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It is difficult to think of western society today without modern technology. The last decades of the twentieth century have witnessed a proliferation of high-tech computers, mobile phones, text messaging, the Internet and the World Wide Web. Software is now pervasive, and it is an integral part of automobiles, airplanes, televisions and mobile communication. The pace of change as a result of all this new technology has been extraordinary. Today consumers may book flights over the World Wide Web as well as keep in contact with family members in any part of the world via e-mail or mobile phone. In previous generations, communication often involved writing letters that took months to reach the recipient. Communication improved with the telegrams and the telephone in the late nineteenth century. Communication today is instantaneous with text messaging, mobile phones and e-mail, and the new generation probably views the world of their parents and grandparents as being old-fashioned.
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Of course, it is essential that the population of the world moves towards more sustainable development to ensure the long-term survival of the planet for future generations. This involves finding technological and other solutions to reduce greenhouse gas emissions as well as moving to a carbon neutral way of life. The solution to the environmental issues will be a major challenge for the twenty-first century.
Tutankamun was a minor Egyptian pharaoh who reigned after the controversial rule of Akenaten. Tutankamun’s tomb was discovered by Howard Carter in the Valley of the Kings, and the tomb was intact. The quality of the workmanship of the artefacts found in the tomb is extraordinary, and a visit to the Egyptian museum in Cairo is memorable.
The origin of the word ‘democracy’ is from demos (δημος), meaning people, and kratos (κρατος), meaning rule. That is, it means rule by the people. It was introduced into Athens following the reforms introduced by Cleisthenes. He divided the Athenian city state into 30 areas. Twenty of these areas were inland or along the coast and ten were in Attica itself. Fishermen lived mainly in the ten coastal areas, farmers in the ten inland areas and various tradesmen in Attica. Cleisthenes introduced ten new clans where the members of each clan came from one coastal area, one inland area on one area in Attica. He then introduced a Boule (or assembly) which consisted of 500 members (50 from each clan). Each clan ruled for 1/ 10th of the year.
The Athenian democracy involved the full participations of the citizens (i.e. the male adult members of the city state who were not slaves) whereas in representative democracy the citizens elect representatives to rule and represent their interests. The Athenian democracy was chaotic and could also be easily influenced by individuals who were skilled in rhetoric. There were teachers (known as the Sophists) who taught wealthy citizens rhetoric in return for a fee. The origin of the word ‘sophist’ is the Greek word σοϕος, meaning wisdom. One of the most well known of the sophists was Protagorus. The problems with the Athenian democracy led philosophers such as Plato to consider alternate solutions such as rule by philosopher kings. This is described in Plato’s Republic.
The Elgin marbles are named after Lord Elgin who moved them from the Parthenon in Athens to London in 1806. The marbles show the Pan-Athenaic festival that was held in Athens in honour of the goddess Athena after whom Athens is named.
The origin of the word Hellenistic is from Hellene (‘Ελλην), meaning Greek.
The hanging gardens of Babylon were one of the seven wonders of the ancient world.
A positional numbering system is a number system where each position is related to the next by a constant multiplier. The decimal system is an example, for example 546 = 5 * 10 2 + 4 * 10 1 + 6.
The decorations of the tombs in the Valley of the Kings record the life of the pharaoh including his exploits and successes in battle.
The cartouche surrounded a group of hieroglyphic symbols enclosed by an oval shape. Champollion’s insight was that the group of hieroglyphic symbols represented the name of the Ptolemaic pharaoh ‘Ptolemy’.
The Rhind papyrus is sometimes referred to as the Ahmes papyrus in honour of the scribe who wrote it in 1832 B.C.
The length of a side of the bottom base of the pyramid is b 1and the length of a side of the top base is b 2.
The Pythagoreans took a vow of silence with respect to the discovery of incommensurable numbers. However, one member of the society is said to have shared the secret result with others outside the sect, and an apocryphal account is that he was thrown into a lake for his betrayal and drowned. The Pythagoreans obviously took mathematics seriously back then.
The town of Aswan is famous today for the Aswan high dam which was built in the 1960s. There was an older Aswan dam built by the British in the late nineteenth century. The new dam led to a rise in the water level of Lake Nasser and flooding of archaeological sites along the Nile. Several archaeological sites such as Abu Simbel and the temple of Philae were relocated to higher ground.
The origin of the word ‘odometer’ is from the Greek words ‘οδοζ’ (meaning journey) and ‘μετρον’ meaning (measure).
The figures given here are for the distance of one Roman mile. This is given by π2 2 * 400 = 12.56 * 400 = 5,024 (which is less than 5,280 ft for a standard mile in the Imperial system).
Socrates was a moral philosopher who deeply influenced Plato. His method of enquiry into philosophical problems and ethics was by questioning. Socrates himself maintained that he knew nothing (Socratic ignorance). However, from his questioning, it became apparent that those who thought they were clever were not really that clever after all. His approach obviously would not have made him very popular with the citizens of Athens. Socrates had consulted the oracle at Delphi to find out who was the wisest of all men, and he was informed that there was no one wiser than him. Socrates was sentenced to death for allegedly corrupting the youth of Athens, and the sentence was carried out by Socrates being forced to take hemlock (a type of poison). The juice of the hemlock plant was prepared for Socrates to drink.
Chrysippus was the head of the Stoics in the third century B.C.
Aquinus’s (or St. Thomas’s) most famous work is Sumna Theologicae.
The Aenid by Virgil suggests that the Romans were descended from survivors of the Trojan war and that Aeneas brought surviving Trojans to Rome after the fall of Troy.
Carthage was located in Tunisia, and the wars between Rome and Carthage are known as the Punic wars. Hannibal was one of the great Carthaginan military commanders, and during the second Punic war, he brought his army to Spain, marched through Spain and crossed the Pyrnees. He then marched along southern France and crossed the Alps into Northern Italy. His army also consisted of war elephants. Rome finally defeated Carthage and destroyed the city.
The Celtic period commenced around 1000 B.C. in Hallstaat (near Salzburg in Austria). The Celts were skilled in working with Iron and Bronze, and they gradually expanded into Europe. They eventually reached Britain and Ireland around 600 B.C. The early Celtic period was known as the ‘Hallstaat period’, and the later Celtic period is known as ‘La Téne’. The later La Téne period is characterised by the quality of ornamentation produced. The Celtic museum in Hallein in Austria provides valuable information and artefacts on the Celtic period. The Celtic language would have similarities to the Irish language. However, the Celts did not employ writing, and the Ogham writing used in Ireland was developed in the early Christian period.
The origin of the word ‘Calculus’ is from Latin and means a small stone or pebble used for counting.
Augustus was the first Roman emperor, and his reign ushered in a period of peace and stability following the bitter civil wars. He was the adopted son of Julius Caesar and was called Octavion before he became emperor. The earlier civil wars were between Caesar and Pompey, and following Caesar’s assassination, civil war broke out between Mark Anthony and Octavion. Octavion defeated Anthony and Cleopatra at the battle of Actium.
The origin of the word ‘Moor’ is from the Greek work μυοροζ meaning very dark. It referred to the fact that many of the original Moors who came to Spain were from Egypt, Tunisia and other parts of North Africa.
The Moorish influence includes the construction of various castles ( alcazar), fortresses ( alcalzaba) and mosques. One of the most striking Islamic sites in Spain is the palace of Alhambra in Granada, and this site represents the zenith of Islamic art.
The Catholic Monarchs refer to Ferdinand of Aragon and Isabella of Castille who married in 1469. They captured Granada (the last remaining part of Spain controlled by the Moors) in 1492.
The origin of the word ‘algorithm’ is from the name of the Islamic scholar Al-Khwarizmi.
I am aware of no other mathematician who was also a poet.
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O’Regan, G.: Mathematical Approaches to Software Quality. Springer, London (2006) MATH
de Solla Price, D.J.: An ancient greek computer. Sci. Am. 200, 60–67 (1959) CrossRef
Resnikoff, H.L., Wells, R.O.: Mathematics in Civilisation. Dover Publications, New York (1984)
Smith, D.E.: History of Mathematics, vol. 1. Dover Publications, New York (1923) MATH
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