bluuebunny/crossref_metadata_2025 huggingface dataset:
Zeno, Aristotle, Weyl and Shuard: two-and-a-half millenia of worries over number
Authors: Kilmister C. W.
Published: January 2007

It has been common in recent years, if not entirely obligatory, for your President to address you on this occasion about the difficulties and opportunities he has found in the practice of teaching, and this year will be no exception. But following the excellent example of all past Presidents, as far back as I have investigated, I intend to confine my address to that part of the activity about which I am practically conversant. So while I hope that the general ideas and conclusions of my talk will be enjoyable and possibly useful to everyone here, I shall deal in detail only with the narrow problem of first-year undergraduates. I say simply ‘problem’ because I believe that the various different questions (the ‘interface’, the content of first-year pure/applied courses, how should the sixth form teacher best prepare the future university entrant,…) are all aspects of a single problem. For the sake of precision I shall deal with only one aspect of this problem, as it arises in analysis. Knowing me, you might have expected rather that I would have discussed the difficulties of teaching mechanics, or of persuading young people of 18 plus (although many of them have been brought up since five years of age on a practical approach to mathematics!) that there is any possibility at all of making an application of mathematics in the external world. My depression about that aspect is too strong, and my involvement in it is probably too deep, for me to see it clearly. But my experiences supervising small groups of students who are making their first genuine acquaintance with the real number field suggest to me the possibility of improving matters.
The Mathematics of a Driving Hazard
Authors: Baylis John
Published: January 2007

The standard procedure for turning right at a cross-road is first to move as far over to the right as possible, while remaining on one’s side of the road, which leaves other traffic free to go straight on or to turn left, provided the road is wide enough.
The Laws of Mechanics
Authors: Dampier M. D.
Published: January 2007

The two great monuments of Western science are Euclid’s Elements and Newton’s Principia. Both are severely mathematical works; both set forth cosmological theories; in their day both were considered daring and speculative; both achieved unprecedented accuracy in application, so much so that at one time they were thought to be based upon a priori truths of reason, and even today are preferred to experiment over a wide range of phenomena. These two theories remain indispensable as elements of modern scientific thought despite the fact that they were simultaneously superseded in 1915 when Einstein published his theory of gravitation, a theory even more mathematical and boldly speculative than its predecessors. (One must, of course, remember that the nineteenth century discovery of non-euclidean geometry, whilst destroying the belief that Euclid’s geometry was true a priori, did not shake the belief that it was true as a matter of fact.)
Triangular Square Numbers
Authors: Potter D. C. D.
Published: January 2007

Shiu has shown [1] that there are infinitely many triangular numbers that are also square. He remarked that while his theorem did give a list of such numbers, it did not give all of them. It seemed that there might be a reiterative method, working in integers, that gave more of these triangular square numbers, and which included all the known smaller numbers.
The left-over matches
Authors: Bradley Christopher
Published: January 2007

Matches of a certain popular brand are contained in a box designed to hold 100 matches. This box has two compartments so that if you open the box casually and without thought as I do, then you will select a match at random from one compartment or the other with equal probability. At some stage you will empty one of the compartments; and having more statistical insight, perhaps you will be less surprised than me by the large number of matches often left unused in the other compartment.
Bertrand’s paradox
Authors: Tissier P. E.
Published: January 2007

An interesting and important problem in probability theory is known as ‘Bertrand’s paradox’. Consider a chord chosen ‘at random’ inside a circle: what is the probability that the length of the chord exceeds the length of side of the inscribed equilateral triangle? Three different answers have been given to this problem p = ½, ⅓ or ¼.
A problem of astronomical proportion
Authors: Harvey P.
Published: January 2007

It is easy to design simple gearing enabling a clock or instrument to indicate hours, minutes and seconds, since the ratios are ‘man-made’ integers. If an instrument is required to indicate astronomical data we find that nature is not so considerate, and the gearing presents an interesting problem.
Smooth curves of constant width
Authors: Tennison Robert L.
Published: January 2007

The construction of curves of constant width using circular arcs is well known; the procedure may be found, for example, in [1]. This article describes a different method for constructing a family of ‘smooth’ curves of constant width. Basic properties of such curves may be found in [1].

Let C be a regular, smooth, and convex curve in the euclidean plane. Regularity implies that each point of C lies on only one support line and each support line contains only one point of C, smoothness implies the existence of derivatives at each point of C, and convexity implies the curve is a simple closed curve whose interior points form a convex set. Select a point O on C as origin, use the support line to C at O as the x-axis, and give the curve a counter-clockwise orientation (see Fig. 1).
Quanta for the quick
Authors: Matthews Geoffrey , Lewis Bob
Published: January 2007

The aim of this note is simply to encourage dialogue between mathematics and physics teachers. In most school physics and chemistry courses, any mention of quantum theory has been limited to a brief qualitative discussion, or has been restricted to the simple Bohr theory. The new Nuffield Advanced Physics material [1] goes much further than this, with the opportunity to apply some quite simple mathematics, supported by a computer analysis. We shall here give a gross simplification of the end of a long story in the physics course.
Functions which permute the roots of an equation
Authors: Budden F. J.
Published: January 2007

An amusing exercise to give to a mathematical sixth form is:

If the roots of the equation

F1(x) ≡ x3 + x2 − 2x − 1 = 0 (1)

are α, β, γ, form the equation whose roots are α2 − 2, β2 − 2, γ2 − 2.

The usual methods used will be, either to find the coefficients of the new equation by forming the appropriate symmetric functions of α, β, γ; or else to eliminate x from the relation y = x2 – 2 and the given cubic equation.
The Mathematics of Borrowing Money
Authors: Gaines Fergus J.
Published: January 2007

Many people have had the experience of borrowing a sum of money which is to be repaid with interest by making equal monthly payments over a year or a number of years. Two problems suggest themselves:

1. If the annual rate of interest is known what is the value of each monthly payment?

2. If the monthly payment is known, what is the annual rate of interest?
A line-and-conic theorem having a visual correlate
Authors: Nickalls R.W.D.
Published: January 2007

This article describes a new and general line-and-conic property, leading to a consideration of a ‘six-point’ circle and the related geometry of an interesting visual illusion.
Rings of small order
Authors: Fletcher Colin R.
Published: January 2007

Most students in their undergraduate careers ensure that they have many examples of groups at their finger tips. These include not only whole systems such as cyclic groups and symmetric groups but also specific examples, in particular groups of small order. These latter groups are useful for trying out new ideas as soon as they are encountered, such as the bogeys of cosets, normal subgroups and factor groups. If we consider only groups of order 7 or less, then we already are furnished with nine examples of cyclic, non-cyclic, abelian and non-abelian groups.
How commutative can a non-commutative group be?
Authors: MacHale Desmond
Published: January 2007

Let G denote a finite non-commutative group. What can we say about the number of ordered pairs (x,y), where x,y ϵ G, such that xy = yx?

In order to prepare ourselves to answer this question, let us examine the Cayley table of S3, the symmetric group on three symbols. We take as generators the reflection (12) and the rotation (123). It is clear that we are examining the Cayley table for symmetry about its main diagonal.
On a certain diophantine equation
Authors: McCutcheon J. J. , Forfar D. O.
Published: January 2007

The unit of currency on Mars is the zonk, which consists of a whole number of zinks. An enlightened, though somewhat green, government recently decided to revamp the taxation system, which at the time was manifestly unfair to male Martians as it required them to pay less tax than females. (Martians are very unselfish and feel aggrieved if they are better off than other Martians.)

Previously, only females had had to pay ‘Population Tax’, each having to pay a certain number of zonks, that number being the total number of males. (The idea was to encourage polygamous marriages.) After the change, all Martians, male and female, were to pay Population Tax, which was to be a certain number of zinks, that number being the total number of males and females.
Patience rewarded
Authors: Gates L. W.
Published: January 2007

When I was younger, and had nothing better to do with my spare time, I sometimes used to play my own game of ‘patience’. I would take a pack of 52 playing cards and arrange them in order, ace to king of each suit and then the four suits one on top of the other. I would begin my game by taking the card at the top of the pack and putting it at the bottom; then taking the second card and placing it face upwards on the table; then the third card was transferred to the bottom of the pack; then the fourth card was placed on top of the second on the table; and so on, until all the cards had been placed in a new pile on the table. I would then turn the pack on the table face downwards and perform the whole operation again with the cards arranged in this new order. My aim was to see if, by repeating the whole operation enough times, I could get the cards back into their original order. If I had known that I would need to perform the operation 840 times, I probably would not have bothered to continue with my game.
(2)… by efficient cooperation
Authors: Wilker J.B.
Published: January 2007

Let D and R be two non-empty sets. A function f: D → R is a rule for assigning to each element x belonging to D a single element y = f(x) belonging to R. The set D is called the domain of the function f and the set R is called its range.
Rational approximations: a basic approach
Authors: Phillips G. M.
Published: January 2007

Last year I ran 1147 miles. Early in that December I had checked my ‘running total’ and found that it had already passed 1000 miles. I pondered on what might be an appropriate figure to aim at and toyed with 1040 miles (20 miles per week), 1095 miles (three miles per day) and 1111 miles (easy to remember). Finally, the combined dementia of runner and mathematician resulted in the choice and achievement of 1147 miles, chosen to give the closest possible daily average to π miles. The quotient 1147/365 exceeds π by about 0-0009.
Parallels
Authors: Giblin P. J.
Published: January 2007

Given a straight line L in the plane, how can we find all lines parallel to L? Here is one way: at each point P of L draw a straight line perpendicular to L. Now choose a number d and measure a distance d down these lines, always in the same direction. Joining up the points P′ so obtained gives the parallel to L at distance d.
Additive frieze patterns and multiplication tables
Authors: Shephard G. C.
Published: January 2007

A frieze pattern is an array of numbers arranged in staggered rows, like the bricks in a wall. In the case of a multiplicative frieze pattern the top and bottom rows consist entirely of ones, and for each ‘diamond’ of four elements

the unimodular rule

ad = bc + 1 (2)

holds. These frieze patterns have many curious properties, and for further details the reader is referred to the article Triangulated polygons and frieze patterns by J. H. Conway and H. S. M. Coxeter which appeared in Gazette 57, 87–94 and 175–183 (1973).
Problems faced by mathematics students at the school/higher education interface
Authors: Towers David
Published: January 2007

I, in common with many others, dislike pretentious titles, particularly ones which disguise human problems in the jargon of computer hardware, so I sympathise if mine leaves you cold. The difficulties which I want to address are the emotional and academic ones so often encountered in the transition from secondary education to a degree course containing a major component of mathematics. They are difficulties of which I have been aware for many years, but on which my attention has been focused more sharply by two recent conferences: the first was the Mathematical Association annual conference in Manchester at which I was asked to lead splinter group discussions on this topic, and the second was the latest University of Nottingham Undergraduate Mathematics Teaching Conference at which I participated in a group discussing “Perennial difficulties” (and which will issue a report later this year). The very title used at the latter meeting expresses clearly the intractability of many of these problems.
The twenty-one card trick
Authors: Anderson Oliver D.
Published: January 2007

1. Introduction

Nearly forty years ago (and I barely knowing the three times table), my father taught me the twenty-one card trick, amid background murmuring from mother as to its mysterious mathematical nature. Now, with a rather more questioning six year old, I have been made to look at how it works, and see what variations a budding Paul Daniels might introduce.
Pitfalls in the use of computers for the Newton-Raphson method
Authors: Mackie D. , Scott T.
Published: January 2007

It is generally accepted that the presentation of numerical methods will depend to a large extent on the type of student being taught. Mathematics students should be exposed to error analysis and possible pitfalls of the various techniques. However, other groups of students, such as engineers or physicists, usually require a different approach, and the emphasis tends to be more on showing how to use the method on a calculator or, preferably, a computer. Indeed, at Napier College, students are encouraged to write their own programs and/or use the microcomputer laboratory. This practice, though commendable, does have the danger that the students begin to believe every answer that the computer/calculator generates. They forget that rounding errors can become important, and in fact teachers often forget to mention this, since more than 8 figure accuracy can always be assumed.
How Slowly can a Series Converge?
Authors: Shiu P.
Published: January 2007

Let f(x) (x≥0) be a positive continuous function. Associated with f(x), we can define a sequence of numbers {an} by setting an = f(n). Conversely, given any sequence of positive numbers {an}, we can find a positive continuous function f(x) such that f(n) = an. Of course, in this latter case, there is more than one such function f(x), but this is not relevant.
Solids of Constant Breadth
Authors: Gray Cecil G.
Published: January 2007

The Reuleaux triangle of Figure 1(a) is obtained by drawing three circular arcs of radius d with centres at the vertices of an equilateral triangle of side d. It can be rolled between a pair of parallel lines at distance d apart and is said to be of constant breadth d.

Applying an analogous construction in three dimensions to a regular tetrahedron of side d, we obtain a solid figure bounded by four spherical triangles intersecting in six circular arcs, the centre of each spherical portion being at the opposite vertex of the tetrahedron and its radius of curvature being d. This figure has two modes of rolling between parallel planes. In the first mode a vertex touches one of the planes and the opposite spherical surface rolls on the other; in the second mode, opposite circular edges touch the planes. The distance separating the planes in the first mode is d; in the second mode, the separation is d when the points of contact with the tetrahedron are at the opposite ends of the circular arcs, but this distance increases to d(√3 − ½√2), or l·025d, when the centres of the circular edges touch the planes. By slightly rounding one edge in each of the three opposed pairs, a solid of constant breadth may be produced. The geometry of this process is illustrated at Figure 1(b).
Finding a matrix multiplier by least squares
Authors: Richards N. W.
Published: January 2007

The method of least squares is a well known technique of curve fitting, giving estimates for the values of the coefficients in equations such as y = ax, y = ax + b, etc, in terms of observed values of the variables x, y. It is less widely realised that the technique can be extended to estimating matrix coefficients.
Fibonacci properties by matrix methods
Authors: Silvester J. R.
Published: January 2007

The Fibonacci sequence

0, 1, 1, 2, 3, 5, 8, 13, …

is defined by u0 = 0, u1 = 1, and un = un−1 + un−2 for . There are many elementary formulae relating the various un, most of which, since the sequence is defined inductively, are themselves usually proved by induction.
The linear group SL (2, 3) as a source of examples
Authors: Mackiw George
Published: January 2007

In introductory courses in abstract algebra the cyclic groups Zn, the dihedral groups Dn, and the symmetric and alternating groups Sn and An, for various integers n, are often used to provide examples of various concepts. The intent of this note is to argue that another group could readily be added to this list: SL (2, 3), the multiplicative group of two by two invertible matrices of determinant 1 with entries from the field with three elements. Though this non-abelian group of order 24 does not appear often in introductory presentations, it is an excellent source of group theoretic examples and is also accessible to beginners, who at this stage of their study most likely have had some experience with matrices. Thus computations in SL (2, 3) can be implemented almost as easily as in the cyclic groups, and defining relations need not be introduced.
Anyone for tennis?
Authors: Roper Tom
Published: January 2007

The Independent [1], prior to the 1996 Wimbledon tournament, carried a story to the effect that Tennis had a problem. Rackets were getting longer and, so the International Tennis Federation (ITF) claimed, rallies were getting shorter as the serve dominated. The story provided some surprising figures. The current limit to the length of a racket is 32 inches, but the longer rackets which are the cause of the problem are 29 inches, 2 inches longer than the standard racket. The article claimed that such rackets 'give players up to 14 per cent more power than standard models'. The article went further,

‘Michael Chang of the United States, placed fourth in the world, has been using a 29 in. racquet (sic) since 1994, and says it has been key in raising his ranking.’ [1]
On the symmetries of a Grecian urn
Authors: O’Rell Diogenes
Published: January 2007

While musing on the graceful sylvan sceneDepicted on a classic Grecian urn,John Keats declared that “truth” and “beauty” meanThe same, and here this statement’s worth we learn.

“Thou still unravish’d bride of quietness!Thou foster-child of Silence and slow Time”,Wrote Keats [1], the um’s calm beauty to express,While he, by permutations of the rhyme,Did generate its group of symmetries,Which is dihedral and of order six.The um and its inversion therefore matchAnd all its patterns replicate in threes:So triplet dancers demonstrate their tricksWhile silent pipers play a triple catch.
Greeting cards and fractals
Authors: Hilton Peter , Pedersen Jean , Walser Hans
Published: January 2007

We will discuss in this article a fractal-like structure made from a flat piece of paper. What will motivate most people to want to make the structure is that it is pretty. In fact, the exercise has two rather obvious uses. First, greeting card companies may want to use the idea to manufacture interesting 3-dimensional cards which fit conveniently into envelopes; and, second, teachers may wish to teach students how to make it (and this process will also involve teaching them some beautiful mathematics). The structure itself is a model for a stage in a self-similarity process leading to a fractal. Building the model involves scoring a flat piece of paper in a prescribed manner, cutting along some of the score lines, and then folding some lines as ‘mountain’ folds and others as ‘valley’ folds.
Ask Marilyn: the mathematical controversy in Parade Magazine
Authors: Bello Anthony Lo
Published: January 2007

Marilyn vos Savant is listed in the Guinnes Book of World Records Hall of Fame as the human being with the highest IQ; she makes herself useful by answering questions in her column Ask Marilyn, which appears, for example, in Parade Magazine, a publication inserted into the Sunday editions of several American newspapers.
Evolution of finite sequences of integers …
Authors: Pompili Fulvio
Published: January 2007

In the March 1996 issue of the Gazette, [p. 36] the following conjecture by Sir Bryan Thwaites appeared: ‘Take any set of n rational numbers. Form another set by taking the positive differences of successive members of the first set, the last such difference being formed from the last and first members of the original set. Iterate. Then in due course the set so formed will consist entirely of zeroes if and only if n is a power of two.’
The truth behind ‘famous name’ mathematics
Authors: Luoma Keith
Published: January 2007

Before reading this article, you may like to turn to page 297, where you will find a quiz on ‘famous-name’ mathematics. In each of the questions it seems reasonable to suppose that the mathematician indicated in the title of the result is the discoverer or inventor of the result. But a careful look at mathematical history shows, in each case, that there is a ‘story behind the story’. As you read on, keep in mind that even the answers given below are subject to revision as new historical data is found and interpreted.
Probabilities for the Name Game
Authors: Hopkins David
Published: January 2007

A children's television game is played as follows: Four postcards from children who have written in to the programme are selected at random and the children's names are written on a board. The presenters then draw letters of the alphabet one by one from a bingo-style randomising machine and, after each letter is drawn, all occurrences of that letter in any of the children's names are crossed off. The winner of the game is the first child whose name is completely crossed off.
Lewis Carroll - Mathematician
Authors: Eperson D. B.
Published: January 2007

Over 60 years ago an article with the above heading appeared in the Mathematical Gazette, shortly after the celebration in 1932 of the centenary of the birth of Charles Lutwidge Dodgson, better known and admired universally as the author of the Alice books, Lewis Carroll.

At that time a literary critic expressed his opinion that ‘only a mathematician could have written the Alice books’, perhaps because they contain several references to arithmetic. In Wonderland, Alice met the irascible Ugly Duchess. ‘If everybody minded their own business’, the Duchess said in a hoarse growl, ‘the world would go round a great deal faster than it does’.
Word problems and equations: an historical activity for the algebra classroom
Authors: Ofir Ron , Arcavi Abraham
Published: January 2007

The following activity is one of a series developed for junior high school students (age 12-15). Each of the activities involves a historical discussion of a subject related to a certain curriculum topic, and takes the form of a teacher directed presentation/discussion with accompanying transparencies and worksheet.

The choice and development of the activities was guided by certain general principles. The connection between the regular curriculum and the selected subject is meant to give relevance to the history and also, to motivate and deepen student understanding of subject matter. The structure of the activity enables the teacher to change, omit, or to add if he wishes. Points for discussion and questions to be worked are deliberately inserted at intervals to activate students, because in previous trial versions which were closer to the lecture format we found that students lost the thread and hence, also interest. Reactions to the present format were much more encouraging.
Historical stories in the mathematics classroom
Authors: Führer Lutz
Published: January 2007

Some years ago when I was co-editor of the German periodicalMathematik lehrenwe decided to prepare an issue on the history of mathematics. To secure the interest of our usual readership, we planned to elaborate a few hints, recommendations, or suggestions on how to include historical items in the ordinary teaching of mathematics in school. It soon became clear however that this methodological problem would be the critical point of our project. It turned out, as I had feared from the beginning, that only a very few of my colleagues could be talked into writing about this feature of the subject. It was easy to get papers on historical facts or on hypothetical developments, but everyone found it hard to write about practical ways of teaching history in the mathematics classroom.
The Bible and Pi
Authors: Deakin Michael A. B. , Lausch Hans
Published: January 2007

It is widely, almost universally, believed that the Hebrew Bible gives the value of π as the crude approximation 3, a value much less accurate than those adopted by other ancient civilisations, such as the Babylonian, the Egyptian and the Chinese. In the English of the Authorised Version, the biblical source goes:
‘And he made a molten sea, ten cubits from one brim to theother: it was round all about, and his [i.e. its] height was fivecubits: and a line of thirty cubits did compass it round about.’
Solitary Solarians and densely packed spheres - from Stephen Hales to Thomas Hales
Authors: Stephenson Paul
Published: January 2007

In Isaac Asimov's novel Foundation and Earth (Grafton 1987) the inhabitants of the planet Solaria have evolved from early Earth space explorers. They have developed a society with many robots and few people. The small population of Solarians live as far from each other as possible. These solitary people are confined to their estates, which are distributed evenly across the planet. In this article I investigate the pretty problem of even distribution of points on a sphere. With the exception of one piece of spherical trigonometry the work needed to derive my (admittedly restricted) set of results is routine for sixth-form mathematicians but has the interesting pay-off announced in the title.
The Site of Prostanna
Authors: Ballance M. H.
Published: January 2007

The Pisidian city of Prostanna is mentioned in only two literary sources: Ptolemy (V, 5, 7) gives it as Prostama, while the list of bishops attending the Council of Constantinople in 381 includes Attalus Prostamensis among the Pisidian bishops.

The only official inscription mentioning it is one from Delos, in which the Demos of the Prostaenneis honoured a quaestor propraetore of the Province Asia in 113 B.C. The comparatively numerous coins give the name as Prostanna, and some of them bear representations of a conical mountain entitled Viaros (Οὐιαρος) or of a river-god Tioulos.

As long ago as 1890, Ramsay proposed to equate Mt. Viaros with the conspicuous sugar-loaf of rock at the southern end of Lake Eğirdir, immediately above the town of Eğirdir itself.
A Church of the Iconoclast (?) Period in Byzantine Isauria
Authors: Gough Michael
Published: January 2007

The rock-cut church of Al Oda (the Red Room) does not seem to have been visited in the past by any European traveller. In September, 1953, on the advice of Bay Neşri Atlay, then headmaster of the Primary School at Mut, a party consisting of Mr. and Mrs. Michael Gough, Mr. Michael Ballance and Mr. David Wilson visited the site and made a preliminary investigation. It was then decided to carry out a full examination at a later date, and this was done in August, 1955. The work was under the immediate charge of Mr. Martin Harrison of Lincoln College, Oxford, who also made reproductions in water-colour of some of the paintings and of the mosaics.
A Temple and Church at Ayaş (Cilicia)
Authors: Gough Michael
Published: January 2007

Less than two thousand years ago Western Cilicia, the Cilicia Aspera of the Romans, supported a large population. Settlements in the interior were comparatively few, for the rugged character of the country forbids agriculture on any considerable scale, and communications are exceedingly difficult. On the sea-coast, however, those bays and natural anchorages which had been first the ports, and later the refuge of the pirate fleets that terrorised the Mediterranean until Pompey's campaign of 67 B.C., were thriving centres of seaborne commerce. Among the most famous of these were Corycus and Elaeusa (later Sebaste).
Cilician Survey
Authors: Seton-Williams M. V.
Published: January 2007

The survey, the results of which are detailed below, was conducted by the writer as Fellow of the British Institute of Archaeology in Ankara in company with the Misses du Plat Taylor and Munn-Rankin, Dr. J. Waechter and J. Mellaart, with the approval of the Director-General of Antiquities, Bay Hayrullah Örs and with the aid of a grant from the British Academy. The primary object was to examine and record the pre-classical sites in the Plain of Cilicia and round the Gulf of Iskenderun and to determine as far as possible the periods of their occupation, but many later settlements, usually under modern villages, were discovered and recorded. The survey was carried out during June and July, 1951, the best season for travel in this swampy area, but even so much time was lost owing to thunderstorms and heavy rains making the roads impassable for days.
The Find of Urartian Bronzes at Altin Tepe, Near Erzincan
Authors: Barnett R. D. , Gökce N.
Published: January 2007

In 1938 Near Erzincan an important find of Urartian metal-work was made, which is now in the Ankara Museum. In view of the rarity of Urartian material as yet recovered and of the brief character of the only publication of this find, we thought it desirable to publish a fuller account.
Beycesultan Excavations Second Preliminary Report, 1955
Authors: Lloyd Seton , Mellaart James
Published: January 2007

The Second Excavating season at Beycesultan lasted from 1st May to 6th July, 1955. As a result of a motor accident on 30th April Mr. Seton Lloyd was unable to take charge of the work until 21st May and his place was taken by Mr. James Mellaart, Institute Fellow for 1955–56. The field staff also included Mr. G. R. H. Wright as architect and surveyor, Mrs. Wright as housekeeper and registrar, Mr. T. Burton Brown as visiting adviser, Mr. Maurice Cookson, whose services as photographer were kindly lent to us by the London Institute of Archaeology, and Mr. John Carswell as draughtsman. The Turkish Antiquities Department was represented by Bayan Nihal Dönmez, who relieved the Director of much administrative work. The expedition was once more housed in tents and rented accommodation in Menteş, village: thanks are again due to the Turkish Ministry of Education for the loan of the local school building as museum and workshop.

The season's work divided itself into three distinct phases. The first part of the excavations was confined to the eastern summit of the mound, where the great Burnt Palace had been discovered in 1954 (see Fig. 1), and consisted in the successive examination and clearance of the four uppermost levels (I–IV) over an area about thirty metres square, in order to gain access to the palace beneath. This work occupied the expedition throughout the greater part of May. The second phase was concerned with the extension of the palace excavations themselves in a north-westerly direction.
The Sultantepe Tablets (continued) VII. The Myth Of Nergal and Ereshkigal
Authors: Gurney O. R.
Published: January 2007

The myth of Nergal and Ereshkigal has long been known to Assyriologists from a Middle Babylonian tablet found among the diplomatic archives of Tell El Amarna. The tablet had apparently been imported into Egypt, perhaps from Syria, together with a similar one inscribed with the myth of Adapa, as a school-text for the training of scribes. It was only in 1951 that fragments of a late Assyrian version of the tale were unearthed at Sultantepe. In 1953, after the numerous fragments had been baked and joined, the text was identified by the present writer and a preliminary account of it was given by him in a lecture delivered early in 1955. The cuneiform text was published in 1957 and a full edition was promised for this journal. The present article is intended to fulfil that promise. The Sultantepe tablet remains the sole authority for the late Assyrian version of the tale, not a single fragment having come to light from any other source.
The Castle of Vahga
Authors: Dunbar J. G. , Boal W. W. M.
Published: January 2007

The castle of Feke, formerly known as Vahga, stands at a height of 1,250 m., less than 10 km. NE. of the modern town of the same name, and about 60 km. NNE. of Kozan. The site is a prominent rock outcrop overlooking the right-hand bank of a principal tributary of the River Seyhan, the Gök Su, whose valley here carries one of the lesser passes of the Anti-Taurus range southwards into Cilicia.

The castle played an important part in the establishment of the Armenian kingdom of Cilicia. The fortress appears to have been among the first to fall into Armenian hands, Constantine, son of Roupen, capturing the castle from its Byzantine garrison by a stratagem during the last decade of the 11th century, at a time when the Armenian princes were consolidating their positions in the mountain passes of the Taurus and Anti-Taurus preparatory to their descent upon the Cilician plain.
Excavations at Can Hasan: Fourth Preliminary Report, 1964
Authors: French D. H.
Published: January 2007

The work this year at Can Hasan took place, as usual, in the autumn. Excavation began on 6th September and finished on 10th October. A further week was spent on the detailed work of planning, photography and pottery study. We employed this year, as in previous years, Veli Karaaslan as foreman, Rifat Çelimli, Mustafa Duman, and Bekir Kalaycı as ustas; from Menteş, we employed three men and from Canasun village five men. During the season, parts of the excavated area, which had not been completely covered, were filled in with earth from this year's excavation. At the end of the season only those areas where further work is planned remained open. The fence, of posts and wire, was repaired. The watchman now lives in the dig-house on the edge of the mound.

For this year there was a staff of twelve: Messrs. N. H. S. Kindersley, D. C. Biernoff, R. W. Dutton, S. Payne, and J. E. Reade, field assistants; Mr. I. J. Walls, architect; Mrs. D. C. Biernoff and the Misses M. A. White, T. Martin, V. Pemberton-Piggott, P. M. Pratt, and R. J. Worth, house assistants. In addition, Mr. Kindersley worked on photography and planning, Mr. Dutton assisted the architect, Mr. Biernoff took charge of the bone material and Mr. Payne of the obsidian. Mrs. Biernoff, Miss White, Miss Martin and Miss Pratt were conservators. Bay Hayrettin Solmaz of the Konya Museum represented the Turkish Government.
Çayboyu 1970–71
Authors: Aksoy Behin , Diamant Steven
Published: January 2007

Short preliminary notices of the work at Çayboyu have appeared in recent issues of this journal and the METU series of preliminary reports (Diamant 1971, 1972; Diamant & Aksoy 1972, 1973). No further excavation has taken place since the initial two short seasons (1970–1). What follows is thus only a slightly more detailed summary of the material recovered up to this time.

The mound of Çayboyu lies about one kilometre east of Aşvan village, on the edge of a small wadi. It is barely visible on the northwest side as one approaches from the village, since the change in elevation is very gradual. However, on the southeastern side the wadi and subsidiary irrigation channels have eroded away what may be as much as half of the original mound, leaving an exposed cross-section of it about three metres high. One of the modern irrigation channels runs periodically just at the base of this scarp, from which pottery and obsidian artifacts have been collected.
The Palaeoecology of South Central Anatolia at the end of the Pleistocene and the beginning of the Holocene
Authors: Cohen Harold R.
Published: January 2007

The origins of agriculture and domestication have long been identified, in theory, with the beginning of permanent settlements; the beginning of the Early Neolithic Period is known, in fact, to be synchronous with the ending of the Last Ice Age. To some scholars, fact and theory have suggested that this synchronism implies a causal relationship between certain assumed climatic changes and the beginnings of food production; for others, this synchronism is not more than a misleading coincidence. It is not the purpose of the writer to discuss the validity of these assumptions except to indicate that opinion seems to be hardening that food production may have had a more complicated and lengthy history than these assumptions suggest. There has grown up over the last 25 years a considerable body of literature expressing the most varied opinion about the causes for the origins of food production, and its variety has not narrowed with the emergence of new evidence. In my opinion, the basis for the solution of this problem will be derived essentially from palaeoecological analyses of selected areas and regions in various parts of the world, and not only in the Near East. This paper is intended to open such a study for the region of south central Anatolia. As might be expected in an ecological study, the evidence derives from a number of disciplines, and, accordingly, several colleagues have contributed to the formulation of the suggested ecological pattern. That pattern itself, however, is the responsibility of the writer.
Some Geographical and Political Aspects of Mursilis' Arzawan Campaign
Authors: Bryce T. R.
Published: January 2007

At the beginning of his reign, the Hittite king Mursilis II was confronted with widespread unrest amongst the territories subject to Hittite control. One of the early challenges to his authority came from Arzawa whose king Ukha-zitis defied an order to hand over rebels from Attarimma, Huwarsanassa, and Suruta who had sought refuge in his country. Mursilis answered this challenge by conducting in person a two-season military campaign against Arzawa, the details of which are recorded in the Annals for his third and fourth years. His personal intervention indicates the importance which he attached to this particular area, and there can be little doubt that Arzawa occupied a key position amongst Hittite holdings in the south west of Asia Minor in the latter half of the second millennium B.C.
A Study of Roman Roads in Anatolia: Principles and Methods
Authors: French D. H.
Published: January 2007

It is my intention, here, to present the background to my work in a field which I have adopted, perhaps rashly and unwisely, in the spirit of an interested amateur. The work has been centred on the road systems of Roman Asia Minor and is concerned with the surviving evidence for the course and route of Roman roads, and the topographical and geographical problems which follow on from the elucidation of these roads. At a higher level of investigation I have been considering the grade of information which is afforded by the surviving literary evidence e.g. the itineraries. My ultimate purpose is to provide material for a fresh appraisal of the historical geography of Asia Minor: such material as I can collect is specifically intended to be a contribution to a new map or maps of Roman Asia Minor.

In this article I wish to offer an outline of:

(1) the principles which underlie my approach,

(2) the definition of the categories of desired information,

(3) a practical demonstration of the methods and techniques adopted in the work.
Twenty-five Years
Authors: Lloyd Seton
Published: January 2007

The Council have asked me to speak to you about the history of this Institute over the past twenty-five years; and, since I myself regard it as a “success story”, I shall try to make it something rather more than a mere sequence of reminiscences. I want therefore to tell you how the Institute came to be founded in 1947. I want to go back and recollect some of our archaeological experiences in the very different world of the nineteen-fifties – to remind you about the Institute's expansion, after Michael Gough took over the Directorship from me in 1961 – and finally to say something about how things are going in the nineteen-seventies, under the direction of Dr. D. H. French – ably assisted, as you know, by his wife and other associates. But I also want to add something about what (to use a very hackneyed expression) one may call the “wind of change” in archaeology; I mean changes in the approach to, and even in the ultimate purpose of excavating, as they are now frequently explained to me by people younger than myself.

So, let me begin at the beginning and remind you that the foundation of our Institute was almost entirely due to the initiative of one man: the late Professor John Garstang, whom everyone remembers because, as Herodotus wrote the first history of the Greeks, Garstang wrote the first history – at least in this country – and also the first geography of the Hittite Empire.
The Date of the Neo-Hittite Enclosure in Karatepe
Authors: Ussishkin David
Published: January 2007

The dating of the Neo-Hittite enclosure in Karatepe, discovered about twenty years ago by H. Th. Bossert and his Turkish colleagues, forms a problem of primary importance, the solution of which could have deep repercussions on wide fields of study. Even though Azitawadda, the builder and ruler of Karatepe, has left a relatively long bilingual inscription, it lacks the direct and conclusive evidence which might have proved its dating. It is not surprising, then, that several scholars differ widely on the date of Karatepe.

The dating generally accepted today is the one put forward by Bossert in 1948, who proposed that Karatepe was built, and Azitawadda reigned, during the second half of the eighth century B.C. This dating is mainly based on three arguments each of a different kind: firstly, it was assumed that “Awrikku king of the Dannunites” (Á-wa+ri-ku-sof the Hittite hieroglyphic inscription), whom Azitawadda mentioned as his benefactor, must be identified with “Urikki of Que” who, as related in the annals of Tiglath-Pileser III, paid a tribute to Assyria probably in 738 B.C. Secondly, a palaeographical analysis of the script of Azitawadda's Phoenician text indicated that the letters are of a rather “developed” and late type, a fact which points to as late a date as possible for this inscription. Thirdly, the artistic style of the reliefs seemed to be late, and as argued by E. Akurgal, to be much influenced by Assyrian art.
The Heroic Age of Phrygia in Ancient Literature and Art
Authors: Carrington Peter
Published: January 2007

The object of this paper is to re-examine the Greek literary traditions concerning a Phrygian migration from Europe to Asia Minor and the early movements of that people within Asia Minor, also allusions to these traditions in local legends and coin-types of the Roman period. Such archaeological and philological evidence as there may be for a migration is not considered: a superficial examination would seem to indicate that neither of these disciplines can yet suggest a clearcut picture of population movement which we can relate to that presented by the literary evidence, and I am not qualified to take part in the creation of one. Without supporting evidence from either of these disciplines it must be emphasised that the historicity of the events recorded in the traditions must remain open to doubt. The discussion that follows is concerned with the development of the traditions, especially that which we shall call the “Anatolian tradition”, as purely literary constructions, not as historical accounts.
The God on the Stag: A Late Hittite Rock-Relief on the River Karasu
Authors: Hellenkemper Hansgerd , Wagner Jörg
Published: January 2007

The number of known Hittite rock-reliefs in Anatolia is limited: Karabel, Manisa, Yazılıkaya, Gavurkalesi, Fıraktin, İmamkulu, Taşcı, İvriz, Gezbeli, Sirkeli, and Hemite. Except the Late Hittite relief of Ivriz, the monuments, mostly scattered on the fringe of the highland, have to be ascribed to the Imperial Age (1450–1200 B.C.). Their geographic distribution allows some conclusions as to the extent of the Hittite sphere of influence. The question of the monuments' function is but one of the numerous problems still to be solved.

Apart from the reliefs of Yazılıkaya, Gavurkalesi and Fıraktin, which are all part of a sanctuary, the majority of the monuments at first sight seem to have been put up to demonstrate political power and may be interpreted as representations of the kings (Imamkulu, Taşcı, Gezbeli, Sirkeli and Hemite) or of local dynasts (Karabel and Manisa). This applies especially to the reliefs of Gezbeli and Hemite, which in their overall conception are so designed that the political element seems to dominate over the religious. Upon closer examination, however, we must admit that this explanation applies only perhaps to some of the Imperial Age monuments; those monuments in which the kings are shown in an attitude of prayer or as gods appear to have been erected with religious motives in mind. A further indication of religious function is the fact that the monuments are often associated with water in the form of a spring or a river.
Oinoanda: The Doric Building (Mk 2)
Authors: Coulton J. J.
Published: January 2007

The investigation of the building which is the subject of this paper was undertaken in 1975, 1977, and 1981 in the course of the survey of Oinoanda conducted by the British Institute of Archaeology at Ankara. I am most grateful to Mr. A. S. Hall, director of the survey, for inviting me to participate in it and for supporting my work on the site, to Bay Sırrı Özenir, Bay Osman Özbek and Bay Edip Özgür, successive representatives of the Turkish government, for much assistance, and to Mr. P. Forster and students of the Department of Land Survey of the North-East London Polytechnic for more technical aid.

Before discussing the building itself, some general remarks on the development of the survey are required. The initial survey of the site was begun in 1974 by a group from the North-East London Polytechnic led by Mr. A. Slade. An arbitrary bearing was defined as grid north and a datum point for levelling was arbitrarily allotted a height of 1000 m. Extension of the survey in 1977 established that the level of the acropolis summit in terms of this arbitrary datum is approximately 1095 m., whereas the actual height above sea level is 1532 m.
Termessians at Oinoanda
Authors: Coulton J. J.
Published: January 2007

When in the late nineteenth century inscriptions from Oinoanda in the Kibyratis (Fig. 1) began to be recorded and published in quantity, the relationship between Termessos Minor and Oinoanda caused a good deal of discussion. For it was in the city which everybody agreed to be Oinoanda that inscriptions set up by the boule, demos, and gerousia of the Termessians were to be found. Holleaux and Paris supposed that the two communities shared the Oinoanda hill, and Cousin added the suggestion that the late Roman fortification wall (traditionally known as the Great Wall) separated them.