510. Project Euler #510 : Tangent circles.

This is a recent problem, so not now, difficulty rating is not determined.  I think difficulty rating is about 50%.

At my middle school hood, math teacher said that geometry problem can be solved if you draw lines properly.

This problem is sam.

This picture is that added lines and triangles on original problem image.

Make repairs to the line L in circle A, make repairs to the line L in circle B, doing circles in the center of the A side and the L-lining, we draw a line parallel to the L in the center of the circle C.

Then, as shown in Figure, three right triangles, A, B, and C are made by drawing lines.

The explanation of this issue from just the three of a right triangle. Since this course Pythagoras law to establish a right triangle. However, the base of the triangle A, B the base of the triangle, the basis on which the base of the triangle C, this can be thought of as a natural picture On no. Of course A, the sum of the base of B is equal to the length of it, you can see the base of C.

Be the first to reveal that it still displays the radius of each circle for each triangle.

Second, you should not be the judgment on the natural log base line.

If you properly apply mentioned above, even though you may be a little long to answer. I'd probably take longer if the order of a few minutes to several hours. Improving the speed can not be got only two of the above.

Project Euler sites be presented values ​​of S (100), can be difficult to determine the algorithm is correct.

Less the value of one on here.

S(100) = 3072

S(1000) = 311709

S(10000) = 31418891