Mathematical Mysteries in Byzantium

2013 ◽  
Author(s):  
Judith Herrin
Keyword(s):  
Seventeenth Century ◽  
Third Century ◽  
Greek Text ◽  
Nontrivial Solutions ◽  
Fermat's Last Theorem ◽  
The Third ◽  
Fermat’S Last Theorem ◽  
Mathematical Problems ◽  
The One

This chapter examines how the mathematical mysteries of Diophantus were preserved, embellished, developed, and enjoyed in Byzantium by many generations of amateur mathematicians like Pierre de Fermat, who formulated what became known as Fermat's last theorem. Fermat was a seventeenth-century scholar and an amateur mathematician who developed several original concepts in addition to the famous “last theorem.” One of his sources was the Arithmetika, a collection of number problems written by Diophantus, a mathematician who appears to have flurished in Alexandria in the third century AD. It was through the Greek text translated into Latin that Fermat became familiar with Diophantus's mathematical problems, and in particular the one at book II, 8, which encouraged the formulation of his own last theorem. Fermat's last theorem claims that “the equation xn + yn = zn has no nontrivial solutions when n is greater than 2”.

Neo-Pythagoreanism

2018 ◽  
Author(s):  
Hermann S. Schibli
Keyword(s):  
First Century ◽  
Third Century ◽  
Way Of Life ◽  
The Third ◽  
The One ◽  
Immortality Of The Soul

Neo-Pythagoreanism is a term used by modern scholars to refer to the revival of Pythagorean philosophy and way of life in the first century bc. It coincides with the redevelopment of Platonic thought known as Middle Platonism. Neo-Pythagoreans elaborated a mathematical metaphysics in which the highest level of being was occupied by a transcendent principle, equated with ‘the One’ or ‘the Monad’ and regarded as the source of all reality. Neo-Pythagorean anthropology reaffirmed the ancient Pythagorean belief in the immortality of the soul. Although Neo-Pythagoreanism is often indistinguishable from Middle Platonism, it is characterized by a tendency to see Pythagoras as the father of all true philosophers, including Plato. In the third century ad Neo-Pythagoreanism was absorbed into Neoplatonism.

scholarly journals The Aśokan Empire

2021 ◽  
pp. 51-70
Author(s):  
William J. Long
Keyword(s):  
Soft Power ◽  
Third Century ◽  
Political Pluralism ◽  
The Third ◽  
First Case ◽  
Administration Of Justice ◽  
Medical Facilities ◽  
Ancient Times ◽  
The One

AbstractThis chapter introduces the first case study that serves as empirical referent for a Buddhist approach to statecraft in ancient times by considering the early kingdom of Aśoka. This chapter and the one that follows offer “proofs of concept” for the possibility of applying Buddhist ideas in the practice of politics and statecraft. Aśoka governed according to the dharma, meaning principles and policies that reflect Buddha’s teachings, although Aśoka expressed his principles and policies in edicts written in nonreligious, nonexclusive language. Aśoka’s rule was characterized by the promotion of nonviolence; social welfare; environmental protection; religious tolerance; political pluralism; the fair and compassionate administration of justice; and sound and responsive public administration meaning transparency, accessibility, impartiality, and accountability. His foreign policy was founded on principles of nonviolence, nonaggression, conciliation, stability, and improved understanding among international actors through diplomacy and mutually beneficial commerce. Aśoka even practiced the exercise of “soft power” by establishing medical facilities in foreign lands, sharing beneficial plants, and installing infrastructure beyond his immediate borders as acts of goodwill toward neighboring countries. While these governing principles and policies may be commonplace today, Aśoka, it should be remembered, governed in Asia in the third century B.C.E.

V. Republican Veii

1961 ◽  
Vol 29 ◽  
pp. 52-57 ◽  
Author(s):  
J. B. Ward-Perkins
Keyword(s):  
First Century ◽  
The Other ◽  
Third Century ◽  
Roman Poet ◽  
The Third ◽  
History Of ◽  
The One ◽  
Short Time ◽  
The Temple ◽  
The Town

‘O Veii veteres, et vos tum regna fuistisEt vestro posita est aurea sella foro:Nunc intra muros pastoris bucina lentiCantat, et in vestris ossibus arva metunt.’(Propertius IV, 10, 27–30.)So the Roman poet Propertius, writing in the closing years of the first century B.C., only a very short time before the establishment of the Augustan municipality on the site of the ancient town; and it is the conventional reading of the history of Veii that the four hundred odd years intervening between the sack of the town in 396 B.C. and the foundation of the Municipium Augustum Veiens were years of abandonment and desolation. This view has been challenged recently by Dr. Maria Santangelo in her publication of two small jugs of the third century B.C. with archaic latin dedicatory inscriptions, the one from the Portonaccio cemetery, inscribed L(ucius) Tolonio(s) ded(et) Menerva(e), the other from the Campetti votive deposit Caere (or Crere) L(ucius) Tolonio(s) d(edet). These two dedications are evidence not only of the survival of at least two of the sanctuaries, but also of the continuing residence at or near Veii of a descendent of the Velthur Tulumne who dedicated a bucchero cup in the same Portonaccio sanctuary three centuries earlier (Not. Scav., 1930, pp. 341–343), and of the Lars Tolumnius who was killed in battle and whose armour hung, for all to see, in the temple of Jupiter Feretrius (Prop. loc. cit.).

A tentative glossary of Thracian words

1963 ◽  
Vol 8 (2) ◽  
pp. 97-110
Author(s):  
George Sotiroff
Keyword(s):  
Third Century ◽  
Distant Future ◽  
Archaeological Material ◽  
The Third ◽  
The One

While the only Thracian inscription known so far remains the one on the golden ring brought to light in 1912, in Ezerovo, near Philippopolis, the possibility cannot be ruled out of finding other inscriptions in this language in the not too distant future. At least two important discoveries have been made recently on the territory of ancient Thrace: the richly decorated royal tomb, near Kazanlak, dating from the third century B.C., which was found in 1944, and the objects excavated at the site of Seuthopolis, a city which seems to have gone down in flames around 229 B.C., after a life of some 130 years. The site was allowed to disappear at the bottom of a man-made lake, following the completion of a hydro-electric project in 1954. Prior to that, valuable archaeological material had been recovered, including more than 1,100 ancient coins, and an interesting inscription in Greek, concerning relations between Thrace and Macedon.

Notes on Some Minor English Mathematical Serials

1929 ◽  
Vol 14 (200) ◽  
pp. 379-400 ◽  
Author(s):  
Raymond Clare Archibald
Keyword(s):  
Eighteenth Century ◽  
Seventeenth Century ◽  
Mathematical Society ◽  
The Third ◽  
The Past ◽  
Female Sex ◽  
Mathematical Problems ◽  
First Time

While major mathematical problems were discussed already in the seventeenth century in such serial publications as the Philosophical Transactions (1665) and Acta Eruditorum (1682), it was not till the early part of the eighteenth century that serials containing elementary problems of wide appeal commenced to appear. The first of these seems to have been the Lady’s Diary, started in London in 1704, and “designed for the sole use of the female sex”. It had an immediate success, and continued to appear in various forms for 168 consecutive years. Of the second, Delights for the Ingenious, there were only eight numbers, in 1711. The third publication of the kind was possibly Kunstfrüchte 1. Sammlung (1723), a publication (I have not seen it) of the Hamburg mathematical society, founded thirty-three years before. The Jahrbriefe of this same society were published irregularly during the 140 years 1732-1871. For the fifth and sixth publications we come back to England, Miscellanece Curiosce (York, 1734-35) and Gentleman’s Diary, started in 1741 and continued for a century before its union with the Ladies’ Diary. Then followed five other English serials before Holland’s Mathematische Liefhebberye (Purmerende, 1754), issued annually for seventeen years. During the next 175 years the number of these minor publications became very large. It is my purpose to bring together brief notes on minor English serials and their editors of the past two and a quarter centuries, and to indicate where more information regarding them may be found. It will not be possible, within the limits of this article, to indicate more than very occasionally anything of the contents (often rich and varied) of such serials, many results appearing in their pages for the first time. Problems and their solutions usually occupied the greater part of the space, and most of the prominent English mathematicians of the time were contributors. While some may incline to frown upon such mathematical occupations, it may be recalled that “Sätze und Aufgaben” were to be found in such an exalted source as Crelle’s Journal, so recently as 1858.

Alkohol im Tank – Bio-Kraftstoffe und die Grenzen moderner Mobilität

2004 ◽  
Vol 34 (136) ◽  
pp. 455-468
Author(s):  
Hartwig Berger
Keyword(s):  
Third World ◽  
Fossil Fuel ◽  
Energy Resources ◽  
The Third ◽  
Political Conflicts ◽  
The Future ◽  
Long Time ◽  
Food Market ◽  
The One ◽  
The Third World

The article discusses the future of mobility in the light of energy resources. Fossil fuel will not be available for a long time - not to mention its growing environmental and political conflicts. In analysing the potential of biofuel it is argued that the high demands of modern mobility can hardly be fulfilled in the future. Furthermore, the change into using biofuel will probably lead to increasing conflicts between the fuel market and the food market, as well as to conflicts with regional agricultural networks in the third world. Petrol imperialism might be replaced by bio imperialism. Therefore, mobility on a solar base pursues a double strategy of raising efficiency on the one hand and strongly reducing mobility itself on the other.

Al-Rasm al-ʿUthmānī: Towards Correct Pronunciation and the Preclusion of Ambiguity

2011 ◽  
Vol 13 (2) ◽  
pp. 201-171
Author(s):  
Nāṣir Al-Dīn Abū Khaḍīr
Keyword(s):  
Specific Pattern ◽  
Writing Style ◽  
The Third ◽  
The Past ◽  
Different Ages ◽  
Correct Pronunciation ◽  
The One ◽  
The Mind

The ʿUthmānic way of writing (al-rasm al-ʿUthmānī) is a science that specialises in the writing of Qur'anic words in accordance with a specific ‘pattern’. It follows the writing style of the Companions at the time of the third caliph, ʿUthmān b. ʿAffān, and was attributed to ʿUthmān on the basis that he was the one who ordered the collection and copying of the Qur'an into the actual muṣḥaf. This article aims to expound on the two fundamental functions of al-rasm al-ʿUthmānī: that of paying regard to the ‘correct’ pronunciation of the words in the muṣḥaf, and the pursuit of the preclusion of ambiguity which may arise in the mind of the reader and his auditor. There is a further practical aim for this study: to show the connection between modern orthography and the ʿUthmānic rasm in order that we, nowadays, are thereby able to overcome the problems faced by calligraphers and writers of the past in their different ages and cultures.

Detection and representation of the basic peculiarities of vegetation cover by the mapping method (experience based on a research of goltsy-taiga territories)

2013 ◽  
pp. 32-47
Author(s):  
S. V. Osipov
Keyword(s):  
Vegetation Cover ◽  
Mapping Method ◽  
Vegetation Changes ◽  
Large Classes ◽  
High Rise ◽  
The Third ◽  
Altitudinal Belts ◽  
The One ◽  
Dynamic Series ◽  
River Valleys

Geobotanical mapping of the territory in riverheads Bureya of 4500 sq.km is carried out and the map of a actual vegetation cover of scale 1 : 200 000 is prepared. The legend of the map is presented in the form of the text with three-level hierarchy of classes. At the heart of structure of a legend of the map such regularities of a vegetation cover, as its latitudinal zonality / altitudinal belts, situation in a relief and dynamic series lie. The largest divisions of the legend reflect, first, change of large classes of mesocombinations of vegetation at the level of belts and, secondly, distinction in a boreal - forestry belt between a vegetation cover of tops and slopes of mountains, on the one hand, and the bottoms of river valleys, with another. Divisions of the legend of the second level reflect, first, vegetation changes in the form of high-rise and barrier changes of subbelts, secondly, distinctions of a vegetation cover in different geomorphological conditions (small and average river valleys, northern slopes, etc.). Divisions of the legend of the second level correspond to dynamic series of units of the third level. Essential addition to it are block diagrams of dynamics of a vegetation cover.

Historical Fragments’ Mobile Echo

Transfers ◽  
2017 ◽  
Vol 7 (2) ◽  
pp. 115-119 ◽  
Author(s):  
Susan E. Bell ◽  
Kathy Davis
Keyword(s):  
Nineteenth Century ◽  
Twentieth Century ◽  
Eighteenth Century ◽  
Cultural Revolution ◽  
Ming Dynasty ◽  
Third Century ◽  
Refugee Crisis ◽  
The Third ◽  
Opium War ◽  
The Subject

Translocation – Transformation is an ambitious contribution to the subject of mobility. Materially, it interlinks seemingly disparate objects into a surprisingly unified exhibition on mobile histories and heritages: twelve bronze zodiac heads, silk and bamboo creatures, worn life vests, pressed Pu-erh tea, thousands of broken antique teapot spouts, and an ancestral wooden temple from the Ming dynasty (1368–1644) used by a tea-trading family. Historically and politically, the exhibition engages Chinese stories from the third century BCE, empires in eighteenth-century Austria and China, the Second Opium War in the nineteenth century, the Chinese Cultural Revolution of the mid-twentieth century, and today’s global refugee crisis.

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