Eureka (word)
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Archimedes exclaiming ''Eureka''. In his excitement, he forgets to dress and runs nude in the streets straight out of his bath (drawing by Pietro Scalvini, engraving by Carlo Orsolini, 1737) ''Eureka'' () is an
interjection An interjection is a word or expression that occurs as an utterance on its own and expresses a spontaneous feeling, situation or reaction. It is a diverse category, with many different types, such as exclamations ''(ouch!'', ''wow!''), curses (''da ...
used to celebrate a discovery or invention. It is a
transliteration Transliteration is a type of conversion of a text from one script to another that involves swapping letters (thus '' trans-'' + '' liter-'') in predictable ways, such as Greek → and → the digraph , Cyrillic → , Armenian → or L ...
of an exclamation attributed to Ancient Greek mathematician and inventor
Archimedes Archimedes of Syracuse ( ; ) was an Ancient Greece, Ancient Greek Greek mathematics, mathematician, physicist, engineer, astronomer, and Invention, inventor from the ancient city of Syracuse, Sicily, Syracuse in History of Greek and Hellenis ...
.


Etymology

''Eureka'' comes , which is the first person
singular Singular may refer to: * Singular, the grammatical number that denotes a unit quantity, as opposed to the plural and other forms * Singular or sounder, a group of boar, see List of animal names * Singular (band), a Thai jazz pop duo *'' Singula ...
perfect
indicative A realis mood ( abbreviated ) is a grammatical mood which is used principally to indicate that something is a statement of fact; in other words, to express what the speaker considers to be a known state of affairs, as in declarative sentence Dec ...
active of the verb . It is closely related to ''
heuristic A heuristic or heuristic technique (''problem solving'', '' mental shortcut'', ''rule of thumb'') is any approach to problem solving that employs a pragmatic method that is not fully optimized, perfected, or rationalized, but is nevertheless ...
'', which refers to experience-based techniques for problem-solving, learning, and discovery.


Pronunciation

The accent of the English word is on the second
syllable A syllable is a basic unit of organization within a sequence of speech sounds, such as within a word, typically defined by linguists as a ''nucleus'' (most often a vowel) with optional sounds before or after that nucleus (''margins'', which are ...
, following
Latin Latin ( or ) is a classical language belonging to the Italic languages, Italic branch of the Indo-European languages. Latin was originally spoken by the Latins (Italic tribe), Latins in Latium (now known as Lazio), the lower Tiber area aroun ...
rules of accent, which require that a penult (next-to-last syllable) must be accented if it contains a
long vowel In linguistics, vowel length is the perceived or actual duration of a vowel sound when pronounced. Vowels perceived as shorter are often called short vowels and those perceived as longer called long vowels. On one hand, many languages do not d ...
. In the Greek pronunciation, the first syllable has a high
pitch accent A pitch-accent language is a type of language that, when spoken, has certain syllables in words or morphemes that are prominent, as indicated by a distinct contrasting pitch (music), pitch (tone (linguistics), linguistic tone) rather than by vol ...
, because the Ancient Greek rules of accent do not force accent to the penult unless the ultima (last syllable) has a long vowel. The initial is dropped in
modern Greek Modern Greek (, or , ), generally referred to by speakers simply as Greek (, ), refers collectively to the dialects of the Greek language spoken in the modern era, including the official standardized form of the language sometimes referred to ...
and in several other European languages, including Catalan, French, Italian, Spanish, Portuguese, Dutch, and English, but preserved in others, such as Finnish, Danish, and German.


Archimedes

The exclamation "Eureka!" is attributed to the ancient Greek scholar
Archimedes Archimedes of Syracuse ( ; ) was an Ancient Greece, Ancient Greek Greek mathematics, mathematician, physicist, engineer, astronomer, and Invention, inventor from the ancient city of Syracuse, Sicily, Syracuse in History of Greek and Hellenis ...
. He reportedly proclaimed "Eureka! Eureka!" after he had stepped into a bath and noticed that the water level rose, whereupon he suddenly understood that the
volume Volume is a measure of regions in three-dimensional space. It is often quantified numerically using SI derived units (such as the cubic metre and litre) or by various imperial or US customary units (such as the gallon, quart, cubic inch) ...
of water displaced must be equal to the volume of the part of his body he had submerged. (This relation is ''not'' what is known as
Archimedes' principle Archimedes' principle states that the upward buoyant force that is exerted on a body immersed in a fluid, whether fully or partially, is equal to the weight of the fluid that the body displaces. Archimedes' principle is a law of physics fun ...
—that deals with the '' upthrust'' experienced by a body immersed in a fluid.) He then realized that the volume of irregular objects could be measured with precision, a previously intractable problem. He is said to have been so eager to share his discovery that he leapt out of his bathtub and ran naked through the streets of Syracuse. Archimedes' insight led to the solution of a problem posed by Hiero of Syracuse, on how to assess the purity of an irregular golden votive crown; he had given his goldsmith the pure gold to be used, and correctly suspected he had been cheated by the goldsmith removing gold and adding the same weight of silver. Equipment for weighing objects with a fair amount of precision already existed, and now that Archimedes could also measure volume, their ratio would give the object's
density Density (volumetric mass density or specific mass) is the ratio of a substance's mass to its volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' (or ''d'') can also be u ...
, an important indicator of purity (as gold is nearly twice as dense as silver and therefore has significantly greater weight for the same volume).


Authenticity

This story first appeared in written form in
Vitruvius Vitruvius ( ; ; –70 BC – after ) was a Roman architect and engineer during the 1st century BC, known for his multi-volume work titled . As the only treatise on architecture to survive from antiquity, it has been regarded since the Renaissan ...
's books of architecture, two centuries after it supposedly took place. Some scholars have doubted the accuracy of this tale, on the grounds that the votive crown was a fine item, thus an impure crown would displace water only minutely, compared to a pure one. Precise means needed to measure this minute difference was not available at the time. For the problem posed to Archimedes, though, there is a simple method which requires no precision equipment: using a balance, compare the weight of the crown against pure gold. While they are still suspended from the arms of the balance, simultaneously submerge the crown and the gold in water. If the volumes are the same, the balance remains in equilibrium, meaning that their densities are the same and therefore the crown must be pure gold. But if the density of the crown is less (due to being alloyed with another metal like silver), increased buoyancy of the crown results in imbalance.
Galileo Galilei Galileo di Vincenzo Bonaiuti de' Galilei (15 February 1564 – 8 January 1642), commonly referred to as Galileo Galilei ( , , ) or mononymously as Galileo, was an Italian astronomer, physicist and engineer, sometimes described as a poly ...
himself weighed in on the controversy, suggesting a design for a hydrostatic balance that could be used to compare the dry weight of an object with the weight of the same object submerged in water.


Names and mottos


California

The expression is also the state motto of California, referring to the momentous discovery of gold near
Sutter's Mill Sutter's Mill was a water-powered sawmill on the bank of the South Fork American River in the foothills of the Sierra Nevada in California. It was named after its owner John Sutter. A worker constructing the mill, James W. Marshall, found go ...
in 1848. The California State Seal has included the word ''Eureka'' since its original design by Robert S. Garnett in 1850; the official text from that time describing the seal states that this word's meaning applies "either to the principle involved in the admission of the State or the success of the miner at work". In 1957 the state legislature attempted to make "In God We Trust" the state motto as part of the same post WWII anti-Communist movement that successfully added the term "under God" to the American Pledge of Allegiance in 1954, but this attempt did not succeed and "Eureka" was made the official motto in 1963. The city of
Eureka, California Eureka ( ; Wiyot: ; Hupa: ; ) is a city and the county seat of Humboldt County, located on the North Coast of California. The city is located on U.S. Route 101 on the shores of Humboldt Bay, north of San Francisco and south of the Oreg ...
, founded in 1850, uses the California State Seal as its official seal. Eureka is a considerable distance from Sutter's Mill, but was the jumping off point of a smaller gold rush in nearby Trinity County, California in 1850. It is the largest of at least eleven remaining US cities and towns named for the exclamation, "eureka!". As a result of the extensive use of the exclamation dating from 1849, there were nearly 40 locales so named by the 1880s in a nation that had none in the 1840s. Many places, works of culture, and other objects have since been named "Eureka"; see Eureka (disambiguation) for a list.


Australia

"Eureka" was also associated with a gold rush in
Ballarat Ballarat ( ) () is a city in the Central Highlands of Victoria, Australia. At the 2021 census, Ballarat had a population of 111,973, making it the third-largest urban inland city in Australia and the third-largest city in Victoria. Within mo ...
, Victoria,
Australia Australia, officially the Commonwealth of Australia, is a country comprising mainland Australia, the mainland of the Australia (continent), Australian continent, the island of Tasmania and list of islands of Australia, numerous smaller isl ...
. The Eureka Stockade was a revolt in 1854 by gold miners against unjust mining license fees and a brutal administration supervising the miners. The rebellion demonstrated the refusal of the workers to be dominated by unfair government and laws. The Eureka Stockade has often been referred to as the "birth of
democracy Democracy (from , ''dēmos'' 'people' and ''kratos'' 'rule') is a form of government in which political power is vested in the people or the population of a state. Under a minimalist definition of democracy, rulers are elected through competitiv ...
" in Australia.


Mathematics

Another mathematician,
Carl Friedrich Gauss Johann Carl Friedrich Gauss (; ; ; 30 April 177723 February 1855) was a German mathematician, astronomer, geodesist, and physicist, who contributed to many fields in mathematics and science. He was director of the Göttingen Observatory and ...
, echoed Archimedes when in 1796 he wrote in his diary, "ΕΥΡΗΚΑ! num = Δ + Δ + Δ", referring to his discovery that any positive
integer An integer is the number zero (0), a positive natural number (1, 2, 3, ...), or the negation of a positive natural number (−1, −2, −3, ...). The negations or additive inverses of the positive natural numbers are referred to as negative in ...
could be expressed as the sum of at most three triangular numbers. This result is now known as Gauss's Eureka theorem and is a special case of what later became known as the Fermat polygonal number theorem.


See also

* * *


References

{{reflist, 30em Archimedes Greek words and phrases Interjections State mottos of the United States Symbols of California