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#!/usr/bin/perl -w
# Copyright 2016, 2017 Kevin Ryde
# This file is part of Math-PlanePath.
#
# Math-PlanePath is free software; you can redistribute it and/or modify it
# under the terms of the GNU General Public License as published by the Free
# Software Foundation; either version 3, or (at your option) any later
# version.
#
# Math-PlanePath is distributed in the hope that it will be useful, but
# WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
# or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
# for more details.
#
# You should have received a copy of the GNU General Public License along
# with Math-PlanePath. If not, see <http://www.gnu.org/licenses/>.
use 5.006;
use strict;
use warnings;
use Math::BaseCnv 'cnv';
use Math::Libm 'M_PI', 'hypot';
use Math::PlanePath::GosperReplicate;
$|=1;
# uncomment this to run the ### lines
# use Smart::Comments;
{
# islands convex hull
# not in OEIS: 6,84,726,5448,39162,276948
# not in OEIS: 1,14,121,908,6527,46158
# [1,14,121,908,6527,46158] - [1, 8, 57, 404, 2839, 19884]
# not in OEIS: 0, 6, 64, 504, 3688, 26274
# v=[1,14,121,908,6527,46158]
# for(i=2,#v,print(v[i]-7*v[i-1]))
# 2*2839 + 2*404 - 6527
require Math::Geometry::Planar;
my $path = Math::PlanePath::GosperReplicate->new;
my @values;
foreach my $k (1 .. 6) {
my ($n_lo,$n_hi) = $path->level_to_n_range($k);
my $points = [ map{[$path->n_to_xy($_)]} $n_lo .. $n_hi ];
my $planar = Math::Geometry::Planar->new;
$planar->points($points);
if (@$points > 4) {
$planar = $planar->convexhull2;
$points = $planar->points;
}
my $area = $planar->area / 6;
my $whole_area = 7**$k;
my $f = $area / $whole_area;
my $num_points = scalar(@$points);
print "k=$k hull points $num_points area $area cf $whole_area ratio $f\n";
push @values,$area;
}
require Math::OEIS::Grep;
Math::OEIS::Grep->search(array => \@values, verbose=>1);
exit 0;
}
# GP-DEFINE nearly_equal_epsilon = 1e-15;
# GP-DEFINE nearly_equal(x,y, epsilon=nearly_equal_epsilon) = \
# GP-DEFINE abs(x-y) < epsilon;
# GP-DEFINE b_angle = arg(b)
# not in OEIS: 0.333473172251832115336090
# GP-DEFINE b_angle_degrees = b_angle * 180/Pi
# not in OEIS: 19.1066053508690943945174
# GP-Test nearly_equal( b_angle, atan(sqrt3/5) )
# GP-Test b_angle_degrees > 19.10
# GP-Test b_angle_degrees < 19.10+1/10^2
{
require Math::BigInt; Math::BigInt->import(try => 'GMP');
my $path = Math::PlanePath::GosperReplicate->new;
my $n_max = Math::BigInt->new(0);
my $pow = Math::BigInt->new(1);
foreach my $k (0 .. 50) {
my $m_max = 0;
my $new_n_max = 0;
foreach my $d (1 .. 6) {
my $try_n = $n_max + $pow*$d;
my ($x,$y) = $path->n_to_xy($try_n);
my $m;
$m = $x;
$m = $x+$y; # 30 deg
### $try_n
### $m
if ($m > $m_max) {
$m_max = $m;
$new_n_max = $try_n;
}
}
$n_max = $new_n_max;
my $n7 = cnv($n_max,10,7);
my $m7 = cnv($m_max,10,7);
print "k=$k $n_max\n $n7\n X=$m_max $m7\n";
$pow *= 7;
}
exit 0;
}
{
# X maximum in level by points
# k=0 0 0 0 0
# k=1 1 1 2 2
# k=2 8 11 7 10
# k=3 302 611 20 26
# k=4 2360 6611 57 111
# k=5 16766 66611 151 304
# k=6 100801 566611 387 1062
# k=7 689046 5566611 1070 3056
# k=8 4806761 55566611 2833 11155
my $path = Math::PlanePath::GosperReplicate->new;
foreach my $k (0 .. 10) {
my ($n_lo,$n_hi) = $path->level_to_n_range($k);
my $m_max = 0;
my $n_max = 0;
foreach my $n ($n_lo .. $n_hi) {
my ($x,$y) = $path->n_to_xy($n);
my $m;
$m = -$x+$y;
$m = $x;
$m = $x+3*$y; # 60 deg
$m = $x+$y; # 30 deg
if ($m > $m_max) {
$m_max = $m;
$n_max = $n;
}
}
my $n7 = cnv($n_max,10,7);
my $m7 = cnv($m_max,10,7);
print "k=$k $n_max $n7 $m_max $m7\n";
}
exit 0;
}
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