Throw a brick to attract jade, draw a 2007 circle (update 2011)

The answer given by the subject is 2012. When I saw many people firmly believe that it was 2000, I tried to draw a more “compressed” situation, but the difference between 2012 and 2000 is not big. It is difficult to be precise in the geometric position. Computer painting.

The following ideas are not strict, so it is not the best solution in 2007. It is mainly because many people in the comments take it for granted.

Idea:

The diameter of the circle is fixed. The position is determined to be the center of the circle. The center of the circle is in the range of 1×999.
Irresponsibly confirm that the first circle is in the upper left corner, the second center is from the first center 1 (tangent), and on the blue arc, take a random point.
Irresponsibly determine the third center of the circle at the intersection of the dotted line
Irresponsible intersection, draw the fourth center, the result exceeds the red border
The center line forms a diamond with two equilateral triangles. Rotate the diamond so that the fourth dot is on the red line.
Irresponsibly put the 5th circle on the red line, like the first circle, which constitutes a circle of four circles. For counting, the blue box is treated as a loop length.
The measurement is calculated 501 times and the blue box is enlarged 501 times horizontally.
To the other end of the rectangle, there is a section outside the blue box that can fit into 3 circles.

A total of 501×4 + 3 = 2007 rounds.


Great god in the comment

You are a diamond in the form of four round rows. Change to a triangle with three round rows to make the unit better.

335 x 6 +1 = 2011

Calculate the verification,

\frac{999}{1+\sqrt{1-(1-\sqrt{3}/2)^{2}}+\sqrt{1-(1-\sqrt{3}/2)^{2}}}=335.013