Editing Archimedes (section)

===Golden wreath===
[[File:Displacement-measurement.svg|thumb|Measurement of volume (a) before and (b) after an object has been submerged, with (∆V) indicating the rising amount of liquid is equal to the volume of the object]]
Another story of a problem that Archimedes is credited solving with in service of Hiero II is the "wreath problem."{{sfn|Dijksterhuis|1987|p=18}} According to [[Vitruvius]], writing about two centuries after Archimedes' death, [[Hiero II of Syracuse|King Hiero II of Syracuse]] had commissioned a golden wreath for a temple to the immortal gods, and had supplied pure gold to be used by the goldsmith.<ref>[[Vitruvius]], ''De Architectura'', Book IX, 3</ref> However, the king had begun to suspect that the goldsmith had substituted some cheaper silver and kept some of the pure gold for himself, and, unable to make the smith confess, asked Archimedes to investigate.{{sfn|Dijksterhuis|1987|p=19}} Later, while stepping into a bath, Archimedes allegedly noticed that the level of the water in the tub rose more the lower he sank in the tub and, realizing that this effect could be used to determine the golden crown's [[volume]], was so excited that he took to the streets naked, having forgotten to dress, crying "[[Eureka (word)|Eureka]]!{{efn|{{langx|el|"εὕρηκα}}, ''heúrēka''!)}}, meaning "I have found [it]!"{{sfn|Dijksterhuis|1987|p=19}} According to Vitruvius, Archimedes then took a lump of gold and a lump of silver that were each equal in weight to the wreath, and, placing each in the bathtub, showed that the wreath displaced more water than the gold and less than the silver, demonstrating that the wreath was gold mixed with silver {{sfn|Dijksterhuis|1987|p=19}}

A different account is given in the ''Carmen de Ponderibus'',<ref>''Metrologicorum Scriptorum reliquiae'', ed. F. Hultsch (Leipzig 1864), II, 88</ref> an anonymous 5th century Latin didactic poem on weights and measures once attributed to the grammarian [[Priscian]].{{sfn|Dijksterhuis|1987|p=19}} In this poem, the lumps of gold and silver were placed on the scales of a balance, and then the entire apparatus was immersed in water; the difference in density between the gold and the silver, or between the gold and the crown, causes the scale to tip accordingly.<ref>''Carmen de Ponderibus'', lines 124-162</ref> Unlike the more famous bathtub account given by Vitruvius, this poetic account uses the [[hydrostatics]] principle now known as [[Archimedes's principle|Archimedes' principle]] that is found in his treatise ''[[On Floating Bodies]]'', where a body immersed in a fluid experiences a [[buoyancy|buoyant force]] equal to the weight of the fluid it displaces.{{sfn|Dijksterhuis|1987|pp=20-21}} [[Galileo Galilei]], who invented a [[hydrostatic equilibrium|hydrostatic balance]] in 1586 inspired by Archimedes' work, considered it "probable that this method is the same that Archimedes followed, since, besides being very accurate, it is based on demonstrations found by Archimedes himself."<ref>{{cite web |author=Van Helden, Al |title=The Galileo Project: Hydrostatic Balance |url=http://galileo.rice.edu/sci/instruments/balance.html |access-date=14 September 2007 |publisher=[[Rice University]]}}</ref>