread that leads us onward is the story of an elaborate design.
The Sultantepe Tablets (Continued) III. The Poem of the Righteous Sufferer
Authors: Lambert W. G. , Gurney O. R.
Published: January 2007

The discovery of new tablets of Ludlul bêl nêmeqi, which was announced in Anatolian Studies, II, p. 28, comes as a very welcome supplement to the extant Akkadian Wisdom literature, a field which has been singularly barren in new finds for several decades now, as a recent writer has commented. There are parts of two tablets: the lower portion of a well-preserved copy of tablet I, and a copy of tablet II made up from several fragments, the lower quarter of which is badly damaged. The first is particularly valuable as this tablet has been known previously only from a few small fragments and some odd lines quoted in a native commentary. Of the second tablet quite a number of sizeable pieces are already published. The new text offers the customary scribal variants, one of which is clearly superior to the reading of an Assurbanipal tablet (l. 17), and restores some of the lacuna which exists in the middle of the tablet. It is at this place, however, that the new tablet is defective, and so some half dozen lines are still only half preserved.
“Hyksos” Scarabs from Canaan
Authors: Tufnell Olga
Published: January 2007

When Professor Garstang excavated part of the Middle-Late Bronze Age Necropolis at Jericho between the years 1930–1936, he made special mention in one of his reports of a scarab in a group of six from Tomb 13 (LAAA., XX 1933, pp. 36–7 and Fig. 11). He described it briefly as follows:—

“Figure of a Canaanite wearing robe and cap with Syro-Hyksos hieroglyphs in the field.”

Twenty years have elapsed since then, and other scarabs have come to light which show figures wearing the same type of dress, so that it does seem worth while to assemble them on one page to see if they form a consistent and instructive group.
Excavations at Hacılar Third Preliminary Report, 1959
Authors: Mellaart James
Published: January 2007

A third season of excavations at Hacılar, carried out under the auspices of the British Institute of Archaeology at Ankara, lasted from 10th August to 11th September, 1959.

The Assistant Director was in charge of the excavations, ably assisted by Mrs. Mellaart, Miss Clare Goff (surveyor), Mr. David Stronach (field assistant and photographer) and Mr. David French (pottery expert). Mr. David French also kindly provided the transport for the expedition. The Turkish Department of Antiquities was again represented by Bay Osman Aksoy, whose efficiency relieved the Director of much administrative anxiety.

Once again we record our gratitude to Mr. Seton Lloyd for his help and advice, to the Department of Antiquities and to the local authorities in Burdur.

Among the visitors to the Hacılar excavations, we must mention Mr. and Mrs. Seton Lloyd, the Vali of Burdur and a party of local dignitaries from Burdur, Mr. Charles Burney and Miss Burney, who kindly drew our figurines, Professor Machteld Mellink, Bay Burhan Tezcan, Mrs. I. D. Stronach and Mr. and Mrs. J. Lanfear.
Measured Plans of Urartian Fortresses
Authors: Burney C. A. , Lawson G. R. J.
Published: January 2007

This article comprises descriptive and explanatory notes on a number of plans made during a plane-table survey carried out by the authors in the Van region in the summer of 1957. In addition to the plans and photographs, there are two details, one being an elevation. The form of publication is partly determined by the appearance of sketch-plans of most of these Urartian fortresses in a preliminary article. Apart from correction of certain errors in that article, the general information given therein will not be repeated. For the position of the various fortresses reference should be made to the map published in that preliminary report. To the sites marked thereon should be added two more, Aznavur and Kancıklı, both near Patnos, on the road north-west from Erciş. to Karaköse and thus some way north of Lake Van. Both are of major importance: Aznavur lies one mile north-west of Patnos and Kancıklı some nine miles south-east.
Two Door Latches from the Konya Plain
Authors: Alcock N. W.
Published: January 2007

The interest of the excavation staff at Çatalhüyük was caught by the ingenious door latches used in the village of Küçükköy, 50 km. S.E. of Konya. The houses in the village show many traditional features, some of which, such as the wall decorations, may even survive from the Neolithic period; many houses have Seljuk style stalactites on cut-away corners. Generally each property consists of a courtyard surrounded by a wall, containing one or more houses and other buildings.

There are two types of door latch, one for courtyard doors and one for house doors, and both are sufficiently interesting to be worth recording. (They work considerably better than the modern Turkish iron latches.) In a village with such traditional houses it is impossible to guess at what date such door latches might have come into use. They would have been suitable for any house with a properly hung door.
On the Dating of some Groups of Reliefs from Carchemish and Til Barsib
Authors: Ussishkin David
Published: January 2007

A large number of Hittite hieroglyphic inscriptions and Neo-Hittite reliefs were uncovered in Carchemish by the British Museum expeditions. The profusion of Hittite hieroglyphic texts enabled Woolley and Barnett to attribute many of the monuments to different kings and to establish a reliable chronological list of the kings of Carchemish. Sangara, who reigned in Carchemish during the middle of the ninth century, is known from the Assyrian annals only and is not mentioned in even one of the hieroglyphic inscriptions found in Carchemish or elsewhere. Therefore, none of the buildings and monuments unearthed there could be attributed to him and he is not considered to have played a significant role in the history of this Neo-Hittite state. The main purpose of this article is to try to prove that Sangara was an important and prosperous king, victorious in battle and a great builder, to whom a large part of the reliefs found in Carchemish must be assigned.
An Anatolian Greek Belt Handle
Authors: Boardman John
Published: January 2007

The bronze belt handle shown in Plate LXIV was acquired by the British Museum in 1962 and illustrated by Dr. Barnett in BMQ XXVII, Pl. 31g. I am indebted to him for the photographs used here and for permission to study the piece and present this account of it. It belongs to a class of objects which has been discussed by the writer in Anatolia VI (1961) 179 ff. They are fibula-like attachments to metal belts of a distinctive type which was apparently invented in Phrygia, but copied in Ionia where examples dating from the early seventh century to the sixth are known from Chios, Samos, Smyrna and Ephesus. Unfortunately the Phrygian series is not as yet as well known as the Greek.
Çatal Hüyük—The Textiles and Twined Fabrics
Authors: Burnham Harold B.
Published: January 2007

Ancient textiles in archaeological excavations are preserved only under unusual circumstances, and it is for this reason that the discoveries at Çatal Hüyük in 1961, and repeated in following seasons, of woven and twined materials possess an excitement out of all proportion to their visual appearance. Until these were found, the earliest woven fabrics known were from the Fayûm in Egypt which are usually dated to the fifth millennium B.C. The finds in Level VI of Çatal Hüyük push the history of the textile arts back to the beginning of the sixth millennium.

For textiles to survive in a more or less natural state requires either extremely arid conditions as in Egypt or Peru, or permafrost as in the Norse burials in Greenland, and in the tombs of the Scythian and Hunnish princes in Siberia. The presence of certain chemicals may act as a preservative: tannin in the Bronze Age burials in Denmark or metallic salts impregnating the fibres of the silks found in the patina of Chinese bronzes of the early dynasties. At Çatal Hüyük, a simpler agent is responsible for the survival of the fragments that have been found. In the fire that apparently destroyed the buildings of Level VI in which they were found, they were subject to intense heat. Due to the scarcity of oxygen in the space in which they were confined under the low clay platforms, the fabrics were not consumed, but only thoroughly carbonized. This made them chemically inert, and no longer subject to the growth of the destructive moulds that under normal conditions lead to the total decay of most animal and vegetal matter.
Excavations at Çatal Hüyük: First Preliminary Report, 1961
Authors: Mellaart James
Published: January 2007

The site of Çatal Hüyük was discovered during our survey of the Konya Plain in November, 1958. Rich in surface finds of a type hitherto only known from Professor J. Garstang's excavations at Mersin on the south coast of Anatolia, its importance was soon realised. However, at the time of the discovery, we were engaged in the excavation of the equally important site of Hacılar and it was not until after the completion of excavations there that digging could be contemplated at Çatal Hüyük. After the final season at Hacılar in 1960, we were free to devote our attention to this new site.

As Hacılar showed a gap in its culture sequence exactly during the Early Neolithic period, which surface finds showed was best represented at Çatal Hüyük, it was decided to start excavations at this site to complete the sequence and throw further light on Hacılar.
Sites Old and New in Rough Cilicia
Authors: Bean G. E. , Mitford T. B.
Published: January 2007

In June 1961 the writers gave three weeks to exploring the country in the neighbourhood of Alânya, the ancient Coracesium, and Gazipaşa, formerly Selinti, the ancient Selinus. This region proved to be rewarding; and we hope to pursue our investigations both there and to the east of Anamur in future years—the more so since our predecessors have been few and often hampered by the difficulties of the terrain. Some indeed, like Beaufort, travelled almost exclusively by sea; others found themselves detained by the archaeological richness of the Olba–Lamos area, and then, like Sterrett and Theodore Bent, diverted up the Calycadnus gorge into the hinterland of Isauria. Explorers of the coastlands between Manavgat and Silifke are in effect reduced to Heberdey and Wilhelm (quoted hereafter as HW) in 1892, Paribeni and Romanelli in 1913, Wilhelm and Keil in 1914. To those familiar with this country it is revealing to learn that Wilhelm's visits—for example to Sinekkalesi and Syedra, extensive sites, heavily scrub-covered—were often brief affairs; that his exploration of Seleucia above Side and indeed of all the coast lying immediately to the east of the Melas river was cut short by repeated thunder-storms.
Building Inscriptions of Carchemish: The Long Wall of Sculpture and Great Staircase.
Authors: Hawkins J. D.
Published: January 2007

With the publication in 1952 ofCarchemish, part III, Sir Leonard Woolley attempted to allocate the excavated buildings and monuments to reigns and dates. For the epigraphic evidence of the Hieroglyphic Hittite inscriptions, he relied upon the chapter contributed to the publication by R. D. Barnett. Here Barnett constructed a chronological framework based on the names and genealogies appearing in the inscriptions. He was, however, working in the immediate aftermath of the discovery of Karatepe, before even the preliminary publication of the bilingual was complete, so that a number of his readings required subsequent correction. Detailed epigraphic criticism was offered particularly by Güterbock and Meriggi in their reviews of the volume. The efforts of all these scholars considerably advanced our knowledge of the chronology of the buildings and sculpture, and subsequent treatments of the art and archaeology of Carchemish have naturally relied heavily upon them.

More recently however, the study of the hieroglyphic inscriptions, which are for the most part concerned mainly with the erection of buildings and sculptures, has fallen behind that of the monuments to which they relate. This remains true even after the new edition of some of these inscriptions published by Meriggi in what is primarily a philological study. It would therefore seem desirable to present editions of the Carchemish building inscriptions as complete as their fragmentary nature and persistent difficulties interpretation will permit; and on this basis to review the chronology of the buildings and sculptures described therein. It is the purpose of this article therefore to examine the inscriptions relating to the Long Wall of Sculpture and the Great Staircase, which elucidate to some extent the history of the construction of that complex.
The Metals amūtu and aši'u in the Kültepe Texts.
Authors: Maxwell-Hyslop Rachel
Published: January 2007

Professor Seton Lloyd's interest in all aspects of archaeology and his distinguished work both in Turkey and in the Diyala valley, Iraq, may justify the publication of this note on iron in Anatolia offered to him on the occasion of his 70th birthday. It was at Khafajah in 1931 that one of the earliest daggers with remains of a blade of terrestrial iron was discovered; the possible use of terrestrial rather than meteoric iron in Anatolia at the time of the Assyrian merchant colonies is discussed below.

The Kültepe textCCT4 4a (lines 3, 23, 27, 38, 44) has been translated in theCAD(s.v.amūtu) and referred to by Garelli when discussing the meaning of the wordamūtuand its Sumerian equivalent KÙ.AN.
Tituli Comanorum Cappadociae Iterum Suppleti.
Authors: Harper Richard P.
Published: January 2007

Professor Seton Lloyd has since the time of his Directorship of the Institute been interested in the site of Comana of Cappadocia at Şar, and has often helped and encouraged my work there and elsewhere in Turkey. I am therefore glad to be able to offer him this brief supplement to the corpus of inscriptions of Comana which has already appeared in the pages of Anatolian Studies in 1968 and 1969.

After the season of excavation at Şar in 1968 conducted by Mrs. İnci Bayburtluoǧlu and myself, a depot of stone monuments was entrusted to the care of the former Muhtar, Bay Mustafa Yergök. In 1971, with the new Adana regional museum nearing completion it was decided to move this material to the museum so that Comana should be represented in the museum's collections.
A Byzantine Lamp Hoard from Anamur (Cilicia)
Authors: Williams Hector , Taylor Peter
Published: January 2007

In the course of excavating a well-preserved late Roman bath building at Anemurium (modern Eski Anamur) during the summer of 1968 a large hoard of some six hundred and fifty whole terracotta lamps plus fragments were found stacked in a disused hypocaust system. Since that time many fragments of similar lamps and a mould have also been discovered in other parts of the site in mixed fills containing pottery of the fifth to mid-seventh centuries A.D. As few lamps of similar types have been published from the eastern Mediterranean from datable contexts the value of the Anamur hoard both as a chronological indicator and as a stage in the development of late Byzantine and early Islamic lamps is evident.

Although no datable material was found with the lamps themselves the abandonment of such a considerable body of material may perhaps be best explained by events at the site in the mid-seventh century. At this time the city seems to have been deserted, probably as a result of Arab raids on the coastal cities of Cilicia, and was only briefly reoccupied six centuries later. As there are no marks of burning on any of the lamps and as some filling and wick holes are incompletely punched through, the hoard may well be the stock of a shop or merchant hastily put away at some moment of danger and never reclaimed.
A History of Deforestation as Indicated by Charcoal Analysis of Four Sites in Eastern Anatolia
Authors: Willcox G. H.
Published: January 2007

During the 1972 season of the Aşvan excavations (see French, 1973, p. 77) it was decided that, given the huge quantity of charcoal recovered (292 samples) from the four sites by water-sieving and trench sampling from strata which cover a period of c. 4,500–5,000 years, an analysis of the charcoals would prove revealing. Part of the aim of the research is to evaluate what information is available from charcoals recovered by modern methods, and to determine if it is possible to draw sound conclusions about vegetational changes which have not been fully recorded for the late Holocene in Eastern Anatolia. Although some data has been made available through pollen analysis (see van Zeist, 1968, pp. 19–39) the distribution, duration and composition of the forest which existed before deforestation is not entirely understood.

A dearth of necessary data on which to base this work made contemporary studies a prerequisite. Firstly an adequate comparative collection of identified modern woods had to be built up to aid identification of ancient charcoals. Secondly, a reliable method of sub-sampling had to be devised in order to deal with the copious material.
Phrygian Painted Animals: Anatolian Orientalizing Art
Authors: Sams G. Kenneth
Published: January 2007

As early as 1900, with the Körte brothers' excavation of Tumulus III at Gordion, Anatolian archaeology has been aware of the existence of a Phrygian linear animal style. In 1941, further examples of the same style were retrieved from the mound of Alaettin Tepe in Konya. Since 1950 and the beginning of the University of Pennsylvania's excavations at Gordion, the corpus of examples of this style has grown considerably. While important in itself as the only attested school of early Phrygian figure painting, the style also bespeaks importance in a larger sphere, for the evidence at hand strongly suggests that the forms were derivative, adopted by the Phrygians from the world of North Syrian art. As such, the style represents an important addition to the growing list of fields in which Phrygian indebtedness to the North Syrian sphere can be documented. The present study will use the evidence of Gordion as its focal point, since this city has yielded the greatest number of examples of Phrygian linear animals.
Excavations at Can Hasan, 1967, Seventh Preliminary Report
Authors: French D. H.
Published: January 2007

The seventh season of excavation at Can Hasan began on 9th September and stopped on 28th October; a further week was spent working on the finds and on the site. Site supervisors were Bay Altan Atılgan, and Messrs. S. W. Helms, R. Howell, and J. N. Postgate. In the House the work was undertaken by Bayan Behin Aksoy, Bayan Ülge Göker, Miss Carolyn Prater, Mrs. Cressida Ridley and Miss Monika van der Zwann. Bay Bedri Yalman represented the Turkish Government for a short period until called away to military service; his place was taken by Bay Cengiz Karadağ.

A new method of sieving was introduced this year at the suggestion of Mr. Sebastian Payne. Instead of small hand sieves, “shakers”, built under Mr. Payne's supervision, were used. Basically this type of “shaker” is three removable trays with mesh of differing size (10 mm., 5 mm., 1 mm.) set on a sprung metal framework. It was also found more practicable with soils containing a lot of grain to “wash out” the grain from the soil remaining in the last tray after the soil had received preliminary hand-searching.
A New Look at the Chronology of Alalakh Level VII: A Rejoinder
Authors: Collon Dominique
Published: January 2007

In a recent article Dr Nadav Na'aman suggested that two rulers called Yarimlim and two called Ammitakumma succeeded each other in alternation during the period of the Level VII archive at Alalakh. This reconstruction of the chronology fails, as do all previous reconstructions, to take into account the seal impressions on the tablet envelopes. These seal impressions have now been published and the chronology which they enabled me to reconstruct is substantially that established by Rowton and Kupper. A close study of Dr Na'aman's article has not led me to alter my views and I should like to make the following points.

Dr Na'aman questions the generally accepted chronology for Alalakh on the grounds that YḪammurapi I (grandfather),AYarimlim (father) and AAmmitakumma (son) “reigned over a period of at least 125 years” and that “six kings reigned in Yamḫad concurrently with two Kings at Alalakh”. He accepts a date “circa the twenties of the 18th century B.C. (or slightly earlier)” for the beginning of the archive and therefore, presumably, for the beginning of the reign of AYarimlim.
Hunting and Shooting
Authors: Collon Dominique
Published: January 2007

When I was still a student, Dr. Barnett gave me the part-time job of sorting the cylinder seal collection in the Western Asiatic Department of the British Museum, of which he was then Keeper. Now, some twenty years later, the catalogue of Akkadian to Ur III seals, which this led to, has just appeared, and this article is based on two “firsts” (as S. N. Kramer would put it) to which my attention was drawn while I was studying the seals. I have found seals a fascinating and continuous source of inspiration and information and the fact that I am still writing about them after twenty years is a measure of the debt I owe Dr. Barnett.

Hunting: Cylinder seal BM 105159 (Pl. XVII(a)), is cut with a presentation scene: a deity leads a worshipper before a seated god. Behind the worshipper is a figure (Pl. XVll(b)), who wears a skirt, raises his left arm and holds, in his right hand, what I thought was a footed cup in which was a stirring rod or spoon. However, when I took this, and other seals, to the British Museum (Natural History) for identification of the animals, it was pointed out to me, by Mr. Colton, that the “cup” might be a falcon sitting on a falconer's wrist.
Mesopotamian Gardens
Authors: Wiseman D. J.
Published: January 2007

Tribute must be paid to Richard Barnett for his contributions,inter alia, to the interpretation of many of the scenes on the Assyrian sculptures. His studies have drawn attention to the detailed information which may be drawn from this important source. In many conversations with me as a colleague in the British Museum he showed particular interest in the Assyrian landscape and representation of nature. Thus he identified the Assyrian garden in the reliefs of Ashurbanipal's N. Palace at Nineveh (Plate XXXIIIa). In this the garden is drawn as planned around a hill, or high feature, on top of which is a garden house. Watering was by aqueduct and channels arranged so that in the downhill flow no material part was inaccessible to irrigation. Trees which provided some shade, also served as supports for vines planted between them. In the Assyrian tradition temples also had similar gardens associated with them.
Western Anatolia in the Thirteenth Century B.C. according to the Hittite Sources
Authors: Singer Itamar
Published: January 2007

The redating of certain Hittite texts – notably the Indictment of Madduwatta and the annals of Tudhaliya and Arnuwanda – from the end of the thirteenth century to the turn of the fifteenth has been one of the most discussed Hittitological subjects in recent years. The sudden availability of sources covering a previously poorly known period in Hittite history has naturally brought about an intense preoccupation with the Early Hittite Empire, largely overshadowing the less “fortunate” side of the redating, the “deprivation” of the main body of sources relating to western Anatolia in the second half of the thirteenth century. The situation is aptly demonstrated in the most recent comprehensive study on Arzawa, where the chapter dealing with the period after Muwatalli to the end of the Hittite Empire barely covers 16 pages, in contrast to the far more abundant documentation on the fourteenth century.