Module: FigurateNumbers::PlaneFigurateNumbers

Extended by:
PlaneFigurateNumbers
Included in:
FigurateNumbers, PlaneFigurateNumbers
Defined in:
lib/figurate_numbers/plane_figurate_numbers.rb

Overview

Module containing methods for generating 2D figurate number sequences.

Instance Method Summary collapse

Instance Method Details

#aztec_diamond ⇒ Object 



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# File 'lib/figurate_numbers/plane_figurate_numbers.rb', line 509

def aztec_diamond
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << (2 * delta) * (delta + 1)
    end
  end
end

#centered_decagonal ⇒ Object 



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# File 'lib/figurate_numbers/plane_figurate_numbers.rb', line 296

def centered_decagonal
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << 5 * delta**2 - 5 * delta + 1
    end
  end
end

#centered_dodecagonal ⇒ Object Also known as: star 



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# File 'lib/figurate_numbers/plane_figurate_numbers.rb', line 312

def centered_dodecagonal
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << 6 * delta**2 - 6 * delta + 1
    end
  end
end

#centered_hendecagonal ⇒ Object 



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# File 'lib/figurate_numbers/plane_figurate_numbers.rb', line 304

def centered_hendecagonal
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << (11 * delta**2 - 11 * delta + 2) / 2
    end
  end
end

#centered_heptadecagonal ⇒ Object 



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# File 'lib/figurate_numbers/plane_figurate_numbers.rb', line 354

def centered_heptadecagonal
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << (17 * delta**2 - 17 * delta + 2) / 2
    end
  end
end

#centered_heptagonal ⇒ Object 



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# File 'lib/figurate_numbers/plane_figurate_numbers.rb', line 272

def centered_heptagonal
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << (7 * delta**2 - 7 * delta + 2) / 2
    end
  end
end

#centered_hexadecagonal ⇒ Object 



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# File 'lib/figurate_numbers/plane_figurate_numbers.rb', line 346

def centered_hexadecagonal
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << 8 * delta**2 - 8 * delta + 1
    end
  end
end

#centered_hexagonal ⇒ Object 



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# File 'lib/figurate_numbers/plane_figurate_numbers.rb', line 264

def centered_hexagonal
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << 3 * delta**2 - 3 * delta + 1
    end
  end
end

#centered_icosagonal ⇒ Object 



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# File 'lib/figurate_numbers/plane_figurate_numbers.rb', line 378

def centered_icosagonal
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << 10 * delta**2 - 10 * delta + 1
    end
  end
end

#centered_icosidigonal ⇒ Object 



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# File 'lib/figurate_numbers/plane_figurate_numbers.rb', line 394

def centered_icosidigonal
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << 11 * delta**2 - 11 * delta + 1
    end
  end
end

#centered_icosihenagonal ⇒ Object 



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# File 'lib/figurate_numbers/plane_figurate_numbers.rb', line 386

def centered_icosihenagonal
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << (21 * delta**2 - 21 * delta + 2) / 2
    end
  end
end

#centered_icosiheptagonal ⇒ Object 



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# File 'lib/figurate_numbers/plane_figurate_numbers.rb', line 434

def centered_icosiheptagonal
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << (27 * delta**2 - 27 * delta + 2) / 2
    end
  end
end

#centered_icosihexagonal ⇒ Object 



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# File 'lib/figurate_numbers/plane_figurate_numbers.rb', line 426

def centered_icosihexagonal
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << (13 * delta**2 - 13 * delta + 1)
    end
  end
end

#centered_icosinonagonal ⇒ Object 



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# File 'lib/figurate_numbers/plane_figurate_numbers.rb', line 450

def centered_icosinonagonal
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << (29 * delta**2 - 29 * delta + 2) / 2
    end
  end
end

#centered_icosioctagonal ⇒ Object 



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# File 'lib/figurate_numbers/plane_figurate_numbers.rb', line 442

def centered_icosioctagonal
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << (14 * delta**2 - 14 * delta + 1)
    end
  end
end

#centered_icosipentagonal ⇒ Object 



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# File 'lib/figurate_numbers/plane_figurate_numbers.rb', line 418

def centered_icosipentagonal
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << (25 * delta**2 - 25 * delta + 2) / 2
    end
  end
end

#centered_icositetragonal ⇒ Object 



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# File 'lib/figurate_numbers/plane_figurate_numbers.rb', line 410

def centered_icositetragonal
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << 12 * delta**2 - 12 * delta + 1
    end
  end
end

#centered_icositrigonal ⇒ Object 



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# File 'lib/figurate_numbers/plane_figurate_numbers.rb', line 402

def centered_icositrigonal
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << (23 * delta**2 - 23 * delta + 2) / 2
    end
  end
end

#centered_mgonal(m) ⇒ Object 



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# File 'lib/figurate_numbers/plane_figurate_numbers.rb', line 466

def centered_mgonal(m)
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << (m * delta**2 - m * delta + 2) / 2
    end
  end
end

#centered_nonadecagonal ⇒ Object 



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# File 'lib/figurate_numbers/plane_figurate_numbers.rb', line 370

def centered_nonadecagonal
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << (19 * delta**2 - 19 * delta + 2) / 2
    end
  end
end

#centered_nonagonal ⇒ Object 



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# File 'lib/figurate_numbers/plane_figurate_numbers.rb', line 288

def centered_nonagonal
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << (9 * delta**2 - 9 * delta + 2) / 2
    end
  end
end

#centered_octadecagonal ⇒ Object 



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# File 'lib/figurate_numbers/plane_figurate_numbers.rb', line 362

def centered_octadecagonal
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << 9 * delta**2 - 9 * delta + 1
    end
  end
end

#centered_octagonal ⇒ Object 



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# File 'lib/figurate_numbers/plane_figurate_numbers.rb', line 280

def centered_octagonal
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << 4 * delta**2 - 4 * delta + 1
    end
  end
end

#centered_pentadecagonal ⇒ Object 



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# File 'lib/figurate_numbers/plane_figurate_numbers.rb', line 338

def centered_pentadecagonal
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << (15 * delta**2 - 15 * delta + 2) / 2
    end
  end
end

#centered_pentagonal ⇒ Object 



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# File 'lib/figurate_numbers/plane_figurate_numbers.rb', line 256

def centered_pentagonal
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << (5 * delta**2 - 5 * delta + 2) / 2
    end
  end
end

#centered_square ⇒ Object Also known as: diamond 



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# File 'lib/figurate_numbers/plane_figurate_numbers.rb', line 246

def centered_square
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << 2 * delta**2 - 2 * delta + 1
    end
  end
end

#centered_tetradecagonal ⇒ Object 



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# File 'lib/figurate_numbers/plane_figurate_numbers.rb', line 330

def centered_tetradecagonal
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << 7 * delta**2 - 7 * delta + 1
    end
  end
end

#centered_triacontagonal ⇒ Object 



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# File 'lib/figurate_numbers/plane_figurate_numbers.rb', line 458

def centered_triacontagonal
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << (15 * delta**2 - 15 * delta + 1)
    end
  end
end

#centered_triangular ⇒ Object 



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# File 'lib/figurate_numbers/plane_figurate_numbers.rb', line 238

def centered_triangular
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << (3 * delta**2 - 3 * delta + 2) / 2
    end
  end
end

#centered_tridecagonal ⇒ Object 



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# File 'lib/figurate_numbers/plane_figurate_numbers.rb', line 322

def centered_tridecagonal
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << (13 * delta**2 - 13 * delta + 2) / 2
    end
  end
end

#cross ⇒ Object 



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# File 'lib/figurate_numbers/plane_figurate_numbers.rb', line 501

def cross
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << 4 * delta - 3
    end
  end
end

#decagonal ⇒ Object 



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# File 'lib/figurate_numbers/plane_figurate_numbers.rb', line 70

def decagonal
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << (8 * delta**2 - 6 * delta) / 2
    end
  end
end

#dodecagonal ⇒ Object 



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# File 'lib/figurate_numbers/plane_figurate_numbers.rb', line 86

def dodecagonal
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << (10 * delta**2 - 8 * delta) / 2
    end
  end
end

#generalized_centered_pol(m, left_index = 0) ⇒ Object 



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# File 'lib/figurate_numbers/plane_figurate_numbers.rb', line 637

def generalized_centered_pol(m, left_index = 0)
  Enumerator.new do |y|
    ((-1 * left_index)..Float::INFINITY).each do |delta|
      y << (m * delta**2 - m * delta + 2) / 2
    end
  end
end

#generalized_hexagonal(left_index = 0) ⇒ Object 



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# File 'lib/figurate_numbers/plane_figurate_numbers.rb', line 628

def generalized_hexagonal(left_index = 0)
  m = 6
  Enumerator.new do |y|
    ((-1 * left_index.abs)..Float::INFINITY).each do |delta|
      y << (delta * ((m - 2) * delta - m + 4)) / 2
    end
  end
end

#generalized_mgonal(m, left_index = 0) ⇒ Object 



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# File 'lib/figurate_numbers/plane_figurate_numbers.rb', line 611

def generalized_mgonal(m, left_index = 0)
  Enumerator.new do |y|
    ((-1 * left_index.abs)..Float::INFINITY).each do |delta|
      y << (delta * ((m - 2) * delta - m + 4)) / 2
    end
  end
end

#generalized_pentagonal(left_index = 0) ⇒ Object 



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# File 'lib/figurate_numbers/plane_figurate_numbers.rb', line 619

def generalized_pentagonal(left_index = 0)
  m = 5
  Enumerator.new do |y|
    ((-1 * left_index.abs)..Float::INFINITY).each do |delta|
      y << (delta * ((m - 2) * delta - m + 4)) / 2
    end
  end
end

#generalized_pronic(left_index = 0) ⇒ Object 



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# File 'lib/figurate_numbers/plane_figurate_numbers.rb', line 645

def generalized_pronic(left_index = 0)
  Enumerator.new do |y|
    ((-1 * left_index.abs)..Float::INFINITY).each do |delta|
      y << delta * (delta + 1)
    end
  end
end

#gnomic ⇒ Object 



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# File 'lib/figurate_numbers/plane_figurate_numbers.rb', line 535

def gnomic
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << 2 * delta - 1
    end
  end
end

#hendecagonal ⇒ Object 



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# File 'lib/figurate_numbers/plane_figurate_numbers.rb', line 78

def hendecagonal
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << (9 * delta**2 - 7 * delta) / 2
    end
  end
end

#heptadecagonal ⇒ Object 



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# File 'lib/figurate_numbers/plane_figurate_numbers.rb', line 126

def heptadecagonal
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << (15 * delta**2 - 13 * delta) / 2
    end
  end
end

#heptagonal ⇒ Object 



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# File 'lib/figurate_numbers/plane_figurate_numbers.rb', line 46

def heptagonal
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << (5 * delta**2 - 3 * delta) / 2
    end
  end
end

#hexadecagonal ⇒ Object 



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# File 'lib/figurate_numbers/plane_figurate_numbers.rb', line 118

def hexadecagonal
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << (14 * delta**2 - 12 * delta) / 2
    end
  end
end

#hexagonal ⇒ Object 



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# File 'lib/figurate_numbers/plane_figurate_numbers.rb', line 38

def hexagonal
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << (4 * delta**2 - 2 * delta) / 2
    end
  end
end

#icosagonal ⇒ Object 



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# File 'lib/figurate_numbers/plane_figurate_numbers.rb', line 150

def icosagonal
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << (18 * delta**2 - 16 * delta) / 2
    end
  end
end

#icosidigonal ⇒ Object 



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# File 'lib/figurate_numbers/plane_figurate_numbers.rb', line 166

def icosidigonal
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << (20 * delta**2 - 18 * delta) / 2
    end
  end
end

#icosihenagonal ⇒ Object 



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# File 'lib/figurate_numbers/plane_figurate_numbers.rb', line 158

def icosihenagonal
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << (19 * delta**2 - 17 * delta) / 2
    end
  end
end

#icosiheptagonal ⇒ Object 



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# File 'lib/figurate_numbers/plane_figurate_numbers.rb', line 206

def icosiheptagonal
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << (25 * delta**2 - 23 * delta) / 2
    end
  end
end

#icosihexagonal ⇒ Object 



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# File 'lib/figurate_numbers/plane_figurate_numbers.rb', line 198

def icosihexagonal
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << (24 * delta**2 - 22 * delta) / 2
    end
  end
end

#icosinonagonal ⇒ Object 



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# File 'lib/figurate_numbers/plane_figurate_numbers.rb', line 222

def icosinonagonal
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << (27 * delta**2 - 25 * delta) / 2
    end
  end
end

#icosioctagonal ⇒ Object 



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# File 'lib/figurate_numbers/plane_figurate_numbers.rb', line 214

def icosioctagonal
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << (26 * delta**2 - 24 * delta) / 2
    end
  end
end

#icosipentagonal ⇒ Object 



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# File 'lib/figurate_numbers/plane_figurate_numbers.rb', line 190

def icosipentagonal
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << (23 * delta**2 - 21 * delta) / 2
    end
  end
end

#icositetragonal ⇒ Object 



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# File 'lib/figurate_numbers/plane_figurate_numbers.rb', line 182

def icositetragonal
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << (22 * delta**2 - 20 * delta) / 2
    end
  end
end

#icositrigonal ⇒ Object 



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# File 'lib/figurate_numbers/plane_figurate_numbers.rb', line 174

def icositrigonal
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << (21 * delta**2 - 19 * delta) / 2
    end
  end
end

#impolite ⇒ Object 



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# File 'lib/figurate_numbers/plane_figurate_numbers.rb', line 493

def impolite
  Enumerator.new do |y|
    (0..Float::INFINITY).each do |delta|
      y << 2**delta
    end
  end
end

#nonadecagonal ⇒ Object 



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# File 'lib/figurate_numbers/plane_figurate_numbers.rb', line 142

def nonadecagonal
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << (17 * delta**2 - 15 * delta) / 2
    end
  end
end

#nonagonal ⇒ Object 



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# File 'lib/figurate_numbers/plane_figurate_numbers.rb', line 62

def nonagonal
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << (7 * delta**2 - 5 * delta) / 2
    end
  end
end

#octadecagonal ⇒ Object 



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# File 'lib/figurate_numbers/plane_figurate_numbers.rb', line 134

def octadecagonal
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << (16 * delta**2 - 14 * delta) / 2
    end
  end
end

#octagonal ⇒ Object 



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# File 'lib/figurate_numbers/plane_figurate_numbers.rb', line 54

def octagonal
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << (6 * delta**2 - 4 * delta) / 2
    end
  end
end

#pentadecagonal ⇒ Object 



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# File 'lib/figurate_numbers/plane_figurate_numbers.rb', line 110

def pentadecagonal
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << (13 * delta**2 - 11 * delta) / 2
    end
  end
end

#pentagonal ⇒ Object 



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# File 'lib/figurate_numbers/plane_figurate_numbers.rb', line 30

def pentagonal
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << (3 * delta**2 - delta) / 2
    end
  end
end

#pentagram ⇒ Object 



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# File 'lib/figurate_numbers/plane_figurate_numbers.rb', line 527

def pentagram
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << 5 * delta**2 - 5 * delta + 1
    end
  end
end

#polite ⇒ Object 



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# File 'lib/figurate_numbers/plane_figurate_numbers.rb', line 485

def polite
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << delta + Math.log(delta + Math.log(delta, 2), 2).floor
    end
  end
end

#polygonal(m) ⇒ Object 



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# File 'lib/figurate_numbers/plane_figurate_numbers.rb', line 6

def polygonal(m)
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << ((m - 2) * delta**2 - (m - 4) * delta) / 2
    end
  end
end

#polygram(m) ⇒ Object Also known as: centered_star_polygonal 



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# File 'lib/figurate_numbers/plane_figurate_numbers.rb', line 517

def polygram(m)
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << m * delta**2 - m * delta + 1
    end
  end
end

#pronic ⇒ Object Also known as: heteromecic, oblong 



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# File 'lib/figurate_numbers/plane_figurate_numbers.rb', line 474

def pronic
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << delta * (delta + 1)
    end
  end
end

#square ⇒ Object 



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# File 'lib/figurate_numbers/plane_figurate_numbers.rb', line 22

def square
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << (2 * delta**2) / 2
    end
  end
end

#tetradecagonal ⇒ Object 



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# File 'lib/figurate_numbers/plane_figurate_numbers.rb', line 102

def tetradecagonal
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << (12 * delta**2 - 10 * delta) / 2
    end
  end
end

#triacontagonal ⇒ Object 



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# File 'lib/figurate_numbers/plane_figurate_numbers.rb', line 230

def triacontagonal
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << (28 * delta**2 - 26 * delta) / 2
    end
  end
end

#triangular ⇒ Object 



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# File 'lib/figurate_numbers/plane_figurate_numbers.rb', line 14

def triangular
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << (delta**2 + delta) / 2
    end
  end
end

#tridecagonal ⇒ Object 



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# File 'lib/figurate_numbers/plane_figurate_numbers.rb', line 94

def tridecagonal
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << (11 * delta**2 - 9 * delta) / 2
    end
  end
end

#truncated_centered_hexagonal ⇒ Object Also known as: truncated_hex 



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# File 'lib/figurate_numbers/plane_figurate_numbers.rb', line 601

def truncated_centered_hexagonal
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << 21 * delta**2 - 33 * delta + 13
    end
  end
end

#truncated_centered_pentagonal ⇒ Object 



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# File 'lib/figurate_numbers/plane_figurate_numbers.rb', line 593

def truncated_centered_pentagonal
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << (35 * delta**2 - 55 * delta) / 2 + 11
    end
  end
end

#truncated_centered_pol(m) ⇒ Object Also known as: truncated_centered_mgonal 



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# File 'lib/figurate_numbers/plane_figurate_numbers.rb', line 567

def truncated_centered_pol(m)
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << 1 + (m * (7 * delta**2 - 11 * delta + 4)) / 2
    end
  end
end

#truncated_centered_square ⇒ Object 



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# File 'lib/figurate_numbers/plane_figurate_numbers.rb', line 585

def truncated_centered_square
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << 14 * delta**2 - 22 * delta + 9
    end
  end
end

#truncated_centered_triangular ⇒ Object 



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# File 'lib/figurate_numbers/plane_figurate_numbers.rb', line 577

def truncated_centered_triangular
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << (21 * delta**2 - 33 * delta) / 2 + 7
    end
  end
end

#truncated_pronic ⇒ Object 



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# File 'lib/figurate_numbers/plane_figurate_numbers.rb', line 559

def truncated_pronic
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << (7 * delta**2) - (7 * delta) + 2
    end
  end
end

#truncated_square ⇒ Object 



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# File 'lib/figurate_numbers/plane_figurate_numbers.rb', line 551

def truncated_square
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << (7 * delta**2) - (10 * delta) + 4
    end
  end
end

#truncated_triangular ⇒ Object 



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# File 'lib/figurate_numbers/plane_figurate_numbers.rb', line 543

def truncated_triangular
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << (3 * delta**2) - (3 * delta) + 1
    end
  end
end