Editing Density (section)

=== Volume vs. density; volume of an irregular shape ===
{{Main|Eureka (word)#Archimedes}}
{{See also|Archimedes#Archimedes and the gold crown}}
In a well-known but probably [[apocrypha]]l tale, [[Archimedes]] was given the task of determining whether [[Hiero II of Syracuse|King Hiero]]'s [[goldsmith]] was embezzling [[gold]] during the manufacture of a golden [[wreath]] dedicated to the gods and replacing it with another, cheaper [[alloy]].<ref>[http://www-personal.umich.edu/~lpt/archimedes.htm Archimedes, A Gold Thief and Buoyancy] {{webarchive|url=https://web.archive.org/web/20070827113533/http://www-personal.umich.edu/~lpt/archimedes.htm |date=August 27, 2007 }} – by Larry "Harris" Taylor, Ph.D.</ref> Archimedes knew that the irregularly shaped wreath could be crushed into a cube whose volume could be calculated easily and compared with the mass; but the king did not approve of this. Baffled, Archimedes is said to have taken an immersion bath and observed from the rise of the water upon entering that he could calculate the volume of the gold wreath through the [[Displacement (fluid)|displacement]] of the water. Upon this discovery, he leapt from his bath and ran naked through the streets shouting, "Eureka! Eureka!" ({{langx|grc|Εύρηκα!||I have found it}}). As a result, the term ''[[Eureka (word)|eureka]]'' entered common parlance and is used today to indicate a moment of enlightenment.

The story first appeared in written form in [[Vitruvius]]' ''[[De architectura|books of architecture]]'', two centuries after it supposedly took place.<ref>[http://webarchive.loc.gov/all/20210420024146/https://penelope.uchicago.edu/Thayer/E/Roman/Texts/Vitruvius/9%2A.html Vitruvius on Architecture, Book IX], paragraphs 9–12, translated into English and [https://penelope.uchicago.edu/Thayer/L/Roman/Texts/Vitruvius/9*.html in the original Latin].</ref> 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.<ref>{{cite journal|doi=10.1126/science.305.5688.1219e|title=EXHIBIT: The First Eureka Moment| year=2004| journal=Science|volume=305|issue=5688|pages=1219e |doi-access=free}}</ref><ref>{{cite news |first=David |last=Biello |title=Fact or Fiction?: Archimedes Coined the Term "Eureka!" in the Bath | work = Scientific American | date = 2006-12-08 |url=https://www.scientificamerican.com/article/fact-or-fiction-archimede }}</ref>

Nevertheless, in 1586, [[Galileo Galilei]], in one of his first experiments, made a possible reconstruction of how the experiment could have been performed with ancient Greek resources<ref>La Bilancetta, Complete text of Galileo's treatise in the original Italian together with a modern English translation [https://math.nyu.edu/~crorres/Archimedes/Crown/bilancetta.html]</ref>