def point_avg(points):
	"""
	Accepts a list of points, each with the same number of dimensions.
	NB. points can have more dimensions than 2

	Returns a new point which is the center of all the points.
	"""
	dimensions = len(points[0])
	
	new_center = []
	
	for dimension in range(dimensions):
		dim_sum = 0  # dimension sum
		for p in points:
			dim_sum += p[dimension]
		
		# average of each dimension
		new_center.append(dim_sum / float(len(points)))
	
	return new_center