265:, 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.
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245:; 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
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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
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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
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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
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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
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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.
326:, 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
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203:. 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
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Ono, Ken; Robins, Sinai; Wahl, Patrick T. (1995). "On the representation of integers as sums of triangular numbers".
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rules of accent, which require that a penult (next-to-last syllable) must be accented if it contains a
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same post WWII anti-Communist movement that successfully added the term "under God" to the
American
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in 1954, but this attempt did not succeed and "Eureka" was made the official motto in 1963.
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must be equal to the volume of the part of his body he had submerged. (This relation is
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The expression is also the state motto of
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704:(1956). "Gauss, the Prince of Mathematicians". In Newman, James R. (ed.).
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Vitruvius on
Architecture, IX: Introduction: 9–12, translated into English
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of an exclamation attributed to
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culture, and other objects have since been named "Eureka"; see
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Density § Volume vs. density; volume of an irregular shape
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Archimedes' insight led to the solution of a problem posed by
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in 1848. The
California State Seal has included the word
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used to celebrate a discovery or invention. It is a
165:and in several other European languages, including
379:entry related to sum of triangular numbers (1796)
343:"Eureka" was also associated with a gold rush in
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138:The accent of the English word is on the second
395:could be expressed as the sum of at most three
191:Archimedes § Archimedes and the gold crown
660:California Place Names, by Erwin Gudde, p. 105
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535:"EXHIBIT: The First Eureka Moment".
33:, engraving by Carlo Orsolini, 1737)
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82:"Eureka" comes from the
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253:Authenticity
243:votive crown
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148:long vowel
108:indicative
72:Archimedes
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500:"Eureka!"
413:Heuristic
389:his diary
362:democracy
353:Australia
339:Australia
259:Vitruvius
209:displaced
207:of water
127:heuristic
78:Etymology
53:romanized
646:Archived
407:See also
349:Victoria
345:Ballarat
228:Syracuse
222:upthrust
140:syllable
121:heurískō
102:singular
62:) is an
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575:4 March
538:Science
464:at the
446:εὑρίσκω
393:integer
292:Minerva
247:density
171:Finnish
167:Catalan
116:εὑρίσκω
105:perfect
94:heúrēka
59:héurēka
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355:. The
308:Eureka
239:purity
205:volume
193:, and
111:active
89:εὕρηκα
48:εὕρηκα
39:Eureka
27:Eureka
760:S2CID
302:near
144:Latin
86:word
716:ISBN
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