Archimedes goes geocaching Mystery Cache

Archimedes of Syracuse (287 BC – 212 BC) was an ancient Greek mathematician, physicist and engineer. Although little is known about his life, he is regarded as one of the most important scientists in classical antiquity. In addition to making important discoveries in the field of mathematics and geometry, he is credited with producing machines that were well ahead of their time.

The Ancient Roman historians showed a strong interest in Archimedes and wrote several biographies relating to his life and works, while the few copies of his treatises that survived through the Middle Ages were a major influence on scientists during the Renaissance.

In the area of calculus, the work that Archimedes produced remains important today. An interesting biography is found on Wikipedia (http://en.wikipedia.org/wiki/Archimedes)

Vi oplever en rivende teknologiske udvikling og hører dagligt om nye imponerende landvindinger indenfor it, medico, rumforskning og andre high-tech områder. Denne udvikling er muliggjort af en lang række af tidligere bidrag fra kloge og flittige personer som for eksempel Achimedes, som var en genial græsk matematiker, fysiker og ingeniør. Archimedes udledte bl. a. værdien af pi og formlen for arealet af en cirkel (begge dele bliver der brug for om lidt). Han opfandt mange nyttige maskiner f.eks. vandsneglen og skruen uden ende (som visse politikere ynder at henvise til!). Archimedes tanker og ideer har inspireret mange senere videnskabsfolk, ingeniører og tænkere, og vi skylder ham stor tak.

Archimedes vandsnegl (anvendes stadig i nogle udviklingslande)

The Archimidean screw pumping device (still used in some developing countries).

Der er en berømt anekdote om hvordan Archimedes opdagede opdriftens princip og formulerede Archimedes lov, der siger at:

Et legeme der nedsænkes i en væske taber det samme i vægt som den fortrængte væskemængde vejer

Vitruvius fortæller, at Kong Hieron havde fået lavet en ny kongekrone, men han var ikke sikker på om guldsmeden havde været ærlig eller havde blandet sølv i guldet til kronen. Archimedes blev bedt om at løse dette problem, men han kunne selvfølgelig ikke smelte kronen om til en terning, og dermed bestemme vægtfylden. En dag han tog bad i byens badehus, slog det ham at vandet steg, da han hoppede i. Han indså, at dette kunne bruges til at måle kronens volumen, og dermed bestemme vægtfylden. Archimedes blev så begejstret over denne opdagelse, at han råbte ”Eureka” (jeg har fundet det!) og glemte at tage tøj på, da han løb hjem gennem byen for at undersøge kronen.

Archimedes lov har stor betydning bl. a. for beregning af skibes stabilitet og lasteevne og vil være kendt af mange. Mindre kendt er det måske, at Archimedes lov også kan bruges til beregning af koordinaterne til geocaching!

Der er gode parkeringsforhold i nærheden af cachen. Cachens koordinater er N 56° 00.X, E012º 35.Y, hvor X og Y skal beregnes som angivet nedenfor:

X: Dybgangen i mm (afrundet til 3 cifre) af en kugle med en diameter på 710 mm og en vægtfylde på 0,7115 g/cm³, der nedsænkes i et kar med destilleret vand ved 4 °C. Der ses bort fra luftens opdrift.

Y: Højdeændringen i mm gange 2 (afrundet til 3 cifre) af vandspejlet i karret, hvis karret er cylindrisk med en diameter på 981mm og vandstanden dybere end X

Umiddelbart før cachen (til højre) er der fine muligheder for at nedsænke sit legeme i vand. Det er ok at råbe ”Eureka” når cachen er fundet, og måske også at løbe nøgen rundt! Vær forsigtig, våde sten kan være glatte.

Dette er en lille cache, som kun indeholder logbog og blyant. FFC vil blive sendt som email til førstefinderen. God tur.

Hvis du ikke har en PC! If you don’t have a PC!

We are living in a time where impressive technological advances within it, medico, space and other high-tech areas are constantly made. The basis for this is the important earlier contributions from bright people one of them being Archimedes a genius Greek mathematician, physicist and engineer. Among many other things Archimedes derived the value of pi and how to calculate the area of a circle (you will use both in a minute). He also invented many useful machines e.g. the screw pumping device and the endless screw (often used by politicians). The ideas and thoughts of Archimedes have inspired many later scientists, engineers and philosophers and we owe him a lot.

The most famous anecdote told about Archimedes is how he discovered the principle of buoyancy, now known as Archimedes principle stating:

A body immersed in a fluid experiences a buoyant force equal to the weight of the displaced fluid.

According to Vitruvius, a new crown in the shape of a laurel wreath had been made for King Hieron, and Archimedes was asked to determine whether it was of solid gold, or whether silver had been added by a dishonest goldsmith. Archimedes had to solve the problem without damaging the crown, so he could not melt it down in order to measure its density as a cube, which would have been the simplest solution. While taking a bath, he noticed that the level of the water rose as he got in. He realized that this effect could be used to determine the volume of the crown, and therefore its density after weighing it. The density of the crown would be lower if cheaper and less dense metals had been added. He then took to the streets naked, so excited by his discovery that he had forgotten to dress, crying "Eureka!" ("I have found it!").

The endless screw. Skruen uden ende.

It is commonly known that Archimedes principle has great importance for the design of ships and other floating objects, diving etc. but maybe less known that the principle can be used to calculate the coordinated for geocaching!

There is convenient parking close to the cache located N 56° 00.X, E012º 35.Y, where X and Y are to be determined as follows:

X: The immersion in mm (rounded off to 3 digits) of a sphere with a diameter of  710 mm and a specific weight of 0,7115 g/cm³, that is put into a vessel with distilled water at 4 °C. The buoyancy of the air is disregarded.

Y: The change in mm times 2 (rounded off to 3 digits) of the water level in the vessel, if the vessel is cylindrical with a diameter of 981mm and the water deeper than X.

You can immerse your body conveniently in water at the right just before you get to the cache. It will be ok to cry ”Eureka” when the cache has been found and maybe also to run naked! Be careful wet stones can be slippery.

You can check your answers for this puzzle on Geochecker.com.