Eureka (word)
Overview
 
"Eureka" is an interjection
Interjection
In grammar, an interjection or exclamation is a word used to express an emotion or sentiment on the part of the speaker . Filled pauses such as uh, er, um are also considered interjections...

 used to celebrate a discovery
Discovery (observation)
Discovery is the act of detecting something new, or something "old" that had been unknown. With reference to science and academic disciplines, discovery is the observation of new phenomena, new actions, or new events and providing new reasoning to explain the knowledge gathered through such...

, a transliteration of a word attributed to Archimedes
Archimedes
Archimedes of Syracuse was a Greek mathematician, physicist, engineer, inventor, and astronomer. Although few details of his life are known, he is regarded as one of the leading scientists in classical antiquity. Among his advances in physics are the foundations of hydrostatics, statics and an...

.
The word comes from ancient Greek
Ancient Greek
Ancient Greek is the stage of the Greek language in the periods spanning the times c. 9th–6th centuries BC, , c. 5th–4th centuries BC , and the c. 3rd century BC – 6th century AD of ancient Greece and the ancient world; being predated in the 2nd millennium BC by Mycenaean Greek...

 εὕρηκα heúrēka "I have found (it)", which is the 1st person
Grammatical person
Grammatical person, in linguistics, is deictic reference to a participant in an event; such as the speaker, the addressee, or others. Grammatical person typically defines a language's set of personal pronouns...

 singular
Grammatical number
In linguistics, grammatical number is a grammatical category of nouns, pronouns, and adjective and verb agreement that expresses count distinctions ....

 perfect indicative
Grammatical mood
In linguistics, grammatical mood is a grammatical feature of verbs, used to signal modality. That is, it is the use of verbal inflections that allow speakers to express their attitude toward what they are saying...

 active
Voice (grammar)
In grammar, the voice of a verb describes the relationship between the action that the verb expresses and the participants identified by its arguments . When the subject is the agent or doer of the action, the verb is in the active voice...

 of the verb heuriskō "I find". The reconstructed Ancient Greek pronunciation
Ancient Greek phonology
Ancient Greek phonology is the study of the phonology, or pronunciation, of Ancient Greek. Because of the passage of time, the original pronunciation of Ancient Greek, like that of all ancient languages, can never be known with absolute certainty...

 is hěu̯rɛːka, while the Modern Greek pronunciation
Modern Greek phonology
This page presents a sketch of the phonology of Standard Modern Greek.-Consonants:The consonantal system of Greek is difficult to describe, as there is considerable debate about which sounds to describe as separate phonemes and which to analyse as conditional allophones...

 is ˈevrika.

The accent of the English word is on the second syllable
Syllable
A syllable is a unit of organization for a sequence of speech sounds. For example, the word water is composed of two syllables: wa and ter. A syllable is typically made up of a syllable nucleus with optional initial and final margins .Syllables are often considered the phonological "building...

, following Latin
Latin
Latin is an Italic language originally spoken in Latium and Ancient Rome. It, along with most European languages, is a descendant of the ancient Proto-Indo-European language. Although it is considered a dead language, a number of scholars and members of the Christian clergy speak it fluently, and...

 accent rules, which require that a penult (next-to-last syllable) must be accented if it has a long vowel
Vowel length
In linguistics, vowel length is the perceived duration of a vowel sound. Often the chroneme, or the "longness", acts like a consonant, and may etymologically be one, such as in Australian English. While not distinctive in most dialects of English, vowel length is an important phonemic factor in...

.
Encyclopedia
"Eureka" is an interjection
Interjection
In grammar, an interjection or exclamation is a word used to express an emotion or sentiment on the part of the speaker . Filled pauses such as uh, er, um are also considered interjections...

 used to celebrate a discovery
Discovery (observation)
Discovery is the act of detecting something new, or something "old" that had been unknown. With reference to science and academic disciplines, discovery is the observation of new phenomena, new actions, or new events and providing new reasoning to explain the knowledge gathered through such...

, a transliteration of a word attributed to Archimedes
Archimedes
Archimedes of Syracuse was a Greek mathematician, physicist, engineer, inventor, and astronomer. Although few details of his life are known, he is regarded as one of the leading scientists in classical antiquity. Among his advances in physics are the foundations of hydrostatics, statics and an...

.

Etymology

The word comes from ancient Greek
Ancient Greek
Ancient Greek is the stage of the Greek language in the periods spanning the times c. 9th–6th centuries BC, , c. 5th–4th centuries BC , and the c. 3rd century BC – 6th century AD of ancient Greece and the ancient world; being predated in the 2nd millennium BC by Mycenaean Greek...

 εὕρηκα heúrēka "I have found (it)", which is the 1st person
Grammatical person
Grammatical person, in linguistics, is deictic reference to a participant in an event; such as the speaker, the addressee, or others. Grammatical person typically defines a language's set of personal pronouns...

 singular
Grammatical number
In linguistics, grammatical number is a grammatical category of nouns, pronouns, and adjective and verb agreement that expresses count distinctions ....

 perfect indicative
Grammatical mood
In linguistics, grammatical mood is a grammatical feature of verbs, used to signal modality. That is, it is the use of verbal inflections that allow speakers to express their attitude toward what they are saying...

 active
Voice (grammar)
In grammar, the voice of a verb describes the relationship between the action that the verb expresses and the participants identified by its arguments . When the subject is the agent or doer of the action, the verb is in the active voice...

 of the verb heuriskō "I find". The reconstructed Ancient Greek pronunciation
Ancient Greek phonology
Ancient Greek phonology is the study of the phonology, or pronunciation, of Ancient Greek. Because of the passage of time, the original pronunciation of Ancient Greek, like that of all ancient languages, can never be known with absolute certainty...

 is hěu̯rɛːka, while the Modern Greek pronunciation
Modern Greek phonology
This page presents a sketch of the phonology of Standard Modern Greek.-Consonants:The consonantal system of Greek is difficult to describe, as there is considerable debate about which sounds to describe as separate phonemes and which to analyse as conditional allophones...

 is ˈevrika.

The accent of the English word is on the second syllable
Syllable
A syllable is a unit of organization for a sequence of speech sounds. For example, the word water is composed of two syllables: wa and ter. A syllable is typically made up of a syllable nucleus with optional initial and final margins .Syllables are often considered the phonological "building...

, following Latin
Latin
Latin is an Italic language originally spoken in Latium and Ancient Rome. It, along with most European languages, is a descendant of the ancient Proto-Indo-European language. Although it is considered a dead language, a number of scholars and members of the Christian clergy speak it fluently, and...

 accent rules, which require that a penult (next-to-last syllable) must be accented if it has a long vowel
Vowel length
In linguistics, vowel length is the perceived duration of a vowel sound. Often the chroneme, or the "longness", acts like a consonant, and may etymologically be one, such as in Australian English. While not distinctive in most dialects of English, vowel length is an important phonemic factor in...

. In the Greek pronunciation, the first syllable has a high pitch accent, because the Ancient Greek rules of accent
Ancient Greek accent
In Ancient Greek, accent varies from word to word, but there are rules of accent determining where it can fall and what type it can be. The rules depend on the length of the vowel in the last syllable and in the syllable being accented.-Mora:...

 do not force accent to the penult unless the ultima (last syllable) has a long vowel. The long vowels in the first two syllables would sound like a double stress to English ears (as in the phrase Maltese cat).

The initial /h/ is dropped in some European languages, including English
English language
English is a West Germanic language that arose in the Anglo-Saxon kingdoms of England and spread into what was to become south-east Scotland under the influence of the Anglian medieval kingdom of Northumbria...

, but preserved in others, such as Finnish
Finnish language
Finnish is the language spoken by the majority of the population in Finland Primarily for use by restaurant menus and by ethnic Finns outside Finland. It is one of the two official languages of Finland and an official minority language in Sweden. In Sweden, both standard Finnish and Meänkieli, a...

 and German
German language
German is a West Germanic language, related to and classified alongside English and Dutch. With an estimated 90 – 98 million native speakers, German is one of the world's major languages and is the most widely-spoken first language in the European Union....

: Heureka
Heureka
Heureka is a science center in Vantaa, Finland, north of Helsinki. Its purpose is to facilitate the access to scientific knowledge and to develop the methods of scientific education. Its exhibits are largely hands-on and many of them are made for children...

.

Archimedes

This exclamation is most famously attributed to the ancient Greek scholar Archimedes
Archimedes
Archimedes of Syracuse was a Greek mathematician, physicist, engineer, inventor, and astronomer. Although few details of his life are known, he is regarded as one of the leading scientists in classical antiquity. Among his advances in physics are the foundations of hydrostatics, statics and an...

. He reportedly proclaimed "Eureka!" when he stepped into a bath and noticed that the water level rose—he suddenly understood that the volume
Volume
Volume is the quantity of three-dimensional space enclosed by some closed boundary, for example, the space that a substance or shape occupies or contains....

 of water displaced
Displacement (fluid)
In fluid mechanics, displacement occurs when an object is immersed in a fluid, pushing it out of the way and taking its place. The volume of the fluid displaced can then be measured, as in the illustration, and from this the volume of the immersed object can be deduced .An object that sinks...

 must be equal to the volume of the part of his body he had submerged. This relation is known as Archimedes' principle
Archimedes' principle
Archimedes' principle relates buoyancy to displacement. It is named after its discoverer, Archimedes of Syracuse.-Principle:Archimedes' treatise On floating bodies, proposition 5, states that...

. 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 through the streets of Syracuse
Syracuse, Italy
Syracuse is a historic city in Sicily, the capital of the province of Syracuse. The city is notable for its rich Greek history, culture, amphitheatres, architecture, and as the birthplace of the preeminent mathematician and engineer Archimedes. This 2,700-year-old city played a key role in...

 naked.

Archimedes' insight led to the solution of a problem posed by Hiero of Syracuse, on how to assess the purity
Carat (purity)
The karat or carat is a unit of purity for gold alloys.- Measure :Karat purity is measured as 24 times the purity by mass:where...

 of an irregular golden votive crown
Votive crown
A votive crown is a votive offering in the form of a crown, normally in precious metals and often adorned with jewels. Especially in the Early Middle Ages, they are of a special form, designed to be suspended by chains at an altar, shrine or image...

; 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 already existed, and now that Archimedes could also measure volume, their ratio would give the object's density
Density
The mass density or density of a material is defined as its mass per unit volume. The symbol most often used for density is ρ . In some cases , density is also defined as its weight per unit volume; although, this quantity is more properly called specific weight...

, an important indicator of purity.

This story first appeared in written form in Vitruvius
Vitruvius
Marcus Vitruvius Pollio was a Roman writer, architect and engineer, active in the 1st century BC. He is best known as the author of the multi-volume work De Architectura ....

's books of architecture
De architectura
' is a treatise on architecture written by the Roman architect Vitruvius and dedicated to his patron, the emperor Caesar Augustus, as a guide for building projects...

, two centuries after it supposedly took place. Some scholars have doubted the accuracy of this tale, saying among other things that the method would have required precise measurements that would have been difficult to make at the time. For the problem posed to Archimedes, though, there is a simple method which requires no precision equipment: balance the crown against pure gold in air, and then submerge the scale with crown and gold in water to see if they still balance.

Names and mottoes

The expression is also quoted as the state motto of California
California
California is a state located on the West Coast of the United States. It is by far the most populous U.S. state, and the third-largest by land area...

, referring to the momentous discovery of gold
California Gold Rush
The California Gold Rush began on January 24, 1848, when gold was found by James W. Marshall at Sutter's Mill in Coloma, California. The first to hear confirmed information of the gold rush were the people in Oregon, the Sandwich Islands , and Latin America, who were the first to start flocking to...

 near Sutter's Mill
Sutter's Mill
Sutter's Mill was a sawmill owned by 19th century pioneer John Sutter in partnership with James W. Marshall. It was located in Coloma, California, at the bank of the South Fork American River...

 in 1848. The California State Seal
Seal of California
The Great Seal of the State of California was adopted at the California state Constitutional Convention of 1849 and has undergone minor design changes since then, the last being the standardization of the seal in 1937...

 has included the word "eureka" since its original design by Robert S. Garnett
Robert S. Garnett
Robert Selden Garnett was a career military officer, serving in the United States Army until the American Civil War, when he became a Confederate States Army brigadier general. He was the first general officer killed in the Civil War.-Early life and career:Garnett was born at the family plantation...

 in 1849; 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, but this attempt did not succeed, and "Eureka" became the official motto in 1963.

The city of Eureka, California
Eureka, California
Eureka is the principal city and the county seat of Humboldt County, California, United States. Its population was 27,191 at the 2010 census, up from 26,128 at the 2000 census....

, founded in 1850, uses the California State Seal
Seal of California
The Great Seal of the State of California was adopted at the California state Constitutional Convention of 1849 and has undergone minor design changes since then, the last being the standardization of the seal in 1937...

 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 Trinity County, California
Trinity County, California
Trinity County is a large, rugged and mountainous, heavily forested county located in the northwestern portion of the U.S. state of California, along the Trinity River and within the Salmon/Klamath Mountains. It covers an area of over two million acres , and as of the 2010 census its population...

 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
Eureka
Eureka may refer to:* Eureka , a famous exclamation attributed to Archimedes* Eureka effect, the sudden, unexpected realization of the solution to a problem- Canada :* Eureka, Nova Scotia in Canada* Eureka, Nunavut in Canada...

 for a list.

"Eureka" was also associated with a gold rush in Ballarat, Victoria
Victoria (Australia)
Victoria is the second most populous state in Australia. Geographically the smallest mainland state, Victoria is bordered by New South Wales, South Australia, and Tasmania on Boundary Islet to the north, west and south respectively....

, Australia
Australia
Australia , officially the Commonwealth of Australia, is a country in the Southern Hemisphere comprising the mainland of the Australian continent, the island of Tasmania, and numerous smaller islands in the Indian and Pacific Oceans. It is the world's sixth-largest country by total area...

. The Eureka Stockade
Eureka Stockade
The Eureka Rebellion of 1854 was an organised rebellion by gold miners which occurred at Eureka Lead in Ballarat, Victoria, Australia. The Battle of Eureka Stockade was fought on 3 December 1854 and named for the stockade structure erected by miners during the conflict...

 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
Democracy is generally defined as a form of government in which all adult citizens have an equal say in the decisions that affect their lives. Ideally, this includes equal participation in the proposal, development and passage of legislation into law...

' in Australia.

Mathematics

Another mathematician, Carl Friedrich Gauss
Carl Friedrich Gauss
Johann Carl Friedrich Gauss was a German mathematician and scientist who contributed significantly to many fields, including number theory, statistics, analysis, differential geometry, geodesy, geophysics, electrostatics, astronomy and optics.Sometimes referred to as the Princeps mathematicorum...

, echoed Archimedes when in 1796 he wrote in his diary
Gauss's diary
Gauss's diary was a record of the mathematical discoveries of C. F. Gauss from 1796 to 1814. It was rediscovered in 1897 and published by , and reprinted in volume X1 of his collected works.-Sample entries:...

, "ΕΥΡΗΚΑ! num = Δ + Δ + Δ", referring to his discovery that any positive integer
Integer
The integers are formed by the natural numbers together with the negatives of the non-zero natural numbers .They are known as Positive and Negative Integers respectively...

 could be expressed as the sum of at most three triangular number
Triangular number
A triangular number or triangle number numbers the objects that can form an equilateral triangle, as in the diagram on the right. The nth triangle number is the number of dots in a triangle with n dots on a side; it is the sum of the n natural numbers from 1 to n...

s. This result is now known as Gauss' Eureka theorem and is a special case of what later became known as the Fermat polygonal number theorem
Fermat polygonal number theorem
In additive number theory, the Fermat polygonal number theorem states that every positive integer is a sum of at most -gonal numbers. That is, every positive number can be written as the sum of three or fewer triangular numbers, and as the sum of four or fewer square numbers, and as the sum of...

.
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