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Pip · 10-05-2005, 05:14 AM

First trip, he goes 1 ft, and is within 2 ft of Achilles, then the band stretches 3 ft. He is then proportionally moved so that he is now 4 ft away from Achilles. He then walks another feet, now he's 3 ft from Achilles. The band stretches 3 ft, he's now 4.5 ft from Achilles, moving again... I put it up in Excel because my analytical skillz have dried away. Distance to Achilles before stretch got lower than one after travelling 10 ft, the band had then stretched to 33 feet. He only needs to go 0.781349 ft to reach Achilles then.

EDIT: Defining xn as the distance to Achilles after a stretch, and setting x0=3 (starting point) one gets
xn=(x(n-1)-1)*n/(n-1)

n will be how far the turtle has actually walked, the length of the rubber band after a stretch will be 3*(n+1).

10-05-2005, 05:14 AM	#11 (permalink)
Pip Likes Hats Location: Stockholm, Sweden	First trip, he goes 1 ft, and is within 2 ft of Achilles, then the band stretches 3 ft. He is then proportionally moved so that he is now 4 ft away from Achilles. He then walks another feet, now he's 3 ft from Achilles. The band stretches 3 ft, he's now 4.5 ft from Achilles, moving again... I put it up in Excel because my analytical skillz have dried away. Distance to Achilles before stretch got lower than one after travelling 10 ft, the band had then stretched to 33 feet. He only needs to go 0.781349 ft to reach Achilles then. EDIT: Defining xn as the distance to Achilles after a stretch, and setting x0=3 (starting point) one gets xn=(x(n-1)-1)n/(n-1) n will be how far the turtle has actually walked, the length of the rubber band after a stretch will be 3(n+1). Last edited by Pip; 10-05-2005 at 05:25 AM..