(a) delta_N bound for N = 1..200000: violations 0;  kappa = 0.620403239401; delta_1 = 0.917503, delta_100 = 0.358113, delta_10^4 = 0.047844, delta_10^6 = 0.004945
(b) hexagon counts: 900 values of N x random position/orientation: count < N in 0 cases; min count/N = 1.0023
    all vertices of the 52 hexagons (N=37 setting, circumradius R) inside the square: True
(c) glued piece Omega_1 = H_1 + remainder: rasterised |Omega_1 symdiff B'| versus c_H a + 2 delta:
    N=  1  a=0.08250  delta=0.91750 (raster remainder 0.91750, raster hexagon area N a = 0.08250 vs 0.08250)   |Om1 symdiff B'| = 0.26424  <=  c_H a + 2 delta = 1.84115 : True
          F <= 1.18174 ;  paper's bound (1-delta) c_H + 3 delta = 2.75865
    N=  2  a=0.06589  delta=0.86823 (raster remainder 0.86823, raster hexagon area N a = 0.13177 vs 0.13177)   |Om1 symdiff B'| = 0.49164  <=  c_H a + 2 delta = 1.74136 : True
          F <= 1.36477 ;  paper's bound (1-delta) c_H + 3 delta = 2.61449
    N=  3  a=0.05632  delta=0.83103 (raster remainder 0.83104, raster hexagon area N a = 0.16896 vs 0.16897)   |Om1 symdiff B'| = 0.34170  <=  c_H a + 2 delta = 1.66626 : True
          F <= 1.18112 ;  paper's bound (1-delta) c_H + 3 delta = 2.50568
    N=  5  a=0.04493  delta=0.77535 (raster remainder 0.77535, raster hexagon area N a = 0.22465 vs 0.22465)   |Om1 symdiff B'| = 0.52498  <=  c_H a + 2 delta = 1.55404 : True
          F <= 1.31371 ;  paper's bound (1-delta) c_H + 3 delta = 2.34277
    N=  8  a=0.03547  delta=0.71628 (raster remainder 0.71628, raster hexagon area N a = 0.28372 vs 0.28372)   |Om1 symdiff B'| = 0.47743  <=  c_H a + 2 delta = 1.43520 : True
          F <= 1.21220 ;  paper's bound (1-delta) c_H + 3 delta = 2.16996
    N= 13  a=0.02699  delta=0.64916 (raster remainder 0.64916, raster hexagon area N a = 0.35084 vs 0.35084)   |Om1 symdiff B'| = 0.52182  <=  c_H a + 2 delta = 1.30032 : True
          F <= 1.19509 ;  paper's bound (1-delta) c_H + 3 delta = 1.97360
    N= 30  a=0.01579  delta=0.52639 (raster remainder 0.52639, raster hexagon area N a = 0.47361 vs 0.47361)   |Om1 symdiff B'| = 0.48986  <=  c_H a + 2 delta = 1.05395 : True
          F <= 1.05035 ;  paper's bound (1-delta) c_H + 3 delta = 1.61443
(d) Cor 1.2:  c_H + 0.03/N <= I_N <= c_H + 3 delta_N
    N = 10^0 : lower 0.10446575   upper 2.826974
    N = 10^1 : lower 0.07746575   upper 2.132654
    N = 10^2 : lower 0.07476575   upper 1.148805
    N = 10^3 : lower 0.07449575   upper 0.495173
    N = 10^4 : lower 0.07446875   upper 0.217998
    N = 10^5 : lower 0.07446605   upper 0.121003
    N = 10^6 : lower 0.07446578   upper 0.089300
    N = 10^7 : lower 0.07446576   upper 0.079169
RESULT PASS
