// Solution to "Boulder Arts & Maths 27" Geocaching puzzle
// http://www.geocaching.com/seek/cache_details.aspx?guid=33f820d4-8bca-4e71-b4ff-40978968c94f

// Include the important definitions for many of these functions.
use navigation.frink

// Wind gauge
lat1  = DMS[39, 59.194] North
long1 = DMS[105, 11.398] West

// Giant Robot!!
lat2  = DMS[40, 00.878] North
long2 = DMS[105, 12.453] West

// DNA
lat3 = DMS[40, 02.056] North
long3 = DMS[105, 14.062] West

// Build a polygon of points
array = [[lat1, long1], [lat2, long2], [lat3, long3]]

perim = earthPerimeter[array]

println["Perimeter is " + (perim -> "statute miles")]
println["Area is " + (earthArea[array] -> "(statute miles)^2")]

println["Verifying against flat earth: "]
s = perim/2

// Ye olde (Euclidean) triangle area formula
area = sqrt[s (s - earthDistance[lat1, long1, lat2, long2]) * (s - earthDistance[lat2, long2, lat3, long3]) * (s - earthDistance[lat3, long3, lat1, long1])]

println["Flat-earth area is " + (area -> "(statute miles)^2")]