Archimedes exclaiming ''Eureka''. In his excitement, he forgets to dress and runs nude in the streets straight out of his bath
''Eureka'' ( grc, εὕρηκα) is an
interjection
An interjection is a word or expression that occurs as an utterance on its own and expresses a spontaneous feeling or reaction. It is a diverse category, encompassing many different parts of speech, such as exclamations ''(ouch!'', ''wow!''), curse ...
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 → , Cyrillic → , Greek → the digraph , Armenian → or L ...
of an exclamation attributed to Ancient Greek mathematician and inventor
Archimedes.
Etymology
"Eureka" comes from the
Ancient Greek
Ancient Greek includes the forms of the Greek language used in ancient Greece and the ancient world from around 1500 BC to 300 BC. It is often roughly divided into the following periods: Mycenaean Greek (), Dark Ages (), the Archaic p ...
word
εὕρηκα ''heúrēka'', meaning "I have found (it)", 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 homology
* SINGULAR, an open source Computer Algebra System (CAS)
* Singular or sounder, a group of boar, ...
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 sentences. Mos ...
active
Active may refer to:
Music
* ''Active'' (album), a 1992 album by Casiopea
* Active Records, a record label
Ships
* ''Active'' (ship), several commercial ships by that name
* HMS ''Active'', the name of various ships of the British Royal ...
of the verb
εὑρίσκω ''heurískō'' "I find". It is closely related to ''
heuristic
A heuristic (; ), or heuristic technique, is any approach to problem solving or self-discovery that employs a practical method that is not guaranteed to be optimal, perfect, or rational, but is nevertheless sufficient for reaching an immediate ...
'', which refers to experience-based techniques for problem-solving, learning, and discovery.
Pronunciation
The accent of the English word is on the second
syllable, following
Latin
Latin (, or , ) is a classical language belonging to the Italic branch of the Indo-European languages. Latin was originally a dialect spoken in the lower Tiber area (then known as Latium) around present-day Rome, but through the power of the ...
rules of accent, which require that a penult (next-to-last syllable) must be accented if it contains a
long vowel. In the Greek pronunciation, the first syllable has a high pitch accent, because the Ancient Greek rules of accent 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 is dropped in
modern Greek
Modern Greek (, , or , ''Kiní Neoellinikí Glóssa''), 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 ...
and in several other European languages, including
Catalan
Catalan may refer to:
Catalonia
From, or related to Catalonia:
* Catalan language, a Romance language
* Catalans, an ethnic group formed by the people from, or with origins in, Northern or southern Catalonia
Places
* 13178 Catalan, asteroid #1 ...
, French, Italian, Spanish, Portuguese, Dutch, and English, but preserved in others, such as
Finnish
Finnish may refer to:
* Something or someone from, or related to Finland
* Culture of Finland
* Finnish people or Finns, the primary ethnic group in Finland
* Finnish language, the national language of the Finnish people
* Finnish cuisine
See also ...
, Danish, and German.
Archimedes
![Archimede bain](https://upload.wikimedia.org/wikipedia/commons/c/c2/Archimede_bain.jpg)
The exclamation "Eureka!" is attributed to the ancient Greek scholar
Archimedes. 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 occupied 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). Th ...
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 (also spelled Archimedes's 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' ...
—that deals with the ''
upthrust
Buoyancy (), or upthrust, is an upward force exerted by a fluid that opposes the weight of a partially or fully immersed object. In a column of fluid, pressure increases with depth as a result of the weight of the overlying fluid. Thus the ...
'' 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
Purity may refer to:
Books
* ''Pureza'' (novel), a 1937 Brazilian novel by José Lins do Rego
* ''Purity'' (novel), a 2015 novel by Jonathan Franzen
** ''Purity'' (TV series), a TV series based on the novel
*''Purity'', a 2012 novel by Jackson P ...
of an irregular golden
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 im ...
; 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 substance's mass per unit of volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' can also be used. Mathematical ...
, an important indicator of purity (as gold is nearly twice as dense as silver and therefore has significantly greater weight for the same volume).
This story first appeared in written form in
Vitruvius
Vitruvius (; c. 80–70 BC – after c. 15 BC) was a Roman architect and engineer during the 1st century BC, known for his multi-volume work entitled '' De architectura''. He originated the idea that all buildings should have three attribut ...
'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) was an Italian astronomer, physicist and engineer, sometimes described as a polymath. Commonly referred to as Galileo, his name was pronounced (, ). He wa ...
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
![AmCyc California - seal](https://upload.wikimedia.org/wikipedia/commons/c/cd/AmCyc_California_-_seal.jpg)
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 gol ...
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
The Pledge of Allegiance of the United States is a patriotic recited verse that promises allegiance to the flag of the United States and the republic of the United States of America. The first version, with a text different from the one used ...
in 1954, but this attempt did not succeed and "Eureka" was made the official motto in 1963.
The city of
Eureka, California
Eureka (Wiyot: ''Jaroujiji'', Hupa: ''do'-wi-lotl-ding'', Karuk: ''uuth'') is the principal city and county seat of Humboldt County in the Redwood Empire region of California. The city is located on U.S. Route 101 on the shores of Humboldt Ba ...
, 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
Trinity County is a county located in the northwestern portion of the U.S. state of California. Trinity County is rugged, mountainous, heavily forested, and lies along the Trinity River (for which it is named) within the Salmon and Klamath Mou ...
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,
Victoria
Victoria most commonly refers to:
* Victoria (Australia), a state of the Commonwealth of Australia
* Victoria, British Columbia, provincial capital of British Columbia, Canada
* Victoria (mythology), Roman goddess of Victory
* Victoria, Seychelle ...
,
Australia. The
Eureka Stockade
The Eureka Rebellion was a series of events involving gold miners who revolted against the British administration of the colony of Victoria, Australia during the Victorian gold rush. It culminated in the Battle of the Eureka Stockade, which ...
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 grc, δημοκρατία, dēmokratía, ''dēmos'' 'people' and ''kratos'' 'rule') is a form of government in which people, the people have the authority to deliberate and decide legislation ("direct democracy"), or to choo ...
" in Australia.
Mathematics
![Eureka Gauss](https://upload.wikimedia.org/wikipedia/commons/c/cd/Eureka_Gauss.png)
Another mathematician,
Carl Friedrich Gauss
Johann Carl Friedrich Gauss (; german: Gauß ; la, Carolus Fridericus Gauss; 30 April 177723 February 1855) was a German mathematician and physicist who made significant contributions to many fields in mathematics and science. Sometimes refer ...
, 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 (), a positive natural number (, , , etc.) or a negative integer with a minus sign ( −1, −2, −3, etc.). The negative numbers are the additive inverses of the corresponding positive numbers. In the languag ...
could be expressed as the sum of at most three
triangular number
A triangular number or triangle number counts objects arranged in an equilateral triangle. Triangular numbers are a type of figurate number, other examples being square numbers and cube numbers. The th triangular number is the number of dots i ...
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
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 integer can be written as the sum of three or fewer triangular numbers, and as the sum ...
.
See also
*
*
References
{{reflist, 30em
Archimedes
Greek words and phrases
Interjections
State mottos of the United States
Symbols of California