Thanks
What is the distance of one lap around prospect park?
Wed, 09/06/2006 - 12:38am
Wed, 09/06/2006 - 6:49am
#1
according to prospectpark.org...(url)
"http://www.prospectpark.org/acti/main.cfm?target=run
> A 3.35-mile running lane is provided along the Park Drive.
> The distance of the sidewalks outside the Park is 3.75 miles."
Wed, 09/06/2006 - 4:30am
#2
Prospect Park Distance
The distance is 3.2 Miles.
Wed, 09/06/2006 - 5:50am
#3
I believe it's actually 3.36miles
-sarah
Wed, 09/06/2006 - 6:19am
#4
The distance is 3.372 miles.
Wed, 09/06/2006 - 7:18am
#5
Well....
Well, here is Archimedes' argument:
The effect of this procedure is to define an increasing sequence
b1 , b2 , b3 , ...
and a decreasing sequence
a1 , a2 , a3 , ...
such that both sequences have limit p.
Using trigonometrical notation, we see that the two semiperimeters are given by
an = K tan(p/K), bn = K sin(p/K),
where K = 3 cross 2n-1. Equally, we have
an+1 = 2K tan(p/2K), bn+1 = 2K sin(p/2K),
and it is not a difficult exercise in trigonometry to show that
(1/an + 1/bn) = 2/an+1 . . . (1)
an+1bn = (bn+1)2 . . . (2)
Archimedes, starting from a1 = 3 tan(p/3) = 3v3 and b1 = 3 sin(p/3) = 3v3/2, calculated a2 using (1), then b2 using (2), then a3 using (1), then b3 using (2), and so on until he had calculated a6 and b6. His conclusion was that
b6 < p < a6 .
So, therefore, the perimeter of Prospect Park (PPP) is:
p < PPP < 4.
~CML
Wed, 09/06/2006 - 7:44am
#6
Wed, 09/06/2006 - 8:55am
#7
Witness! the birth of a gearhead
LOL
Thu, 09/07/2006 - 2:39pm
#8
But that does not account for seasonal variations– The park expands in hotter weather and contracts in colder times. Of course, when it contracts, the hills get steeper, so lost distance could be compensated for by increased incline.
Thu, 09/07/2006 - 3:42pm
#9
And of course
It varies with phases of the moon, as we all know gravitational shifts will have an effect on power output...
Thu, 09/07/2006 - 8:51pm
#10
How fast are you cycling?
I'm sure that I've been passed in Prospect Park by folks riding at 95-98% of the speed of light. Relativistic speeds won't change the distance around the park, but you might want to think about it when you're deciding what cyclocomputer to buy.
Wed, 09/06/2006 - 9:07am
#11
3.35 is the official distance.
Now, calibrate your cyclometers, re-pump your tires and do a perfect elipse around PP, with no change of line to shorten or lengthen the distance - impossible almost. So, settle on 3.35.
