The cache is not at the listed cordinates but F0 is. To find this cache you need to calculate F18 from the posted coordinates. To do this you will need to create a golden spiral using golden rectangles (blocks). You may end up with 4 different answers but only one is correct (See hint). Use flat world and UTM's to calculate the final location.
| F0 |
F1 |
F2 |
F3 |
F4 |
F5 |
F6 |
F7 |
F8 |
F9 |
F10 |
F11 |
F12 |
F13 |
F14 |
F15 |
F16 |
F17 |
F18 |
F19 |
F20 |
| 0 |
1 |
1 |
2 |
3 |
5 |
8 |
13 |
21 |
34 |
55 |
89 |
144 |
233 |
377 |
610 |
987 |
1597 |
2584 |
4181 |
6765 |
You can check your answers for this puzzle on Geochecker.com.
Things around the world that use this Golden Ratio
The Parthenon was perhaps the best example of a mathematical approach to art. Once its ruined triangular pediment is restored, the ancient temple fits almost precisely into a golden rectangle.
Pythagoras' discoveries of the proportions of the human figure had a tremendous effect on Greek art. Every part of their major buildings, down to the smallest detail of decoration, was constructed upon this proportion.
Pythagoras (560-480 BC), the Greek geometer, was especially interested in the golden section, and proved that it was the basis for the proportions of the human figure. He showed that the human body is built with each part in a definite golden proportion to all the other parts.
If we take a cross section of the Great Pyramid, we get a right triangle, the so-called Egyptian Triangle. The ratio of the slant height of the pyramid (hypotenuse of the triangle) to the distance from ground center (half the base dimension) is 1.61804 ... which differs from phi by only one unit in the fifth decimal place. If we let the base dimension be 2 units, then the sides of the right triangle are in the proportion 1:sqrt(phi):phi and the pyramid has a height of sqrt(phi).
The ancient Egyptians were the first to use mathematics in art. It seems almost certain that they ascribed magical properties to the golden section (golden ratio, divine proportion, phi) and used in the design of their great pyramids.
But the number one item that we all use almost every day, that get's its shape from this Golden Ratio, is the credit/debit card.
Cache is hidden near the Golden Rectangle
Here is an email I received as a possible solution from a brilliant geocacher. I have added this elegant solution to this puzzle but it is way more complex then I could have ever created or that you need to solve this puzzle. Note the angle of 12.5 degrees has been corrected in this cachers final answer that was out by only 12 metres.
Amazing
****************************
Method
phi=1.61804 (golden ratio)
r=ph^n, theta=(n-1)*pi/2;
Sketch out the spiral:
f2:1: n=1 r=1.618, theta=0
f3:2: n=2 r=phi^2=2.6, theta=1*pi/2=pi/2
f4:3: n=3 r=phi^3=4.2, theta=2*pi/2=pi
f5:5: n=4 r=phi^4=6.9, theta=3*pi/2=3*pi/2
f6:8: n=5 r=phi^5=11.1, theta=4*pi/2=0
Are these ok - do they match the fig? Yes.
f18:2584 n=17 r=phi^17=3570, theta=16*pi/2=0
Adjust theta by 45-12.5=32.5 deg to account for offset axes
x=r*cos(theta)=*****cos(-32.5*pi/180)=****
y=r*sin(theta)=*****sin(-32.5*pi/180)=-****
Not the correct side - need to add the length of the box to y(****)
x=****, y=****-****=****
Is the angle between this point and f0 between 250 and 260? Yes.
starting coords 48°27.625 N 123°28.937 W
e0=46***5;
n0=53****9;
Add to the UTM, recall that easting numbers increase to the east, (add **** to easting)
e1=e0+x=46***7
and that northing increases to the north (add *** to the northing)
n1=n0+y=53****4
48°**.*** N 123°**.*** W