gistfile1.py

import sys
import math



if len(sys.argv) > 1:
	radius = int(sys.argv[1])
else:
	radius = 5



# The points of interest are on the right of the circle.
# Only half the points on the y axis are taken to preserve symmetry

points = []
for x in xrange(radius):
	for y in xrange(-radius+1, radius):
		if math.sqrt(x**2 + y**2) < radius:
			points.append((x,y))

points.remove((0,0))



polar_points = {}
for p in points:
	if p[0] == 0:
		if p[1] > 0:
			theta = math.radians(90)
		else:
			# we only need half the points on y-axis
			# theta = math.radians(-90)
			continue
	else:
		theta = math.atan(float(p[1])/p[0])

	if theta in polar_points:
		polar_points[theta] += 1
	else:
		polar_points[theta] = 1

# print polar_points
print "Number of polar points:", len(polar_points)

# sorted polar points
thetas = sorted(polar_points.keys())



# --- Hardcore processing begins here ---

def num_in_interval(a, b):
	"Returns # of points between theta=a and theta=b (both exclusive)"
	num_points = 0
	# correct order
	if a > b:
		a, b = b, a
	for theta in thetas[thetas.index(a)+1:thetas.index(b)]:
		num_points += polar_points[theta]
	return num_points


def xuniqueCombinations(items, n):
	"""Just what it says. From http://code.activestate.com/recipes/190465/"""
	if n==0: yield []
	else:
		for i in xrange(len(items)):
			for cc in xuniqueCombinations(items[i+1:],n-1):
				yield [items[i]]+cc

np = 0
for pair in xuniqueCombinations(thetas, 2):

	# keys
	np += (polar_points[pair[0]] * polar_points[pair[1]]) * num_in_interval(pair[0], pair[1])
	
	# print pair[0], pair[1], ":", num_in_interval(pair[0], pair[1])

print "Triangles with center:", np * 2