Hi /sci/, I was fucking around with GeoGebra (shitty math program) and wondering why pi has the value it has. So I decided to check the circumference/diameter-ratios of other regular shapes than the circle. I did this by taking the circumference divided by the longest possible straight line you can draw inside the shape. Obviously the values got closer to pi the more sides the shapes got, but why the fuck do they oscillate towards it?
>pic related, it's the values
>>7970187
GeoGebra ain't to shit man, I like it cause I can drag points where I want them so I can easily manipulate the experimental results from the lab giving me great lab reports :^)
>>7970191
nice, i guess the program is okay for geometry
>>7970195
It does a good job at fitting data as well. I don't think it can (or I don't know how to) plot large amount of data from a file, something like gnuplot's plot "whatever.dat" using 1:2 with lines
>>7970208
i fail to see how that function is related to these values.
>>7970187
The longest possible line you can draw in a triangle is it's side. So the ratio should be 3 for a triangle. And for a pentagon it should be 5/(2sin(3pi/5))
>>7970187
Hint: if you considered longest radius instead of diameter it wouldn't oscillate anymore
Ratio of apothem/diameter of an n sided regular polygon
[eqn] n tan(\frac{\pi }{n}) [/eqn]
thus
[eqn]\lim_{n\to\infty} n tan(\frac{\pi }{n}) = \pi [/eqn]
>>7971350
This equation over real numbers greater than 1 has a horizontal asymptote at pi. The oscillations in your results are due to the dopey way you calculated "circumference."
>>7971367
Seems to me the fact that the shapes with even numbers of sides have diameters that go between to corners, thus overestimating a circle diameter, while those of odd sides go from corner to side, underestimating desu. Could be fixed by just using radii, as another anon said.
