Repaired Greek Cup

Repaired Greek Cup


This “Normal” Drinking Glass Is Actually an Ancient Greek Party Prank

Left: Marble bust of Pythagoras (Photo: Public domain via Wikipedia) | Right: Pythagoras Cup (Photo: Stock Photos from Danio69/Shutterstock)
This post may contain affiliate links. If you make a purchase, My Modern Met may earn an affiliate commission. Please read our disclosure for more info.

If you didn't think the ancient Greeks had a sense of humor, this clever drinking cup might convince you. What looks like an ordinary cup is actually a practical joke waiting to happen and it was invented by none other than Pythagoras. This philosopher and mathematician is probably most commonly known as the man behind the Pythagorean theorem, taught in geometry classes around the world. But there was also a playful side to this scholar, as demonstrated by what's known as the Greedy Cup, Cup of Justice, or Pythagoras Cup.

The chalice looks like any other, but if filled too much all the liquid gets siphoned out of a hole in the bottom. The design means that, at first glance, there's no sign that you might spill your drink, so imagine the surprise of greedy party-goers when they attempted to overpour and ended up with a splash on their laps. By simply applying basic principals of gravity and atmospheric pressure, the ancient philosopher created the ultimate party trick.

In order to understand how it works, you need to look at a cross-section of the Pythagoras Cup. When viewed in this manner, the hidden channel that snakes through the central column is clearly visible. As liquid is poured into the cup, it begins to make its way up the channel. Those who stop their pour just at the top of the central column will be none the wiser and can drink without issue. But, should someone get a bit greedy, the pressure becomes too much and the liquid continues to build up in the channel. From there, gravity does its work. The siphoning effect causes the liquid to spill out through the bottom of the cup until you find yourself without anything in your glass.

These cups are still sold throughout Greece, where they are called o kounenos tis dikaiosynis (the Cup of Justice). If you want to give the prank a try and aren't going to Greece anytime soon, they're also available on Amazon.


Cup (n.)

"small vessel used to contain liquids generally drinking vessel," Old English cuppe , Old Northumbrian copp , from Late Latin cuppa "cup" (source of Italian coppa , Spanish copa , Old French coupe "cup"), from Latin cupa "tub, cask, tun, barrel," which is thought to be cognate with Sanskrit kupah "hollow, pit, cave," Greek kype "gap, hole a kind of ship," Old Church Slavonic kupu , Lithuanian kaupas "heap," Old Norse hufr "ship's hull," Old English hyf "beehive." De Vaan writes that all probably are from "a non-IE loanword *kup- which was borrowed by and from many languages."

The Late Latin word was borrowed throughout Germanic: Old Frisian kopp "cup, head," Middle Low German kopp "cup," Middle Dutch coppe , Dutch kopje "cup, head." German cognate Kopf now means exclusively "head" (compare French tête , from Latin testa "potsherd").

Used of any thing with the shape of a cup by c. 1400 sense of "quantity contained in a cup" is from late 14c. Meaning "part of a bra that holds a breast" is from 1938. Sense of "cup-shaped metal vessel offered as a prize in sport or games" is from 1640s. Sense of "suffering to be endured" (late 14c.) is a biblical image (Matthew xx.22, xxvi.39) on the notion of "something to be partaken of."

To be in one's cups "intoxicated" is from 1610s (Middle English had cup-shoten "drunk, drunken," mid-14c.). [One's] cup of tea "what interests one" is by 1932, earlier used of persons (1908), the sense being "what is invigorating." Cup-bearer "attendant at a feast who conveys wine or other liquor to guests" is from early 15c.

late 14c., "to draw blood by means of cupping glasses," from cup (n.). Meaning "to form a cup" is from 1830. Related: Cupped cupping .


Warren Cup

  1. Click on the image to zoom in. Contains explicit scenes. Copyright Trustees of the British Museum
  2. Another side of the ancient Roman silver cup. Copyright Trustees of the British Museum
  3. Map showing where this object was found. Copyright Trustees of the British Museum

This luxurious silver cup was used at Roman dinner parties. The cup originally had two handles and depicts two pairs of male lovers. One side shows two teenage boys making love, while the other shows a young man lowering himself onto the lap of his elder, bearded lover. A slave-boy peers in voyeuristically from behind a door. The luxurious fabrics and musical instruments indicate that these scenes are set in a world heavily influenced by Greek culture, which the Romans admired and largely adopted.

What was the Roman attitude to relationships between men?

Images like this were not unusual in the Roman world. Some of the boys on this cup are underage by today's standards, but the Romans tolerated relationships between older and younger men. Relationships between men were part of Greek and Roman culture, from slaves to emperors, most famously the emperor Hadrian and his Greek lover, Antinous. Today such ancient images remind us that the way societies view sexuality is never fixed.

Due to it its explicit imagery, the cup was refused entry to the USA in 1953

Life, love, luxury – in one cup

This Roman silver cup is a fascinating and very versatile object, combining drinking, money and sex all in one!

To the Romans it was a drinking cup to be used not just admired. Picture a dinner party, course after course of exotic food and lots of fine wine. The guests talk about politics and love as they pass round the table this luxurious, tactile silver cup. Their host is delighted that they admire its decoration (and its value).

As a work of art it’s a masterpiece – its fine decoration achieved by beating the silver into shape from the inside using fine hammers and chisels. Luxuriant fabrics and musical instruments indicate a world heavily influenced by Greek culture, which the Romans admired and adopted.

So what is so special about the decoration that made it one of the British Museum’s highest-profile and most controversial acquisitions? What kept the piece out of permanent museum collections until 1999, and ensured that its purchase by the British Museum earned it a place in all the British media?

One side of the cup shows two teenage males, while the other shows two older men, all of them caught in the act of making love. The older men are watched by a peeping-tom, a young slave who spies on them from behind the door.

Were the dinner party guests offended by this? Probably not at all. Scenes of love-making were everywhere in Roman art. The cup is unique today, but in Roman times there were many others. Same sex relationships? Love and sex between men, often of differing ages, was part of Greek and Roman culture. One of the boys looks underage to us, but he was of marrying age to the Romans.

So this little cup embraces the Romans’ love of banqueting, their passion for conspicuous shows of wealth, their love of beautiful things and their skill in creating them. It also allows a glimpse into the private life of the Romans, challenging our traditional view of how they lived and loved.

Today some people take the cup out of its Roman context and see it as a symbol, either of sexual liberation, an affirmation of gay identity and proof of this identity through time, or of ancient decadence and a cautionary lesson in modern liberalism.

And here is the real beauty of the piece. It makes you think, and what better tribute could there be for an object from the past than to stimulate and provoke debate in the present?

This Roman silver cup is a fascinating and very versatile object, combining drinking, money and sex all in one!

To the Romans it was a drinking cup to be used not just admired. Picture a dinner party, course after course of exotic food and lots of fine wine. The guests talk about politics and love as they pass round the table this luxurious, tactile silver cup. Their host is delighted that they admire its decoration (and its value).

As a work of art it’s a masterpiece – its fine decoration achieved by beating the silver into shape from the inside using fine hammers and chisels. Luxuriant fabrics and musical instruments indicate a world heavily influenced by Greek culture, which the Romans admired and adopted.

So what is so special about the decoration that made it one of the British Museum’s highest-profile and most controversial acquisitions? What kept the piece out of permanent museum collections until 1999, and ensured that its purchase by the British Museum earned it a place in all the British media?

One side of the cup shows two teenage males, while the other shows two older men, all of them caught in the act of making love. The older men are watched by a peeping-tom, a young slave who spies on them from behind the door.

Were the dinner party guests offended by this? Probably not at all. Scenes of love-making were everywhere in Roman art. The cup is unique today, but in Roman times there were many others. Same sex relationships? Love and sex between men, often of differing ages, was part of Greek and Roman culture. One of the boys looks underage to us, but he was of marrying age to the Romans.

So this little cup embraces the Romans’ love of banqueting, their passion for conspicuous shows of wealth, their love of beautiful things and their skill in creating them. It also allows a glimpse into the private life of the Romans, challenging our traditional view of how they lived and loved.

Today some people take the cup out of its Roman context and see it as a symbol, either of sexual liberation, an affirmation of gay identity and proof of this identity through time, or of ancient decadence and a cautionary lesson in modern liberalism.

And here is the real beauty of the piece. It makes you think, and what better tribute could there be for an object from the past than to stimulate and provoke debate in the present?

Paul Roberts, curator, British Museum

Comments are closed for this object

Comments

Interesting how this beautiful object comments on today's society.

What makes you say some of the boys are underage by our standards? The current age of consent in Britain is 16, so you are saying they are <16 how can you tell?

What a beautiful object. Are reproductions of it available?

Why is it said that women would not have been present at the party? Respectable women were not present at Greek symposia ('drinking-parties') but they were present at Roman dinner-parties.

Now, before we all get carried away saying how wonderful it would be to emulate the enlightened Roman attitudes to sexuality shown on the Warren cup, we may want to bear a few points in mind. First, committed homosexual relationships between adults were frowned upon and ridiculed: gay sex was encouraged only between adult, married men and adolescent boys. Second, the boys were not supposed to enjoy the advances of the men, but to reject them: to encourage such attentions was considered effeminate. Third, homosexual advances were often (though not apparently in this case) forced upon slaves, who had no right of consent or rejection. If consent, adulthood and fidelity to a single partner are considered normative in today's society, modern gay people should really hesitate before lauding Greco-Roman norms as a benchmark of sexual liberation, the work on this cup included.

Simri,
You're posting politically correct historicism. In an age where an English man can be called a pedophile for simply walking through a park alone, one can understand your urge to belittle the sexual freedom depicted on the Warren Cup.

I'm sure ancient Roman boys quite enjoyed sex as much as boys today enjoy sex. Despite the current hysteria a good roll in the hay has always been enjoyable.

Why such a short video (20 seconds vs 2 minutes) compared to the previous objects? Subject still too risky?

BBC is literally afraid of the Warren Cup. Notice how the side that depicts older males having sex is completely zoomable, while the side depicting the boy having sex is a small photograph and not zoomable at all further, the video has been darkened and is difficult to see detail. The altering of history like this is simply a symptom of the hysterical sickness that festers at the heart of British society.

Share this link:

Most of the content on A History of the World is created by the contributors, who are the museums and members of the public. The views expressed are theirs and unless specifically stated are not those of the BBC or the British Museum. The BBC is not responsible for the content of any external sites referenced. In the event that you consider anything on this page to be in breach of the site’s House Rules please Flag This Object.


How Does the Pythagoras Cup Work?

Returning to the Pythagoras Cup, this drinking vessel takes advantage of a natural phenomenon known as the siphon. In the center of the cup is a hollow upside down u-shaped pipe, one end of which opens at the base of the cup, and the other inside the cup. If the cup is overfilled, the liquid within will begin to flow out of the cup through the curved tube. This causes the pressure in the upper part of the pipe to be reduced, thus allowing the higher atmospheric pressure to push the rest of the liquid out via the base of the cup.

Cross section of a Pythagorean cup being filled: at B, the cup may be drunk from, but at C, the siphon effect causes the cup to drain. (Nevit Dilmen / CC BY SA 3.0 )

Whilst an actual ancient Greek Pythagorean Cups has yet to be found, a Roman one was discovered in Croatia in 2012. This is a bowl made of silver with a figure of Tantalus seated on a rock (the pipe is hidden in this rock) in it. This bowl has often been regarded to be ‘the world’s first practical joke’.

Top Image: The Roman Tantalus Bowl, a Pythagorean Cup. ( Journal of Roman Archaeology ) Background: ‘Aeneas and a Sibyl in the Underworld’ by Jan Brueghel the Elder. ( Public Domain )


Mesopotamia

The furniture of Mesopotamia and neighbouring ancient civilizations of the Middle East had beds, stools, chairs, and boxes as principal forms. Documentary evidence is provided chiefly by relief carvings. The forms were constructed in the same manner as Egyptian furniture except that members were heavier, curves were less frequent, and joints were more abrupt. Ornament was richly applied in the form of cast-bronze and carved-bone finials (crowning ornaments, usually foliated) and studs, many of which survive in museums. Mesopotamia originated three features that were to persist in Classical furniture in Greece and Italy and thus were transmitted to other Western civilizations. First was the decoration of furniture legs with sharply profiled metal rings, one above another, like many bracelets on an arm this was the origin of the turned wooden legs so frequent in later styles. Second was the use of heavy fringes on furniture covers, blending the design of frame and cushion into one effect this was much lightened by Classical taste but was revived in Neoclassicism. Third was the typical furniture grouping that survived intact into the Dark Ages of Europe: the couch on which the main personage or personages reclined for eating or conversation the small table to hold refreshments, which could be moved up to the couch and the chair, on which sat an entertainer—wife, hetaira (courtesan), musician, or the like—who looked after the desires of the reclining superior personages. From this old hierarchy of furniture derived the cumbersome court regulations concerning who may sit and on what, that persisted for centuries in the palaces and ceremonies of monarchs.


Nostradamus’ Most Famed Prophecies

It’s clear that Nostradamus isn’t a supernatural figure with powers or abilities — he was just very adept at bibliomancy, or the practice of divining the future by interpreting a passage from a sacred text, like the Bible. In fact, linguist, translator and Nostradamus aficionado Peter Lemesurier expanded upon this idea, and History summarized his notions, explaining that, "[Nostradamus] simply believed that history will repeat itself. …[He] purportedly selected extracts from older sources at random and then used astrological calculations to project its recurrence in the future."

Okay, so he wasn’t claiming to be Cassandra of Troy, but there’s still something kind of dubious about his astrology-informed bibliomancy. So, why all the hype? Well, Nostradamus has seemingly predicted several history-making moments.

Here are excerpts from several well-known quatrains and the events they allegedly relate to:

  • The Death of Henry II: "He will pierce his eyes through a golden cage," Nostradamus wrote. And then Henry II was stabbed through his helmet — and through his eye — during a jousting match, which led to his untimely death.
  • The French Revolution: When the Third Estate stormed the Bastille and took control of Paris, it did seem to parallel the seer’s words, "From the enslaved populace, songs, / Chants and demands / While princes and lords are held captive in prisons."
  • The Discovery of Pasteurization: "Pastor will be celebrated almost as a God-like figure" — and, yes, Louis Pasteur’s last name does translate to "pastor."
  • The Rise of Adolf Hitler: "From the depths of the West of Europe, / A young child will be born of poor people, / He who by his tongue will seduce a great troop / His fame will increase towards the realm of the East," Nostradamus wrote. In another quatrain, he also penned "The greater part of the battlefield will be against Hister," which some believe to be a misspelling of the fascist dictator’s name.
  • The 1918 Influenza Pandemic: "The dreadful war which prepared in the West, the following year the pestilence will come, so very horrible that young, nor old, nor animal (will survive)." The pandemic came on the heels of World War I — enough said.
  • Sept. 11, 2001: Nostradamus spoke of "two great rocks" and "tremors" in a place called "New City," though other parts of the quatrain don’t seem to connect with that tragic day.

The seer is also credited with predicting JFK’s assassination, the Great Fire of London and the bombings of Hiroshima and Nagasaki. And, now, the COVID-19 pandemic.


Hellas Football

This Blog is part of the Hellas Football Group of social media sites. Twitter - @HellasFooty Facebook - @Hellasfooty Email - [email protected] - For up to date Greek Football Scores https://www.flashscore.co.uk/football/greece/

Subscribe to this blog

Follow by Email

A comprehensive look at the History of the Greek Cup By Hellas Football

  • Get link
  • Facebook
  • Twitter
  • Pinterest
  • Email
  • Other Apps

A comprehensive look at the History of the Greek Cup By Hellas Football

The 77th Greek Cup Final between Olympiakos and PAOK is upon us.

It will be the 8th meeting between the clubs in a Greek Cup Final, with Olympiakos leading the Head to Head in Finals, 5 to 2.

It is also 20 years since the last time these 2 clubs have met in the Greek Cup Final. In the 2000/01 edition, PAOK defeated Olympiakos 4-2 in Athens.

PAOK’s road to this year’s Greek Cup Final began with a 7-1 aggregate victory over Larissa, next was a 6-3 aggregate triumph over Lamia. This set up a Semi-Final with AEK, which saw PAOK prevail 3-1 over the 2 legs.

Olympiakos started with a 6-0 aggregate win over Panaitolikos, before despatching Aris 3-2 on aggregate in the next round, setting up a Semi-Final tie with PAS Giannina. Olympiakos got the job done with a 4-2 aggregate victory to reach the Final.

PAOK last claimed the Greek Cup in 2018/19, which was their 3rd successive Cup, following the triumphs of 2016/17 & 2017/18.

While Olympiakos are looking for back to back Greek Cups, having won the 2019/20 Greek Cup.

2020/21 was the 80th season of the Greek Cup, with the 1st season taking place back in 1931/32. AEK won the very 1st Greek Cup Final, defeating Aris 5-3 in Athens.

Overall Greek Cup Winners Tally:

Various Greek Cup statistics:

Most Greek Cup Finals Won – Olympiakos (28).

Most Greek Cup Finals Lost – PAOK (13).

Most Greek Cup Final appearances – Olympiakos (42) (including this season).

Most Greek Cup Final appearances without winning it – Doxa Drama (3).

Most consecutive appearances in the Final – Olympiakos (8) 1955/56�/63.

Most Greek Cup Final Wins in a Row – Olympiakos (5) 1956/57�/61.

Most Greek Cup Final Losses in a Row – AEK (4) 2016/17– 2019/20.

Most Common Greek Cup Final opponents – Olympiakos v. Panathinaikos (12).

Worst Greek Cup Final Record – Aris (1 Win from 9 Greek Cup Finals).

Longest gap between Greek Cup wins – PAOK (27 years) 1973/74�/01.

Biggest Greek Cup Final Victory – AEK 7-1 Apollon Smyrni (1995/96).

Player with most Greek Cup Final wins – Thanasis Bebis (8)

Player with most Greek Cup Final goals – Giorgos Sideris (6).

Cup Finals abandoned – (1) 1961/62 Final between Olympiakos and Panathinaikos.

Cup Finals awarded via walk-over – (2) 1963/64 & 1965/66 – both awarded to AEK.

Greek Cup seasons started then cancelled – (1) 1940/41.

Years the Greek Cup was not held – (10) 1933/34�/38 & 1941/42�/46.

80 Greek Cup Seasons have commenced, up to and including 2020/21.

76 Greek Cup Finals Played + 4 Replays.

10 Greek Cup Finals have gone to extra-time.

7 Greek Cup Finals decided by penalty shoot-out.

3 Greek Cup Finals decided in extra-time.

2 Greek Cup Finals never took place and were declared as walk-overs.

1 Greek Cup Final abandoned, with no Winner determined.

1 Greek Cup season cancelled.

With the final almost upon us, we will see who out of Olympiakos and PAOK, gets their name on the Cup again this weekend.

Below is a list of every Greek Cup Final:

1932/33 – Aris 2-2 Ethnikos – Replay – Ethnikos 2-1 Aris

1933/34 to 1937/38 – Cup Not Held

1939/40 – Panathinaikos 3-1 Aris

1940/41 – 1st round completed, Cup cancelled after Italy’s WW2 invasion of Greece.

1941/42 to 1945/46 – Cup Not Held

1946/47 – Olympiakos 5-0 Iraklis

1947/48 – Panathinaikos 2-1 AEK

1948/49 – AEK 0-0 Panathinaikos – Replay – AEK 2-1 Panathinaikos

1950/51 – Olympiakos 4-0 PAOK

1951/52 – Olympiakos 2-2 Panionios – Replay – Olympiakos 2-0 Panionios

1952/53 – Olympiakos 3-2 AEK

1953/54 – Olympiakos 2-0 Doxa Drama

1954/55 – Panathinaikos 2-0 PAOK

1955/56 – AEK 2-1 Olympiakos

1956/57 – Olympiakos 2-0 Iraklis

1957/58 – Olympiakos 5-1 Doxa Drama

1958/59 – Olympiakos 2-1 Doxa Drama

1959/60 – Olympiakos 1-1 Panathinaikos – Replay – Olympiakos 3-0 Panathinaikos

1960/61 – Olympiakos 3-0 Panionios

1961/62 – Panathinaikos 0-0 Olympiakos – Cup Final was played, but it was abandoned in Extra-Time due to fading light. The 1st half had gone for 66 minutes because of crowd disturbances and interjections following 3, 1st half red cards, no Cup was awarded to either team and no Replay was ordered.

1962/63 – Olympiakos 3-0 Pierikos

1963/64 – No Final was played, AEK were awarded the Cup, who beat Pierikos in their Semi-Final, but were not able to face an opponent in the Final. The other Semi-Final, involving Olympiakos and Panathinaikos was not completed, as both clubs were ejected from the Cup over crowd violence in that match.

1964/65 – Olympiakos 1-0 Panathinaikos

1965/66 – No Final was played, AEK were awarded the Cup, who got passed Kavala in their Semi-Final. Olympiakos who got passed Trikala in the other Semi-Final, failed to show up for the Final. The Federation delayed in determining a date for the Cup Final and Olympiakos had to prepare for the next season's European Cup.

1966/67 – Panathinaikos 1-0 Panionios

1967/68 – Olympiakos 1-0 Panathinaikos

1968/69 – Panathinaikos 1-1 Olympiakos, there was no Extra-Time, Penalties or Replay. The Greek Cup was awarded to Panathinaikos, after they won a post-match coin toss.

1970/71 – Olympiakos 3-1 PAOK

1971/72 – PAOK 2-1 Panathinaikos

1972/73 – Olympiakos 1-0 PAOK

1973/74 – PAOK 2-2 Olympiakos, PAOK won the first ever Cup Final shoot-out 4-3.

1974/75 – Olympiakos 1-0 Panathinaikos

1975/76 – Iraklis 4-4 Olympiakos, Iraklis won the shoot-out 6-5.

1976/77 – Panathinaikos 2-1 PAOK

1979/80 – Kastoria 5-2 Iraklis

1980/81 – Olympiakos 3-1 PAOK

1981/82 – Panathinaikos 1-0 Larissa

1983/84 – Panathinaikos 2-0 Larissa

1985/86 – Panathinaikos 4-0 Olympiakos

1986/87 – OFI 1-1 Iraklis, OFI won the shoot-out 3-1.

1987/88 – Panathinaikos 2-2 Olympiakos, Panathinaikos won the shoot-out 4-3.

1988/89 – Panathinaikos 3-1 Panionios

1989/90 – Olympiakos 4-1 OFI

1990/91 – Panathinaikos 5-1 Athinaikos (2-legged aggregate)

1991/92 – Olympiakos 3-1 PAOK (2-legged aggregate)

1992/93 – Panathinaikos 1-0 Olympiakos

1993/94 – Panathinaikos 3-3 AEK, Panathinaikos won the shoot-out 4-2.


Was It Worth It? Debt-Ridden Greeks Question the Cost of the 2004 Olympics

A view of the disused Olympic softball stadium in Athens on June 11, 2012

The Helliniko Olympic Complex in Athens was supposed to be thriving long after the 2004 Summer Olympics had ended. Built on part of the site of the city’s old airport for the Games, the facility housed the canoe and slalom events as well as arenas and sites for field hockey, baseball, softball, basketball and fencing. There were big plans to turn much of the complex into the largest metropolitan park in Europe, but that never happened, largely because of the bureaucracy that hampers most development in Greece. Today, the complex sits amid overgrown weeds, virtually deserted.

It’s been eight years since Greece, the birthplace of the Games, proudly hosted the Olympics, which London will host this summer. But as the country grapples with the destabilizing effects of the European economic crisis, many Greeks now look back on the Games with more regret than pride.

“It felt good at the time because we were the center of the world, and we got to show off our country,” says gymnast Christos Libanovnos of the Hellenic Gymnastics Federation, which uses the former Olympic complex for training. “But what did it cost? So much money — billions of euros. And now we are bankrupt and everything just gets worse and worse every day. It’s hard not to see a connection. It’s hard not to think that maybe it wasn’t worth it.”

Libanovnos helps train young gymnasts — including some visiting from other countries — in the old Olympic facility, but the place is so run-down that proper practice can be difficult. “We were embarrassed to let them in here. There’s a layer of dust everywhere and no air-conditioning,” he says. “And the trash bins are overflowing because there’s no cleaning staff.”

Hosting the Olympics certainly didn’t cause the country’s financial mess. Greece has a long history of systemic problems with labor productivity, public-sector debt and corruption. But in retrospect, the Athens Games appear now to be a high mark for modern-day Greece. It came at a moment when the euro, which Greece adopted a few years before, had brought the country a remarkable degree of wealth in a short period of time. Greece’s — and Europe’s — financial instability would’ve seemed unimaginable.

But in fact, the 2004 Olympics were a microcosm of Greek economic dysfunction: missed budget estimates, poor planning, financial mismanagement. It cost Greece about $11 billion, at least double what the Greek government had initially budgeted — and that doesn’t include the money the country has spent trying to maintain its rarely used Olympic facilities over the past eight years. It was forced — mainly by the U.S. and the U.K. — to spend $1.2 billion on security alone because of fears over terrorism, and in the months leading up to the opening ceremonies, Athens had to rush its schedule just to get construction projects completed on time.

“If you look at the mistakes they made in preparing for the Games, you could say that similar types of mistakes led Greece into the debt difficulties they’re facing now,” says Mark Spiegel, who works for the Federal Reserve Bank of San Francisco and has written about the economic effects of hosting the Olympics, referring to Greece’s budget and construction problems.

Andrew Rose, a University of California, Berkeley, economics professor who co-authored a paper with Spiegel called “The Olympic Effect,” says that even though Greece’s debt is in the hundreds of billions of dollars today, the Games clearly added to Greece’s fiscal woes. “Such events are almost all wasteful for advanced open economies like Greece,” he says.

For years, studies have shown that holding the Olympics often has severe negative economic effects on host cities, despite the temporary burst of tourism and global attention. The competition between cities often causes governments to go financially overboard merely to win an Olympic bid. Once construction gets under way, governments often fail to budget properly. And after the Games are over, many cities are left with infrastructure that suddenly has no real use.

Not everyone, however, accepts that rationale. Some argue, for instance, that hosting the Olympics brings cities much-needed infrastructure projects.

“Because of the Games, we now have the metro, a new airport and new roads,” says Isidoros Kouvelos of the Hellenic Olympic Committee. “Of course there are idle stadiums — these white elephants — but that’s not the whole story.”

The Summer Olympics in London appear to be no different. Even though the coalition government has made some budget cuts in Olympic spending as part of its attempts to reduce its budget deficit, a new report by Oxford University shows that the London Olympics are on track to be the most overbudget Games since Atlanta in 1996.

Even though the Greeks were jubilant eight years ago, many are completely ignoring the Games this time around.

“No one wants to talk about the Olympics, even though we have athletes at the London Games — and athletes who could win medals,” says Vassilis Sambrakos, a Greek sports-radio personality and columnist. “Many Greeks believe the 2004 Games was all built on a big lie — a lie that we had the money to pay for all these lavish centers and ceremonies. That seems like ancient history.”


Sources and contents of the Elements

Euclid compiled his Elements from a number of works of earlier men. Among these are Hippocrates of Chios (flourished c. 440 bce ), not to be confused with the physician Hippocrates of Cos (c. 460–375 bce ). The latest compiler before Euclid was Theudius, whose textbook was used in the Academy and was probably the one used by Aristotle (384–322 bce ). The older elements were at once superseded by Euclid’s and then forgotten. For his subject matter Euclid doubtless drew upon all his predecessors, but it is clear that the whole design of his work was his own, culminating in the construction of the five regular solids, now known as the Platonic solids.

A brief survey of the Elements belies a common belief that it concerns only geometry. This misconception may be caused by reading no further than Books I through IV, which cover elementary plane geometry. Euclid understood that building a logical and rigorous geometry (and mathematics) depends on the foundation—a foundation that Euclid began in Book I with 23 definitions (such as “a point is that which has no part” and “a line is a length without breadth”), five unproved assumptions that Euclid called postulates (now known as axioms), and five further unproved assumptions that he called common notions. (See the table of Euclid’s 10 initial assumptions.) Book I then proves elementary theorems about triangles and parallelograms and ends with the Pythagorean theorem. (For Euclid’s proof of the theorem, see Sidebar: Euclid’s Windmill Proof.)

Euclid's axioms
1 Given two points there is one straight line that joins them.
2 A straight line segment can be prolonged indefinitely.
3 A circle can be constructed when a point for its centre and a distance for its radius are given.
4 All right angles are equal.
5 If a straight line falling on two straight lines makes the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which the angles are less than the two right angles.
Euclid's common notions
6 Things equal to the same thing are equal.
7 If equals are added to equals, the wholes are equal.
8 If equals are subtracted from equals, the remainders are equal.
9 Things that coincide with one another are equal.
10 The whole is greater than a part.

The subject of Book II has been called geometric algebra because it states algebraic identities as theorems about equivalent geometric figures. Book II contains a construction of “the section,” the division of a line into two parts such that the ratio of the larger to the smaller segment is equal to the ratio of the original line to the larger segment. (This division was renamed the golden section in the Renaissance after artists and architects rediscovered its pleasing proportions.) Book II also generalizes the Pythagorean theorem to arbitrary triangles, a result that is equivalent to the law of cosines (see plane trigonometry). Book III deals with properties of circles and Book IV with the construction of regular polygons, in particular the pentagon.

Book V shifts from plane geometry to expound a general theory of ratios and proportions that is attributed by Proclus (along with Book XII) to Eudoxus of Cnidus (c. 395/390–342/337 bce ). While Book V can be read independently of the rest of the Elements, its solution to the problem of incommensurables (irrational numbers) is essential to later books. In addition, it formed the foundation for a geometric theory of numbers until an analytic theory developed in the late 19th century. Book VI applies this theory of ratios to plane geometry, mainly triangles and parallelograms, culminating in the “application of areas,” a procedure for solving quadratic problems by geometric means.

Books VII–IX contain elements of number theory, where number (arithmos) means positive integers greater than 1. Beginning with 22 new definitions—such as unity, even, odd, and prime—these books develop various properties of the positive integers. For instance, Book VII describes a method, antanaresis (now known as the Euclidean algorithm), for finding the greatest common divisor of two or more numbers Book VIII examines numbers in continued proportions, now known as geometric sequences (such as ax, ax 2 , ax 3 , ax 4 …) and Book IX proves that there are an infinite number of primes.

According to Proclus, Books X and XIII incorporate the work of the Pythagorean Theaetetus (c. 417–369 bce ). Book X, which comprises roughly one-fourth of the Elements, seems disproportionate to the importance of its classification of incommensurable lines and areas (although study of this book would inspire Johannes Kepler [1571–1630] in his search for a cosmological model).

Books XI–XIII examine three-dimensional figures, in Greek stereometria. Book XI concerns the intersections of planes, lines, and parallelepipeds (solids with parallel parallelograms as opposite faces). Book XII applies Eudoxus’s method of exhaustion to prove that the areas of circles are to one another as the squares of their diameters and that the volumes of spheres are to one another as the cubes of their diameters. Book XIII culminates with the construction of the five regular Platonic solids (pyramid, cube, octahedron, dodecahedron, icosahedron) in a given sphere, as displayed in the animation .

The unevenness of the several books and the varied mathematical levels may give the impression that Euclid was but an editor of treatises written by other mathematicians. To some extent this is certainly true, although it is probably impossible to figure out which parts are his own and which were adaptations from his predecessors. Euclid’s contemporaries considered his work final and authoritative if more was to be said, it had to be as commentaries to the Elements.


Watch the video: VW Jetta. The quarter panel repair. Ремонт заднего крыла.