bluuebunny/crossref_metadata_2025_split huggingface dataset:
“A source of much rational entertainment”
Authors: Black M. P. , Howson A. G. 
Published: January 2007

“A certain degree of mathematical science, and indeed no inconsiderable degree, is perhaps more widely diffused in England, than in any other country in the world. The Ladies’ Diary, with several other periodicals and popular publications of the same kind, are the best proofs of this assertion. In these, many curious problems, not of the highest order indeed, but still having a considerable degree of difficulty, and far beyond the mere elements of science are to be met with; and the great number of ingenious men who take a share in proposing and answering these questions, whom one has never heard of anywhere else, is not a little surprising. Nothing of the same kind, we believe, is to be found in any other country.”These words of John Playfair’s are quoted by R. C. Archibald in his survey of the “minor English mathematical serials” which appeared in the celebratory 200th issue of this Gazette. Archibald describes how, early in the eighteenth century, serials containing elementary mathematical problems began to appear. Thus, during a century or more when mathematics had still to establish itself in the curriculum of the country’s leading endowed schools, numerous attempts were made to interest the ‘reading’ public in the subject and to serve those readers who were already ‘scientific’. An earlier, extensive survey of such publications was undertaken in the Mechanics Magazine (1848-1853) by T. T. Wilkinson [3] (who also wrote, inter alia, on that arcane (to two Yorkists!) subject “The origin and progress of the study of geometry in Lancashire”). Little, however, appears to have been done in recent years to examine these early attempts to diffuse mathematical knowledge: to study the mathematics contained in such periodicals and columns, how it was learned and enjoyed, and the people who set and solved the problems. This, in a small way, is what is attempted in this investigation. As our subject we chose to study the mathematical column which appeared in the York Courant during the early years of the nineteenth century.
How to deal with modern mathematicians
Authors: Cornelius M. L. 
Published: January 2007

In the eighteenth century The Ladies’ Diary regularly included mathematical problems. A complete collection of these problems from 1704 to 1760 appears in a volume entitled The Diarian Repository; or Mathematical Register published in 1774 [1]:“... a collection of more than four hundred and seventy Problems, relating to such various parts of the Mathematics as are here collected from the Diaries, together with their Solutions fully investigated will, we doubt not, prove of considerable service to the young Adventurer in this useful branch of learning...”
The envelope of an ellipse
Authors: Brunton James 
Published: January 2007

The reproductions shown here are of p. 49 and Fig. XVI (which refers) from A sure guide to builders by Batty Langley, published in 1729 and dedicated to Thomas Scawen Esq., of Carshalton. The reference is to the construction“of oval-like figures” and the implication, towards the bottom of the page, is clearly that something very close to “an ellipsis” is what Mr. Langley had in mind. The poor plate engraver was hard put to it to draw an ellipse from the instructions in the text and a careful examination of his effort reveals that his final solution was to draw, very faintly, an ellipse and try to fit tangents to it from the divisions along the sides.
61.6 Solving linear diophantine equations using matrices
Authors: Macnicol Malcolm 
Published: January 2007

The method described in this note is, like other standard approaches, based on the “Euclidean algorithm”, but a matrix format is used (assuming the coefficients have no common factor) to reduce the equation ax + by = c to a form such asor a similar equation with matrix (k l),(k −l) or (−1 k). The following lemma is easily verified.
Report on a study tour to Farawaystan
Authors: Tarp Allan 
Published: January 2007

Some time ago I had the opportunity to pay a visit to Farawaystan to study how they treated different educational questions. In the following I am going to tell about my strange experiences. One of the first lessons I attended was in tool science. Here is a section from the textbook:“3.1 definition. A screwdriver is a metal cylinder, of which one end is flattened and the other end is fixed in a cylinderlike, stiff material, whose surface is not smooth. If the material cylinder is rotated through an angle a, the metal cylinder will rotate through an angle b in the same direction and of the same size as a. The diameter of the metal cylinder is smaller than that of the material cylinder. The material cylinder is often called the handle.
Two surprising limits revisited—(2)
Authors: Sullivan D. 
Published: January 2007

In a recent Gazette note (66.31, October 1982) Leonard and Schultz established the limits of two segments of the extended diameter of a unit circle. With reference to Fig. 1, they showed that if an arc of length l and a chord of length l are drawn from a point B on a unit circle, and if a segment, BA, of length l is taken on the tangent at B, then:The purpose of this note is to show that these results are not only interesting, they are exceptional.
Notation and language in school mathematics
Authors: Hersee John 
Published: January 2007

It has now been possible to study the many comments received since the publication of the “interim statement” in Gazette No. 407 (March 1975). The recommendations given below are based on the original suggestions, taking these comments into account. Sidelining indicates a change or modification of the original suggestion.It is proposed also to publish these recommendations as a pamphlet, so that they may be widely available to authors and others.
An Algebraic Theorem Related to the Theory of Relativity
Authors: Dampier M. D. 
Published: January 2007

In a common development of the special theory of relativity one considers two events P and Q, P being the emission of a flash of light and Q the reception of the light. We suppose Q to be infinitesimally close to P and, by using the principle of the invariance of c, the velocity of light, argue that the infinitesimal coordinate differences between P and Q must satisfyIandIIwhere dx; etc. are the coordinate differences in one inertial frame whilst dx' etc. are those in a second inertial frame (e.g. [1], p. 16).
What do you do about 4πr2?
Authors: Mackinnon Nick 
Published: January 2007

The mensuration formulae for curved objects ought to be one of the highlights of everyone’s elementary mathematical education. I get my pupils at 13 and they've already been taught that the area of a circle is πr2. It is very upsetting to find that they usually have seen no sort of justification of this result, so they don’t think of it as surprising when π, which was introduced in the circumference formula, mysteriously pops up again in the area formula.This year I thought I would put some effort into justifying the surface area formula for the sphere. I don’t claim that what follows is very original, and of course the main idea goes back to Archimedes, but I hope this article will save readers a bit of work at least.
Bracelets
Authors: Green Paul , Liebeck Pamela 
Published: January 2007

Our original source for this investigation was an Open University video on Secondary classroom practice (OU video no. PM644). Since then, however, we have seen the problem mentioned in [1], [2] and [3]. The investigation as presented to pupils is as follows:Choose two integers between 0 and 9 (not both 0) and write them down. As an example, we shall choose 0 and 2. Write down their sum, doing the addition modulo 10. Then write down the sum of the last two numbers in the sequence, again doing the addition modulo 10. Repeat this process. Our example gives the sequence
Sieving with sums
Authors: Robertson Jack M. , Webb William A. 
Published: January 2007

A number of deep theorems and unsolved problems ask questions about the relationship of the additive and multiplicative structure of the natural numbers. The famous four squares theorem of Lagrange says that if we form all possible sums of four squares we get the entire sequence of nonnegative integers. Goldbach’s conjecture states that if all possible sums of two odd primes are formed we get every even integer greater than 4.The depth and difficulty of such problems stand in surprising contrast to the similar question: “Which numbers are not generated when all possible sums of two or more consecutive natural numbers are formed?” The answer is all powers of 2 and the proof is accessible to anyone who can sum arithmetic sequences. This result is an excellent discovery exercise for students, particularly appropriate for teacher training courses.
Problems to sharpen the young
Authors: Hadley John , Singmaster David 
Published: January 2007

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

The dice game ‘Jolly Roger’ may be played with 5 regular dice or 5 special
‘Jolly Roger’ dice. A ‘Jolly Roger die is a regular die in which the 1 spot is
replaced by a skull and crossbones (i.e. replaced by a ‘Jolly Roger’). Play cycles
through the players 5 times so that each player has 5 turns in the game. Each turn
consists of 3 rolls of the 5 dice. On a particular roll of the 5 dice a player
(pirate) can score points (capture
cargo) only when some ‘Jolly Rogers’ appear face up. According to
Koplow Games (1993):
“For each ‘Jolly Roger’ that appears on a roll of the dice, the player
can capture one other die and score its points. If three ‘Jolly Rogers’ are
rolled, then only the points on the remaining two dice can be scored. If
five ‘Jolly Rogers’ are rolled, no points are scored, as the pirate fleet
has scared away all cargo ships.”
Farey rabbits
Authors: Arcavi Abraham , Bruckheimer Maxim 
Published: January 2007

The Farey sequence of order n(Fn) is the sequence of all reduced fractions between 0 and 1, whose denominator does not exceed n, arranged in increasing order of magnitude.
For example, F6 is .
The Fibonacci sequence is the sequence for which u1 = 1, u2 = 1 and un = un-1 + un-2,namely, 1, 1, 2, 3, 5, 8, 13, … , un
At first sight, there is little connection between Farey’s fractions and Fibonacci’s integers. The purpose of this note is to show and explore such a connection and hence derive some properties of the Fibonacci sequence directly from previously proved properties of the Farey sequences. The former properties are well-known, but their rather unusual derivation from Farey properties may have some interest.
Greek Potters at Al Mina?
Authors: Boardman John 
Published: January 2007

The subject of this paper is a small group of cups found by Sir Leonard Woolley in his excavations at Al Mina (now in the Turkish Hatay). It has been hitherto ignored because, with some reason, the vases were believed neither to be Greek imports nor the products of Cypriot or North Syrian potters. I hope to demonstrate that they could be the work of Greek potters established at Al Mina towards the end of the 8th century B.C. by discussing their apparent relationship to contemporary Greek, Cypriot and North Syrian work. Most of the cups and fragments are in Oxford, and there are fragments in the London Institute of Archaeology and the Museum of Classical Archaeology in Cambridge which I have seen. Nos.1–23in Fig. 1 and Plates XXIV–XXV illustrate the shapes and all the types of decoration met in the group.All are two-handled cups, the Greek geometricskyphos. The shape, with decoration of this type, is most common in Euboeo-Cycladic vases of the second half of the 8th century, and a considerable number of theseskyphoiwere carried to Al Mina by the Greeks. It was rarely imitated in Cyprus, as we shall see, and is not at home further east.
New Urartian Inscriptions from Adilcevaz
Authors: Hulin P. 
Published: January 2007

Adilcevaz lies on the north shore of lake Van, almost due south of the summit of Süphan Dağ (14,547 ft.). At its west end substantial remains of a lofty wall of later than Urartian times run down from below the Ahlat road to the shore of the lake (and actually into the lake, of which the relative level has evidently risen since the construction of the wall). It was on a largely concealed face (at right-angles to the line of the wall) of a stone block in this wall that it was reported that cuneiform writing could be seen.Accordingly, in September, 1956, the writer inspected the wall, accompanied by his wife, who located the block some fifteen metres below the road in a short secondary wall-surface of dressed blocks, with hard rubble filling behind, parallel with the line of, and running inland from the broken end of a further wall projecting three or four metres in the Adılcevaz direction from, the main wall. The cuneiform writing proved to be visible as a result of the absence, close to the surface, of mortar between the inscribed block and the one lake-ward of it in the same course; and on poking away more mortar between the two blocks and up to the under surface of a third, larger, block, forming part of the next higher, and uppermost surviving, course, it was found that this under surface also bore cuneiform signs.
Anazarbus
Authors: Gough Michael 
Published: January 2007

The site of the Cilician city known during the period of the Roman Empire as Caesarea, Caesarea by Anazarbus, or Anazarbus, is some 28 km. south of Kozan in the Turkish province of Seyhan. The place still retains its name as Anavarza, a hamlet built just outside the walls of the ancient city.The choice of Anazarbus as a subject for research may seem to require some explanation. It was never one of the great cities of antiquity; indeed it is not yet certain that it even existed before the 1st century B.C. It never received more than scant notice from ancient authorities, while modern travellers, hampered by bad communications, a difficult climate, and a lawless population, were unable to spend more than a day or two at the site and consequently could not give more than a general idea of its monuments.In 1949, as Scholar of the British Institute of Archaeology at Ankara, I had decided to study the Classical architecture of Cilicia, and at the same time to collect information on the many mediaeval castles in the district.
Beycesultan Excavations: Fourth Preliminary Report, 1957
Authors: Lloyd Seton , Mellaart James 
Published: January 2007

Short Reports on the Institute's excavations at Beycesultan, dealing with discoveries in the seasons of 1954, 1955 and 1956 have already been published in this journal (vols. V–VII). In the third of these reports, a break in continuity was occasioned by our temporary concentration on a single isolated discovery; and accordingly, before resuming the more general account, a short recapitulation of our operational sequence may be desirable.In the final weeks of the 1955 season, a sounding was made in Area “A” on the western summit (see site-plan, Fig. 1), which revealed the presence in this part of the mound of a large public building of the Middle Bronze Age, corresponding in time to the “Burnt Palace” already partly excavated on the eastern summit (Level V). Some preliminary investigations were also made of three occupation levels (VI, VII and VIII) lying directly beneath this building (see Anatolian Studies VI). In 1956 an extension of this sounding was made in the form of a 5-metre trench more than 40 metres long, running out approximately eastwards towards the flank of the mound (Trench “S”). After passing through the already well established sequence of later occupations, further foundations of the Middle Bronze Age were here encountered and it became clear that the building discovered in Area “A” formed part of an administrative complex, perhaps covering the whole of the western summit, and surrounded by its own substantial enclosure wall.
Urartian Stones in the Van Museum
Authors: Hulin P. 
Published: January 2007

Professor F. W. König published in 1956 a note listing and describing the stones lying in the Van Museum, as far as he was able to do so from photographs of them taken in 1954 by Professor H. Gamerith and placed at his disposal. Professor König's note included two sketches, based on the photographs, of the stones as they lay; and he gave to each stone in the sketches a number by which he referred to it in his list.Visits to the Van Museum made in the course of journeys in eastern Turkey undertaken by the writer in September 1956 (accompanied and assisted by his wife) and in September 1957 (alone) have made possible the following amplified account of the Urartian stones in the museum. The numbers assigned to the stones in König's sketches are used as a means of reference; information already available in König's note or in his Handbuch is not repeated, except that identifications made by him from the photographs are repeated (in parenthesis) to make the list complete; numbers not occurring in the series relate to stones which could not be seen to bear any Urartian inscription.
Excavations at Can Hasan, 1966: Sixth Preliminary Report
Authors: French D. H. 
Published: January 2007

The sixth season of excavations at Can Hasan took place between 28th August and 30th September. Additional work on storing and arranging the non-registered materials from the excavations continued until 12 th October. All materials other than the registered objects from the 1961 to the 1966 seasons are now stored in the depot at Can Hasan. These are the sherds, animal bones, heavy stone objects, the samples of stone, clay and other materials. They are stored by year and by category in locked storerooms in the dig house. In addition to the house bekçi there is now a full-time official bekçi for the Hüyük and for other hüyüks in the neighbourhood.In the 1966 excavations Messrs. D. C. Biernoff, S. Payne and J. N. Postgate were field assistants; Mrs. Payne took charge of the work in the house, assisted by Mr. C. Slack and the Misses M. Bell, C. Prater, and T. Harrington-Smith. In addition Mrs. Payne had charge of the pottery; Mr. Payne of the obsidian, Miss Harrington-Smith of registration and Mr. Slack and Miss Bell of conservation and pottery mending. Bay Bedri Yalman from the Konya Museum represented the Turkish Government.
The Early Minoan Occupation of Knossos: A Note on some new Evidence.
Authors: Evans John 
Published: January 2007

Following their discovery of the “Burnt Palace” at Beycesultan in the mid 1950's, Seton Lloyd and James Mellaart drew attention to a number of features of its architecture which seemed to indicate links with the palace architecture of Minoan Crete, and discussed the possible significance of these similarities (Lloyd and Mellaart, 1956 118–123, 1965 61, 62). Whatever this may be in terms of relationships between the two areas in the second millennium B.C., however, it seems clear that they cannot throw any light on the first appearance of palaces in Crete. The problems of the origin and development of the Cretan Bronze Age palaces are complex, and though they have been much discussed since the first excavations in the early years of the century, a major obstacle to progress has always been the lack of precise evidence, or even of any evidence at all, for the early stages of the process. As they stand, most of the palaces are the product of a series of rebuildings and remodellings over a long period, and it is not always clear just what they were like when first erected. Most frustrating of all, however, is the lack of evidence bearing on the question of whether they were preceded, during the Early Bronze Age, by buildings which were in any respect analogous in form and function.
It has long been clear that the sites of some of the major Middle and Late Minoan palaces were occupied during the Early Minoan period, but at Phaistos and Knossos at any rate extensive clearing and levelling in preparation for the erection of the Middle Minoan palaces has obliterated practically all traces of the Early Minoan buildings. At Phaistos Branigan has hinted that the fragments of walls found by Pernier (1935, pl. VI) on the highest point of the hill might have belonged to a building of some consequence, possibly similar to the Early Minoan II mansion known as the House on the Hill at Vasiliki (Branigan 1970, p. 41). Branigan thinks that in addition to the rooms mentioned by Pernier, there may be traces of a corridor similar to that in the Vasiliki building. Only the bottom two courses of the walls survive, so that it is difficult to say much about their construction, though it seems to be poorer than that of the walls of some Early Minoan private houses later found by Levi on another part of the site.
A Lydian Funerary Banquet
Authors: Ramage Nancy Hirschland 
Published: January 2007

The funerary banquet, a frequent theme in ancient sculpture and painting, has been thoroughly studied in recent years. The addition to the corpus of a newly discovered grave stele from Sardis (Pl. XIIIa) is of particular interest because it is a demonstrably local piece of work, with a Lydian inscription carved above a figured relief.The piece was found in the summer of 1977 by villagers and was reportedly discovered in the east bank of the Pactolus river bed, to the south of the area “Pactolus Cliff”. The slab, which is of local whitish marble, tapers slightly toward the top. Its height is 0·41 m., its width at the bottom is 0·30 m., and its approximate original width at the top was 0·26 m. There is no border at the edge of the stone, but a small ledge protrudes at the bottom of the relief stone. The back has been left rough and unfinished.
Archaische Bauglieder aus Kyzikos
Authors: Koenigs Wolf 
Published: January 2007

Bereits F. W. Hasluck fand bei seinem survey über Kyzikos in den Jahren 1902–1906 drei archaische Kapitellfragmente, die zeigen, dass der Ort auch in diesem Bereich eigenständige Leistungen hervorgebracht hat, und deren Marmormaterial einen gewissen Reichtum der Stadt schon in früher Zeit im Vergleich etwa zu Larisa und Neandria zum Ausdruck brachte.Die beiden leider verschollenen Fragmente eines kleinen ionischen Kapitells mit wenigen breiten, konvexen Volutengängen, ein fachem Rundstab und schalenförmigem Auge, gehörten wegen des geringen Echinusdurchmessers (36 cm.) wohl zu einer Votivsäule.