bluuebunny/crossref_metadata_2025 huggingface dataset:
A straight line is the shortest distance between two points
Authors: Webb J. H.
Published: January 2007

The popular definition of a “straight line” as “the shortest distance between two points” is one of the few pieces of mathematical jargon in general circulation in the English language. This is unfortunate, for it is not a good definition, and one may well wonder who originated it. Euclid is not to blame, for he defined a straight line as “that which lies evenly between its points”. (This is indeed cryptic, and Sir Thomas Heath, in a lengthy analysis of the original Greek, had to confess that “the language is...hopelessly obscure”.)
Chains and Whips in the Teaching of Mathematics
Authors: Rennie B. C.
Published: January 2007

It was at St. Barnabas’ School at Ravenshoe in North Queensland that I met the boy with the stockwhip. I forget his name but it does not matter. His whip was some ten or twelve feet long, and he demonstrated for me a little trick that he used to do. An assistant, the volunteer from the audience, would stand facing him with arms in front of face in case of accidents, the boy would swing the stockwhip towards his assistant with what in lawn tennis is called a forehand drive, the lash at the end would crack behind the assistant’s back, and then curl painlessly round his waist. Presumably the cracking destroyed a lot of kinetic energy.
Sophie Germain: or Was Gauss a feminist?
Authors: Mackinnon Nick
Published: January 2007

This article is focussed on a letter that perhaps the greatest mathematician ever, Carl Frederich Gauss, sent to a female mathematician, Sophie Germain. The letter is interesting because it is the first that Gauss wrote to Germain in the knowledge that she was a woman, and it contains a piece of mathematics that reveals better than the text of the letter what Gauss really thought of Germain. To put the letter in context I shall give some of Germain’s biography and also briefly describe female mathematicians that pre-date Germain.
Magic in base 3
Authors: Long Calvin T.
Published: January 2007

Twelve golf balls appear identical, but eleven weigh exactly the same while one ball is either lighter or heavier than the others. Determine the “odd ball” and whether it is lighter or heavier than the others in just three weighings of the balls on a balance scale.

Puzzle problems like this abound and experience has shown that they are quite attractive to students. But this is particularly true in the present case since a solution exists that appears little short of magic. This problem provides excellent motivation for developing reasoning and communication skills. It also provides strong motivation for learning arithmetic in a base other than base 10 and for developing skill at doing mental arithmetic quickly, easily, and accurately.
A colourful path
Authors: Fung Tat-Sang
Published: January 2007

(This article is the result of some work done by a first-year undergraduate, Tat-Sang Fung, at the University of Hong Kong. It went way beyond what his lecturer, Man-Keung Siu, had asked for, and he was so impressed that he submitted it to the Gazette. I have edited it a little, but the ideas are entirely Tat-Sang’s.)
Quick insights and painted eggs
Authors: Costello John
Published: January 2007

This article provides solutions to three problems. The solutions are interesting in themselves; but the problems, which are very different in nature, have a common characteristic. Each can be solved relatively quickly—some would say, elegantly—by a leap of intuition. On the other hand, all three can be tackled in a more exploratory, pedestrian fashion. Some people may want to argue that one approach is “better” than another; but a more useful discussion concerns the appropriateness of a method in particular circumstances, whether it provides insight into the underlying structure and principles involved, and indeed whether this is important.
Cricket and derangements
Authors: Dennett J. R.
Published: January 2007

Some time last year I clipped from the Guardian a report on the bungled draw for the quarter-finals of the Benson and Hedges Cup. The relevant section is

The problem arose because a competition rule states that sides who play each other in the zonal rounds cannot meet in the quarter-finals. The draw is made by pulling ping-pong balls from two velvet bags—one for the teams who, by topping their preliminary groups, are entitled to a home draw, and the other for those destined to play away.

On each of the first two occasions that the draw was attempted yesterday—by the TCCB chief executive, Alan Smith, and the board’s new secretary of cricket, Tim Lamb—all went smoothly until each bag held only one ball. But those balls said Glamorgan and Hampshire, both from zone D. Only on the third attempt was the result satisfactory.

Smith later conceded that it was “an embarrassing cock-up”. Lamb, he said, had spent “hours” practising. In any other organisation a senior executive who spent his working day pulling table-tennis balls from a velvet bag would soon find himself on the corporate funny farm. But this is Lord’s.
A “simple” integral and the repeated logarithm
Authors: Atkinson Colin
Published: January 2007

A question which I like to ask sixth-formers at their interview for University is to evaluate

not worrying for the moment about the behaviour at x = 0 or x = 1, or the limits of the integral. This question is difficult enough for some students but on a good day one can lead them through to the correct solution (log|log x|) by various suggestions like “try a substitution” (x = et) or “do you know a rule for when the top is the derivative of the bottom?”
Mathematical billiards
Authors: Shultz Harris S. , Shiflett Ray C.
Published: January 2007

A ball is shot at an angle of 45 degrees from the corner of a rectangular billiard table of size m × n (where m and n are integers). It always bounces off from a side at 45 degrees until it lands in a corner pocket. Will it always land in a corner or will it keep bouncing for ever? And how many times will it bounce? And which corner pocket will it land in?

Try it for yourself. For example in the 7 × 4 table shown the ball will bounce 9 times and then fall into the top left-hand corner pocket.

This is a well-known problem but we now present a simpler proof than we've seen elsewhere of the fact that the ball always ends up in a corner pocket, and we derive a formula for the number of bounces and we determine the finishing pocket.
Revision of CSYS Mathematics
Authors: McBride Adam C.
Published: January 2007

This article outlines possible changes to the examinations in Mathematics offered by the Scottish Examination Board as part of the Certificate of Sixth Year Studies. It must be emphasised that, at the time of writing, these changes are still only proposals. Furthermore, any views expressed in the article are the personal views of the author.

The existing CSYS courses were designed as the third stage of a progression in which pupils sat examinations at Ordinary Grade (‘O’ Grade) in S4, at Higher Grade in S5 and at CSYS Level in S6. However, the old order changeth. The Ordinary Grade is being replaced by Standard Grade and the transition will soon be complete. For articulation with Standard Grade courses, Higher Grade is being replaced by Revised Higher Grade. Finally, CSYS courses are being revised to articulate with Revised Higher. Some of the proposed revisions concern content, a good example being the situation regarding matrices. Presently pupils meet matrices in Higher but there is no mention of matrices in the formal contents of Revised Higher, so that CSYS must be adjusted accordingly. Other proposed revisions arise as a result of changes in the teaching approach. At Standard Grade and Revised Higher Grade, one of the aims is to develop pupils' skills in problem-solving. Furthermore, investigations form part of the assessment in both cases. It seems sensible that CSYS courses should continue this philosophy.
How to make sense of the integers and their operations
Authors: Sangalli Arturo
Published: January 2007

We propose an interpretation of the integers as operations on permutations. Addition and multiplication of integers represent operations on these operations. It follows that an equation involving integers, addition and multiplication is valid if and only if the corresponding operations on permutations are the same. In our interpretation, the validity of the fundamental laws of calculation is an immediate consequence of well-known properties of permutations. For example, the ‘Law of signs’: (–1) x (–1) = 1, is valid because the inverse of the inverse of any permutation is the permutation itself.
Locomotion at A level
Authors: Lazenby Paul
Published: January 2007

The need for clarity in the teaching of mechanics in the initial stages is vital if a firm grasp of principle is to be fostered. I had been teaching A level students about locomotion in a conventional way for some years when it occurred to me that something was basically unsound about the way in which textbooks treat the subject. At best they appear unclear and at worst they seem to flout basic principles. Examination papers mirror the textbook treatment.
Video tapes
Authors: Macro W. B.
Published: January 2007

Over the years there have been various articles in the Gazette [1, 2, 3] concerning the running time of cassette tapes, but none of them uses the property described here, although it is relevant to all of them.

Let us assume that the revolution counter on a cassette or video recorder is operated by the run off spool. Let a be the radius of the full spool and r the radius when an angle θ radians has been unwound. Rather as in [2] it is clear that a reasonable continuous model of this situation satisfies the equation
The second iteration: 1991 Presidential address
Authors: Brown Margaret
Published: January 2007

It has been my good fortune in life to have been able to work with inspiring and generous people. When I was writing this address, I found myself thinking particularly of one, Geoffrey Matthews, to whom I still often turn when I need reminding of the funnier aspects of mathematics education. I have vivid memories of his elation, 15 years ago, when he was first approached to be President-Elect of the Mathematical Association. Being a stickler for punctuality, he went straight home and wrote his Presidential Address , more than one year in advance of its delivery. In contrast I started on this address just 10 days ago, and have had to amend it twice since, because of announcements of radical shifts in government policy. Even the title, chosen five months ago, may be out of date for reason which I will explain later.
Semi-magic squares and their orthogonal complements
Authors: Mayoral Fernando
Published: January 2007

Not long ago I came across the following quiz in the Sunday supplement of the Spanish newspaper El País: Check that it does not matter how you take any four numbers from the following array; provided that no two of them lie in the same row or column, their sum is always the same.

This reminded me of magic squares: square matrices where the sum of the elements in each line (row or column) and diagonal is always the same. Magic squares are a topic in recreational mathematics. Usually one looks for magic squares with elements that are integer, positive and different from each other, e.g. 1,2,…, n2 for a n × n as in

According to a Chinese legend, matrix A appeared engraved on the carapace of a turtle about 2000 BC. On the other hand, matrix B appears in Albrecht Dürer’s engraving Melencholia (1514) [1].
Countless Simson line configurations
Authors: Bradley C. J. , Bradley J. T.
Published: January 2007

The Simson line property is normally associated with points on the circumcircle of a triangle. It is embodied by the following theorem.

Given any triangle ABC and a point P in the plane of the triangle, if perpendiculars from P on to the sides BC, CA, AB meet those sides at L, M, N respectively then L, M, N are collinear if and only if P lies on the circumcircle of triangle ABC. The line LMN is then known as the Simson line of P.
A certain sense of the possibility of application
Authors: Ormell Christopher
Published: January 2007

There have been three obvious paradigms which have successively dominated mathematics teaching during my teaching career: three eras of predominant pedagogy. None of the so-called “reforms”, however, achieved a total take-over of the schools. “Traditional mathematics”, the first paradigm, survived right through the era of “new maths for schools”, the second paradigm. In some schools “new maths” was hardly noticed, and probably in no school did “new maths” change everything in the curriculum – there were a number of topics which carried on much as before. Applicable/problem-solving maths, the third paradigm, arrived on the back of Shell, Spode, Cockcroft and SMP 11-16 around 1982.
The law of credulity
Authors: Matthews Robert A.J.
Published: January 2007

Coincidences are a source of amusement and occasional unease in our lives. They often appear to defy the laws of probability – even to demand a supernatural “explanation”. Probability theory reveals the root cause of this disparity between expectation and reality. As I shall show, it stems from the fact that our intuitive estimate of the probability of a coincidence occuring becomes increasingly inaccurate the more “outlandish” the coincidence seems to be.
Dungeons, dragons and dice
Authors: McLean K. Robin
Published: January 2007

My younger son has become interested in the game “dungeons and dragons”. He is intrigued by the shapes of the dice that are used to play the game and by the number of faces they have. Besides the standard cubical die with its 6 faces, there are the other regular solids with 4,8,12 and 20 faces. There is also a die with 10 faces, each in the form of a kite, and my informant points out longingly that our local games shop has a die with 100 faces. “Could you have one with an odd number of faces?” he asks.

His innocent question led me to think about many mathematical aspects of dice. This article answers his question, examines the geometry of dice (highlighting some unnamed solids which deserve to be better known to model-makers), considers surprising aspects of the mechanics of tossing dice and describes sets of unusual dice whose probabilities offer scope for many games which can trap the unwary gambler.
Walls and windows
Authors: Griffin Peter , Mason John
Published: January 2007

When students work through a written proof what is it that they are attending to? At what level are they taking in and making sense of what they see? The mathematical symbols (i.e. diagrams, equations, etc) that are found in proofs are a result of the writer seeing some generality, attempting to express that generality and to convince themselves and others of its validity. We recognise that students, when reading a proof may work directly with the symbols, somebody else's symbols, without attempting to enter into the process of expressing generality for themselves.
A general approach to three-variable inequalities
Authors: Griffiths H. B. , Oldknow A. J.
Published: January 2007

In tackling a problem, we needed to show that a certain 3 × 3 determinant is non-zero. This determinant could be expressed in terms of the symmetric, homogeneous function N = Σx.Σx2 + 6xyz - 2Σx3 of three variables, where, for example Σx2 = x2 + y2 + z2. We first looked into several classical books, to see if there was a relevant inequality. There was not, nor do they contain anything other than ad hoc techniques for dealing with the inequalities they give. In this paper we give a general method for dealing with a certain class of such inequalities; it might be instructive for undergraduates, partly to exercise them in applying a moderately complicated algorithm, and partly to show an application of 2- and 3- variable Calculus.
Sums on Channel 4’s “Countdown”
Authors: Glasbey C. A.
Published: January 2007

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

(7 x 9 + 4) x 8 - 10 = 526.
Geometry and Physics
Authors: Atiyah Michael
Published: January 2007

In my 1982 Presidential Address to the Mathematical Association I tried to explain the general role of Geometry in Mathematics so it seems appropriate, on this centenary occasion, that I should move beyond the confines of Mathematics and discuss the interrelation of Geometry and Physics. There are two very good reasons for doing this. One is historical and arises from the close ties between the two subjects in their early evolution. A second and more topical reason is that, over the past two decades, there has been a remarkable burst of interaction of a quite unexpected kind between Geometry and Physics.
Take it or leave it!
Authors: Fletcher T. J.
Published: January 2007

The development of algorithms has been one of the principal concerns of mathematics throughout its history, but now that machines can perform algorithms more efficiently than people our attitude to algorithms has to adjust. It is hardly possible for a school to implement the National Curriculum in mathematics without having the computer language LOGO among its resources, but the curriculum's prescriptions are minimal, and it is quite possible to introduce the opening steps of the language and then do no more. What further use can be made of the language? In this article I show how LOGO can provide a systematic approach to some traditional problems of combinatorics.
Newton's teaser
Authors: Mackinnon Nick
Published: January 2007

This article looks at some of the history of “Leibniz's series”

and at Newton's riposte in a letter to Leibniz, the Epistola Posterior:

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

Charles M. Whish (of the Madras establishment of the East India Company Civil Service) visited Kerala, in southern India, during the early part of the nineteenth century, and collected some antiquities. The information he could gather about these antiquities was summarised and the curious looking items were displayed in his “showroom”, an article entitled “On the Hindu quadrature of the circle and the infinite series of the proportion of the circumference to the diameter exhibited in the four Sastras, Tantra Sangraham, Yukti-Bhasa, Karana-Paddhati and Sadratnamala.” This paper was read at the Royal Asiatic Society in 1832 and published in 1835 in [12]. Sightseers who passed by Whish's “showroom” were unaware of the worth of its exhibits, and the explorative and organisational labours of Whish remained unrecognised for over a century. By the 1940s though, an occasional enthusiast would wander in and the specimens kept mere amazed them and roused their interest and enthusiasm. Gradually more people were drawn to the antiquities, until by the 1980s Whish's small showroom had become die nucleus of a substantial institution. In this article mere will be a tour of the showroom, and some of the information on me exhibits will be brought up to date.
A gemstone in matrix algebra
Authors: Crilly Tony
Published: January 2007

The history of mathematics is an abundant field for making surprising discoveries. Some luck is necessary, but whereas the literary tradition has been extensively explored by scholars, finding a nugget in the history of mathematics is not so difficult as turning up a new fragment by Jane Austen, or a lost piece by Mozart. In my case I struck lucky in the theory of matrices.

As is well known, the theory of matrices arose during the 1850s – a useful benchmark is the publication of Arthur Cayley's celebrated memoir of 1858, A memoir on the theory of matrices, a paper which generations of mathematicians have taken as signalling the beginning of matrix theory. Even today the opening paragraphs serve as a useful introduction to the subject.
The concept of integration: a fundamental approach
Authors: Hobbs David , Relf Simon
Published: January 2007

According to Richard Courant and Herbert Robbins writing more than fifty years ago in their classic book What is Mathematics? (which is still in print)

‘... today the calculus can be taught without a trace of mystery.’

Sadly for many students entering university with A level Mathematics, and for some leaving university with a degree in Mathematics, this is not so. As was noted by John Smith, for some students there appears to be little understanding of the principles.
Generalising ‘Sums of cubes equal to squares of sums’
Authors: Mason John
Published: January 2007

David Pagni drew attention to a result which is ascribed by Dickson [2, p.
286] to Liouville (1857), that the sum of the cubes of the number of divisors of
each of the divisors of an integer, is equal to the square of their sum. For
example, the divisors of 6 are 1, 2, 3, and 6, which have 1, 2, 2, and 4 divisors
respectively, and

Pagni observed, as have others, including Mason et
al. [4, p. 179], that the reason Liouville’s result works is
because the numbers generated are element-by-element products of sequences of the
form {1, 2, ..., t}, which are well known to have the
sum of their cubes equal to the square of their sum.
Vector products
Authors: Gerrish F.
Published: January 2007

In his thought-provoking Note 82.45 (November 1998) about products of vectors, Bob Ardler asks (p. 454) “Why does dot thrive in n dimensions, but cross only in 3?” and (p. 456) “Which, if any, generalisations of the cross product have been pursued?”

Both of these matters have been treated fairly recently in several journals, including the Gazette, but the subject was first discussed and completely settled in 1942 by B. Eckmann in [1] (see especially pp. 338-339); cf. also [2].
Simple mappings in mechanics
Authors: Bajc Drago
Published: January 2007

Consider the motion of a particle of unit mass acted upon by a homogeneous, central, conservative force f(r), where r is the distance between the centre of force and the particle. In this connection, homogeneity means the following property of the force: there exists a constant α such that for every c
The factorial function: Stirling’s formula
Authors: Fowler David
Published: January 2007

How big is n!? For example, to pluck a number out of thin air, what is the order of magnitude of 272! ?

This is the third note of a series on the factorial. The two previous notes [1] and [2] dealt with the factorial function x! while here we only consider n! when n is an integer, but its main results also apply to non-integer arguments. This note is longer and more elaborate than the previous ones, but the principal result is in the opening section. Only aficionados need go any further.
The ichthyoids
Authors: Cundy H. Martyn
Published: January 2007

A sign similar to Figure 1 has become increasingly common in recent years; many, including the author, carry this ancient Christian symbol on their cars. Probably few know that it is a simple mathematical curve. It is of course questionable whether Apollonius knew it, though he could have done, and even more questionable that early Christians knew their Apollonius. But they certainly knew some form of the symbol. Nowadays it is often crudely reduced to two circular arcs - making steering difficult for the poor fish.
Tumugu Sakuma’s problem
Authors: Suzuki Fukuzo
Published: January 2007

In the years 1603–1867, known as the Edo period, when Japan isolated itself from the western world, the country developed its own style of mathematics, especially geometry. Results and theorems of traditional Japanese mathematics, known as ‘Wasan’, were usually stated in the form of problems; these were originally displayed on wooden boards (‘sangaku’) hung in shrines and temples, but many later appeared in books, either handwritten with a brush or printed from wood blocks. (See [1, 2, 3] for more details.) Solutions to the problems were not given, but numerical answers were sometimes provided. The problems were written in a form of language called ‘Kanbun’, based on Chinese, which cannot be readily understood by modern Japanese readers even though written Japanese makes extensive use of Chinese characters.
The Site of Derbe; A New Inscription
Authors: Ballance M.
Published: January 2007

The question of the site of Derbe has for many years exercised the ingenuity of those who have studied the topography of ancient Lycaonia.

As long ago as 1824 Leake wrote that “of the cities, which the journey of St. Paul has made so interesting to us, the site of one only (Iconium) is yet certainly known. Perga, Antioch of Pisidia, Lystra, and Derbe, remain to be discovered”.

Leake's own conjecture as to the site of Perga was confirmed within thirty years; Antioch was fixed beyond reasonable doubt by Arundell in 1833; and fifty-two years later Sterrett confirmed Leake's suggestion that Lystra lay at Hatunsaray.

The following dedication by the council and people of Derbe, found by the writer in 1956 at Kerti Hüyük, twenty-two kilometres north-north-east of Karaman, provides an answer to the last of Leake's problems and shows that his own location of Derbe at Maden Şehir, based though it was on the slenderest of evidence, was probably closer to the truth than any of those proposed by his successors in the field.
Preliminary Report on a Survey of Pre-classical Remains in Southern Turkey
Authors: Mellaart James
Published: January 2007

During the Autumn of 1951 and from April to November, 1952, a survey of pre-classical remains in still mostly unknown areas of Southern Turkey was undertaken with the grant of a scholarship from the British Institute of Archaeology at Ankara (for the session 1951–2). A renewal of this scholarship in 1953 will make the continuation and completion of the survey possible in 1953–4.

A vast amount of new material, some of which is of great importance for Anatolian prehistory, having been collected, it was considered advisable to write a preliminary report dealing with the pottery in order to make preliminary results immediately available rather than postpone it until the end of the survey. Hence the sketchy nature of this report which deals with pottery groups only, and the unavoidable omission of the description of the sites, size, period and distribution maps and general conclusions.
Ursu and Ḫaššum
Authors: Smith Sidney
Published: January 2007

Professor Garstang, Whose excavations and geographical studies have so notably increased sources of information about, and our knowledge of, eastern Cilicia in early times, will have watched with interest, and perhaps with amusement, the way in which, in modern studies of texts, locations proposed for Ursu have jumped about over a considerable area, in which physical features might be expected to restrict the possibilities. As the story of Ursu in the second millennium ends just before that of Qizzuwadana begins, so far as our present information goes, it may not be inappropriate to dedicate a brief account of the development of evidence about, and the changes of opinion concerning, the situation of the city and the land to the friend who has often discussed Qizzuwadana with me during the last thirty years; the course taken is not without its lessons for criticism, which should be a form of intellectual discipline.

The reason for believing that Ursu was a city in the mountainous region Ibla was an inscription of GU.DE.A, that for identifying Ibla with part of the Amanus was based on texts concerning Naram-Sin. The argument seemed simple and logical enough for Peter Jensen to identify Ursu with Arsuz, by which, probably, he understood no more than a location on the coastal strip west of the Bailan Pass.
Anatolia and Thrace
Authors: Childe V. Gordon
Published: January 2007

Intimate Connections Between Anatolia and Thrace had been suspected ever since Kazarov published his finds from Kyrillovo. Despite the peculiarities in their handles, the vases and bronzes look so distinctively Anatolian that Thrace seemed just a provincial extension of the Early Troadic Bronze Age culture as known in 1914. Since 1945 new finds from Mikhalits, taken in conjunction with Mikov's discoveries at Karanovo and those of Hamit Zubeyr Koşay, at Büyük Güllücek have put these relations in an entirely new light. Mikhalits, near Svilingrad where a depas amphikypellon had been found in 1941, lies so close to the present frontier that fuller excavation since 1945 has been impracticable. But the observations made in that year alone are sufficiently illuminating. The site is not a tell, but occupies the crest of a natural ridge, and was defended by a stone wall enclosing an area of 80–90 m. in diameter.
Beycesultan, 1959: Sixth Preliminary Report
Authors: Lloyd Seton
Published: January 2007

A final season of excavating at Beycesultan was arranged in the autumn of 1959 and lasted from 15th September to 28th October. The work was once more in charge of the Director, who was accompanied by Mrs. Seton Lloyd and a staff consisting of Mr. Martin Harrison (Institute Scholar for 1958–59) and Mrs. Harrison, Mr. Harry Smith of Christ's College, Cambridge, Miss Carol Cruikshank, Mr. Michael Brett as architect and Bay Osman Aksoy as Turkish Government representative. The Assistant Director and Miss Clare Goff also took part in the excavations during the second half of the season.

It had been decided on this occasion to concentrate the entire resources of the expedition on the continued clearance of the Middle Bronze Age palace on the eastern summit of the mound, partly excavated in the seasons of 1954 and 1955, in the hope of recovering as much of the plan as possible before the excavations finally closed down. This was accomplished with considerable success. Two large new areas of the building were cleared and a point reached where any further extension would have met with serious practical difficulties.
The Overland Route across Anatolia in the Eighth and Seventh Centuries B.C.
Authors: Birmingham J. M.
Published: January 2007

An overland route by which oriental merchandise and ideas were transmitted to the Ionian Greeks via the Anatolian plateau and the river valley routes of the west was long ago posited by Hogarth, and supported by Karo, Barnett and others, although there was little evidence from central Anatolia to confirm it. More recently this route was virtually discounted in favour of a sea route from N. Syria, especially Carchemish, through the port of Al Mina, to Greece and Etruria, via Cyprus, Rhodes and Crete, discussed by Sidney Smith, Humphrey Payne, Mrs. Maxwell-Hyslop and others, which is assumed to have been at its height in the earlier eighth century; and Barnett has also shown the importance of a third route, from Azerbaijan to Trebizond and west via the Black Sea, for which the main evidence, a tomb group from the Caucasus, is probably later seventh century.

It is clear that the second of these three routes carried the bulk of Oriental trade to Greece and the west. Undoubtedly the most important Orientalizing influences on Greece, as shown by Payne, were those from the Cypro-Levantine cultural province, and there is ample evidence of the exchange of pottery, terracottas and ornamental bronzes of Cypriot and Phoenician production between the Syrian coast, Cyprus, Rhodes, Samos, Miletus, Chios, Delos and the west.
First Impressions of the Çatal Hüyük Plant Husbandry
Authors: Helbaek Hans
Published: January 2007

The deposits of carbonized grain and seeds excavated at Çatal Hüyük are the largest and best preserved finds of their kind ever recovered from so early periods in the Old World. Indeed the volume is so great that it is a matter of years just to examine the plant remains and put names to the many species. The development of the proper attitude of mind in the examiner is by necessity a slow process when he is faced with so many completely novel cultural circumstances that there is no valid background of reference. However, five months' ecological and floristic studies on the spot have cleared up so many problems that a satisfactory result may be anticipated in due course. The generosity of the Danish Carlsberg Foundation and James Mellaart made this long and extremely useful excursion possible.
Excavations at Çatal Hüyük, 1965, Fourth Preliminary Report
Authors: Mellaart James
Published: January 2007

A fourth season of excavation at Çatal Hüyük took place between 18th July and 25th September 1965 under the auspices of the British Institute of Archaeology at Ankara with Professor O. R. Gurney as director administratively responsible to the Turkish Authorities. The excavation staff were Mr. and Mrs. James Mellaart, Miss Pamela Pratt and Miss Priscilla Berridge as conservators, Miss Raymonde Enderlé Ludovici (artist), Mr. and Mrs. N. Alcock (surveyor), Mr. Ian Todd, Mlle Anne Timonier and Mr. J. Jurriaanse as field assistants. Bayan Nemika Altan and Bay Mehmet Turgut, both from the Ankara Archaeological Museum, were our official Turkish Representatives.

The excavation was sponsored by the British Academy, the Universities of Edinburgh and London, The Royal Ontario Museum, Canada, the Wenner-Gren Foundation for Anthropological Research, the Bollingen Foundation, both in New York, the Australian Institute of Archaeology, the British Institute of Archaeology at Ankara and the German Archaeological Institute in Berlin. BP Aegean Ltd. in Istanbul once again supported the expedition with survey equipment and transport.
Excavations at Alahan Monastery: Second Preliminary Report
Authors: Gough Michael
Published: January 2007

Excavations at Alahan Monastery were continued during the summer of 1962 for a period of exactly eight weeks, from early July until 1st September. The Director was accompanied by Mrs. Gough, and Mr. Robin Guthrie acted as his chief assistant. Messrs. Gerard Bakker and Anthony Harrison, the expedition's architects, were responsible for the survey and partial restoration of newly excavated buildings, and Miss Susan Harrison for pottery and small finds. Miss Caroline Pickard and Mr. David White were field assistants. Bayan Süheyla Keskil, Director of the Antakya Museum, acted as the official representative of the Turkish General Directorate of Museums and Antiquities. To her and to the Kaymakam of Mut the expedition is grateful for their co-operation. An average of twenty-four workmen was employed, many experienced from earlier excavations at Alahan and Dağ Pazarı, and Süleyman Yemenici was again a most efficient foreman. The number of visitors to the site showed a great increase over 1961, and if a jeep road could be built to cover the 300 metres of steep slope from the main road to the monastery, there is no doubt that this outstanding monument of the early Christian period would soon be better known and appreciated (Pl. XXXa).
Churches and Chapels of Central Lycia
Authors: Harrison R. M.
Published: January 2007

The high Anatolian plateau is divided from the south coast of Turkey by the far higher Taurus chain. This extends south-west from Armenia in a vast double-curve, accommodating the coastal plains of Cilicia and Pamphylia and terminating abruptly in the wide, rugged promontory of Lycia (Fig. 1). The width of the promontory is about 120 km.; its mountains rise to 3,000 m., and it was aptly characterized by Strabo as τραχὺς καὶ χαλεπός ἀλλ' εὐλίμενος. Between Fethiye and Antalya steep cliffs give way to sandy beaches in three places, the Xanthus valley and the plains of Demre and Finike. West of Demre, beneath towering cliffs, is the little harbour of Kaş; behind these cliffs the ground drops to a wide inland basin, whose outlet is the long and spectacular Demre gorge. Inland roads, where they exist, are steep and tortuous. The Xanthus valley carries a road to Fethiye; a poor road from Kaş, and a tolerable one from Finike lead to the upland plain of Elmalı, which has roads leading west to Fethiye and north-east to Korkuteli; from this last town there is an easy road north-east towards Burdur, and more difficult routes north-west to Tefenni and south-east to Antalya.
The Çifte Minare Medrese at Erzurum and the Gök Medrese at Sivas
Authors: Rogers J. M.
Published: January 2007

The Architecture of the Seljuk Turks, as well as proving to be their most lasting contribution to history, is also a contribution to the great architecture of world, both from the point of view of technical accomplishment and in its marvellously imaginative use of decoration. Thanks to the pioneering work of Halil Edhem and Max Van Berchem in Part III of their Corpus Inscriptionum Arabicarum (Cairo, 1910–17) [CIA.] and of their many successors our knowledge of the extant, and destroyed, monuments has been increased to the extent that a series of secondary studies, on relations between various groups of monuments in default of more precise details of the relationships between craftsmen and their patrons or employers, or, more ambitiously, general attempts to explain the high place which architecture so obviously held in the Seljuks' estimation, becomes necessary. Moreover, although the individuality of their contribution is comparatively well-known by this time, even in Western Europe, it is still obscure how the manifold influences which the Seljuks in their progress westwards through Persia and the Caucasus underwent were transmuted in Turkey into a style of such originality, strength and charm.
The Chipped Stone Industry of Avla Dağ
Authors: Todd Ian A. , Pasquare Giorgio
Published: January 2007

The mountain Avla Dağ lies c. 245 km. SE. of Ankara, c. 8 km. SSE. of Ürgüp on the east side of the Damsa Çay valley, in the vilayet of Nevşehir.

Obsidian implements were first found on this site by Dr. Giorgio Pasquare of the Maden Tetkik ve Arama Enstitüsü, Ankara, during the course of a geological survey of the Ürgüp area in 1963–4. A considerable quantity of obsidian implements and flakes was collected at the time, and subsequent visits to the area by the authors have resulted in further additions to this collection.

The geological section of this paper was written by Dr. G. Pasquare, and the archaeological section by I. A. Todd.
Prehistoric Sites in the Göksu Valley
Authors: French D. H.
Published: January 2007

The valley of the river Göksu (the ancient Calycadnus) is not unique as a road through the Taurus mountains. At least one other route was used in antiquity; this was by the Cilician Gates (now the Gülek boğazı). The valley of the Göksu, however, provides the easiest means of access from the coast to the plateau and, conversely, the easiest descent from the plateau to the coast. At the upper end of the route lies the Konya Plain with the sites of Çatal, Can Hasan, Karahüyük-Konya and numerous mounds of the Hittite period; at the lower end, the Plain of Adana and the sites of Mersin and Tarsus.

The excavations at Çatal East and West, Can Hasan and Karahüyük-Konya promise to produce an almost complete pottery sequence for the Konya Plain. At certain points in this sequence influence from the south coast has been suggested. Traces of this contact, if it existed, between the two areas might possibily be found in the valley of the Göksu. With this possibility in mind, a re-examination of the Mut area was carried out and, at the same time, an attempt was made to verify the suggested relationship of the Göksu valley to the two “culture-areas”, the Konya Plain and the Plain of Adana, from the Neolithic period until the Iron Age.
Some Byzantine Churches from the Pontus
Authors: Winfield David , Wainwright June
Published: January 2007

The Byzantine antiquities of the Pontus have received little more than a passing glance from either travellers or archaeologists. With the exception of the town of Trebizond, the monuments of which have now been subject to study in some detail, and the monastery of Sumela which has always attracted the attention of travellers, the only published works on the subject are the article by Professor Talbot Rice containing the results of his survey journey in 1929, and the book which he wrote in co-operation with Millet. The “Studia Pontica” of Cumont and Anderson is concerned primarily with classical antiquities although Cumont in his section makes frequent reference to medieval antiquities; and the “Church of Trebizond” by the last Metropolitan of the town, Chrysanthos, is concerned more with history than with descriptions of the monuments. The not inconsiderable body of travellers to Trebizond and eastern Turkey went there, for the most part, by sea and followed one or other of the branches of the caravan road running south-eastwards to Erzurum, and on into Persia and Central Asia. It may, however, be of use to bring these accounts up to date in so far as we have followed in the footsteps of earlier travellers.
Aşvan 1968–72: the Excavations
Authors: French David
Published: January 2007

The purpose of this long, interim report is fourfold:

1. to provide a straightforward preliminary account of results of excavations in the Aşvan region in the years 1968–72;

2. to attempt an explanation of how and why the modern studies were carried out;

3. to offer a tentative demonstration of the relevance of the modern studies to archaeology (i.e. the excavation of objects and structures);

4. to outline, by using concrete examples, the general theory and methods, and thereby to demonstrate the feasibility of a co-ordinated approach.

The Keban Project was founded in 1968 under the aegis of the Middle East Technical University and with the co-operation of the Turkish Government. The stated aim of the Project was the rescue of historical materials from the area to be flooded by the Keban Dam, located just below the confluence of the Murat and the upper Euphrates (Fig. 1). The necessity of immediate action had been demonstrated largely through the efforts of the Faculty of Architecture and Restoration. In the area of the flood zone staff and students had carried out feasibility and recording surveys which then made clear both the nature and requirements of a rescue operation. Their results were published in Doomed by the Dam (METU, Ankara 1967). In 1968 a Committee (METU Keban Dam Area Salvage Project Executive Committee) was set up, under the chairmanship of the then Rector of METU, Dr. Kemal Kurdaş, to co-ordinate the efforts of those various teams, both Turkish and foreign, which had accepted the Committee's appeal for joint action in a rescue operation.
Kill-off Patterns in Sheep and Goats: the Mandibles from Aşvan Kale
Authors: Payne Sebastian
Published: January 2007

Reports on animal bones from archaeological sites often include information about the “kill-off pattern” for each species – i.e. the relative representation of different age-groups in the sample. Osteologists believe that this information can be used as evidence for whether an animal was wild or domesticated, and, if domesticated, about the way in which man managed the animal. In this paper a method is described for recording such data for sheep and goat using mandibles and mandibular teeth; the analysis and interpretation of such data is discussed using excavated samples from Aşvan Kale.

When people keep sheep or goats, the age at which the animals are slaughtered depends on a range of factors: on the relative value placed on the different products, on the characteristics of the stock, and on a range of environmental factors – in particular, seasonal variation in the availability of grazing and feed. If meat production is the aim, most of the young males are killed when they reach the optimum point in weight-gain, only a few being kept for breeding.
A Babylonian Architect?.
Authors: Wiseman D. J.
Published: January 2007

Professor Seton Lloyd's publications and teaching have always been marked by his profound understanding of Mesopotamian architecture. It therefore seems appropriate, in this volume to his honour, to present some hitherto unpublished tablets which may add a little to our knowledge of some aspects of the ancient practice of surveying.

The small tablet BM.38217 (Fig. 1), probably originating from Babylon itself, shows in elevation a six, originally seven, stepped ziggurat with the principal dimensions given, UŠ being used for the length, and SAG (the “short side” of the rectangle as drawn) for the height. The second level is described as “Front (-view) of the dwelling of Anshar” (pa-ni šu-bat an-šár). While this note may well apply to the whole of this unique plan, it is to be observed that the first two storeys have accentuated (and external) markings which must represent the frontal and lateral access. The inner markings are perhaps to show where the ramps or stairway crossed the front of the main building (as in the ziggurat at Ur). The gaps in the base of the third and probably fourth (and higher?) stages may show that a direct frontal stairway to the seventh stage was envisaged. This seems a better explanation than that a five staged ziggurat is shown imposed upon the ground-plan of an adjacent and larger building. The lower stages are certainly not the plan of any two-storied “temple of Anshar” or of a gate-building.
Dedications to Mên Askaenos
Authors: Levick Barbara
Published: January 2007

On my first visit to Turkey, in 1955, I was kindly allowed to copy and photograph a number of dedications to the god Mên which are now housed in the Classical Museum, Konya ; they would have been brought from the hieron on Kara Kuyu hill, just outside the colony of Pisidian Antioch, probably after the excavations conducted by Sir W. M. Ramsay in 1912. (In his article “Studies in the Roman Province Galatia, II : Dedications at the Sanctuary of Colonia Caesarea”, JRS. VIII (1918), 107 ff., he refers by number to a list of inscriptions which he seems never to have published.) Eleven of these stones, with three uninscribed monuments, have since been published by Mr. E. N. Lane in the first part of his work on “A Re-study of the God Men”, Berytus XV (1964), 36 ff. Mr. Lane writes : “It [the unpublished material] was all found ostensibly in the course of the excavations which D. M. Robinson carried out in 1924 on the site of the forum of Antioch”.