Difference between area value calculated by Python and actual value

Question

I have a question regarding the inaccuracy in calculated area by Python and actual value. I searched a lot about it but I didn't find anything. I'm afraid that this difference made my next calculations inaccurate. Here is the code that I calculated with it the area of a circle with radius 1.5:

from shapely.geometry import Point, Polygon

a = Point(1, 1).buffer(1.5)

print (a.area)

and the result that I got is:

7.05723410373

But the actual value for area of the circle with radius 1.5 is:

pi()*(1.5^2) = 7.0685834705

Can anybody explain this difference for me? Should I change any default value on my computer? Also here is the pi() value of my computer:

import math

print (math.pi)

which is exactly as same as actual pi() value:

3.14159265359

Answer 1

From the Shapely User Manual :

object.buffer(distance, resolution=16, cap_style=1, join_style=1, mitre_limit=1.0)
    Returns an approximate representation of all points within a given distance of the this geometric object.

Per the documentation, the returned value is only an approximation. A bit further down in the document is a circle example:

The default (resolution of 16) buffer of a point is a polygonal patch with 99.8% of the area of the circular disk it approximates.

>>> p = Point(0, 0).buffer(10.0)
>>> len(p.exterior.coords)
66
>>> p.area
313.65484905459385

Again, the documentation states it is only an approximation. 99.8% of 7.068, the actual value with a radius of 1.5, is approximately 7.054, which is the value shapely is calculating.

You can increase the accuracy by passing in a higher resolution:

a = Point(1, 1).buffer(1.5, resolution=32)