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A cache by IvarT Send Message to Owner Message this owner
Hidden : 12/29/2006
2.5 out of 5
1.5 out of 5

Size: Size: micro (micro)

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Geocache Description:


Zenons Paradoks (efter Zenon fra Elea) er et tankeeksperiment, der leder til et tilsyneladende paradoks. Det illustrerer nogle af de, sommetider pudsige, følger uendeligheder har inden for matematikken.
Man lader helten fra oldgræsk mytologi, Achilleus, løbe om kap med en skildpadde. Fordi Achilleus nu er sådan en sportslig fyr, giver han skildpadden et forspring på 100 meter.
Han begynder at løbe, og da han når de 100 meter, har skildpadden kravlet 10 meter længere frem.
Han løber derefter de 10 meter, men i mellemtiden har skildpadden nået 1 meter længere frem.
Han løber den ene meter, men i mellemtiden er skildpadden nået 10 centimeter længere frem. ...
Således vil Achilleus blive ved med at komme tættere og tættere på skildpadden, og faktisk kommer han uendelig tæt på den, men han vil aldrig overhale den, skønt han vitterlig løber hurtigere end sin modstander. (Kildetekst:

Vi lader Achilleus og skildpadden starte på cachens startkoordinater.
Skildpadden går med en konstant hastighed på 996,957 m i timen, mens Achilleus løber 10 gange så hurtigt. For at hjælpe skildpadden så får den et forspring på 12 km og 129,64 meter.

Det forudsættes at afstanden for et breddegradsminut er 1,86 km, mens et længdegradsminut er 1,05 km. Der ses bort fra Jordens krumning, så der skal anvendes et plant koordinatsystem. Achilleus og skildpadden løber i en lige linie mod nord og mod vest og de krydser ingen længde- eller breddegrad. Hver gang de kommer 1 meter nærmere Nordpolen så har de bevæget sig 0,82766 meter længere mod vest.

Hvem når først frem til skatten - dig, Achilleus eller skildpadden?

Skatten var en vandtæt plasticbeholder på 18 x 13 x 7 cm. Men den er nu et filmhylster med log.


In the paradox of Achilles and the Tortoise, we imagine the Greek hero Achilles in a footrace with the plodding reptile. Because he is so fast a runner, Achilles graciously allows the tortoise a head start of a hundred feet.
If we suppose that each racer starts running at some constant speed (one very fast and one very slow), then after some finite time, Achilles will have run a hundred feet, bringing him to the tortoise's starting point; during this time, the tortoise has "run" a (much shorter) distance, say one foot.
It will then take Achilles some further period of time to run that distance, during which the tortoise will advance farther; and then another period of time to reach this third point, while the tortoise moves ahead.
Thus, whenever Achilles reaches somewhere the tortoise has been, he still has farther to go. Therefore, Zeno says, swift Achilles can never overtake the tortoise.
Thus, while common sense and common experience would hold that one runner can catch another, according to the above argument, he cannot; this is the paradox. (Thanks to for this part of the text)

We let Achilleus and the tortoise start at the start coordinates of the cache. The tortoise walks at a speed of 996.957 meter/hour, while Achilleus runs 10 times faster. To help the tortoise, we give it a head start of 12 km and 129.64 meter.

We define the distance of a latitude minute as 1.86 km, while a longitude minute is 1.05 km. Do not take the curving of the Earth into consideration but use a flat coordinate system. Achilleus and the tortoise runs in a straigth line towards north and west and they do not cross any parallels or meridians. Every time they move 1 meter towards the North Pole they also get 0.82766 meter towards west.

Who will be the First Finder - You, Achilleus or the tortoise?

The cache was a waterproof container measuring 18 x 13 x 7 cm, but it is now replaced with a film cannister with logbook

Additional Hints (Decrypt)

Xbbeqvangrear sbe pnpuraf fyhgcynprevat une ra erqhprerg giæefhz cå 9 sbe abeq (7 pvser) bt 4 sbe øfg (7 pvser).
Gur qvtvgny ebbg vf 9 sbe Abegu (7 qvtvgf) naq 4 sbe Rnfg (7 qvtvgf). (Pbbeqvangrf sbe gur svany pnpur uvqr)

Decryption Key


(letter above equals below, and vice versa)



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Coordinates are in the WGS84 datum

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