The cache is not at the published coordinates.
Below are fifteen epicycloids (excluding the demonstrative animation), which are curves that can be constructed by tracing the path taken by a point on a circle that rolls around another.
An animation from Wolfram MathWorld
They can also be generated by the parametric equations
x(t) = n * cos(t) - cos(n * t)
y(t) = n * sin(t) - sin(n * t)
where n is 1 more than the ratio of the radii of the stationary circle and the circle rolling around it.
The first nine have this ratio displayed. Hence, with the top left epicycloid, the stationary circle (shown in grey) has the same radius as the rolling circle (hence the ratio of 1), which traced out a shape called a cardioid. Can you figure out the ratios for the remaining six and hence find the values of a to l?
I wrote a little OpenGL program to output these curves just for this puzzle.
Let x = the concatenation of the 12 values a to l into a single 14-digit number.
The real coordinates are: N 54° 16.*** W 000° 25.***
Work out the answer to: (x + 253,170) / 89,621,655
This will give you a 6-digit number to fill in the blanks in the coordinates.
As with any puzzle of mine, feel free to message me if you want help with any aspect of this puzzle.
Congratulations to mandndave for FTF.
Last cache check: 29 October 2023