figuratenum 0.5.0

A complete generator of infinite sequences of figurate numbers

FigurateNum

FigurateNum is a set of figurate number generators based on the book Figurate Numbers (2012) by Michel Deza and Elena Deza.

FigurateNum generates the following types of infinite sequences:

• 20 sequences of plane figurate numbers
• 38 sequences of space figurate numbers
• 18 sequences of multidimensional figurate numbers

What is the purpose of FigurateNum?

FigurateNum facilitates the discovery of new patterns among sequences and enables various numerical calculations in mathematical projects and related endeavors. It can be integrated with other software to visualize the geometric objects described. Moreover, it serves as a valuable companion to the book!

How to install?

pip install figuratenum

• It is advisable to use a virtual environment.

How to import figuratenum?

import figuratenum as fgn

How to use?

>>> seq = fgn.hyperdodecahedral_numbers()

>>> first = next(seq)
>>> second = next(seq)
>>> third = next(seq)
>>> fourth = next(seq)

>>> print(first, second, third, fourth)
1 600 4983 19468

You could get a list of numbers using a loop:

>>> generator = fgn.k_dimensional_centered_hypertetrahedron_numbers(21)
>>> sequence = []
>>> for _ in range(1, 15):
>>>     next_num = next(generator)
>>>     sequence.append(next_num)

>>> print(sequence)
[1, 23, 276, 2300, 14950, 80730, 376740, 1560780, 5852925, 20160075, 64512240, 193536720, 548354040, 1476337800]

Equivalently, using the array module:

import array as arr_num

>>> generator = fgn.aztec_diamond_numbers()
>>> sequence = arr_num.array('i')
>>> for _ in range(1, 15):
>>>     next_num = next(generator)
>>>     sequence.append(next_num)

>>> print(sequence)
array('i', [4, 12, 24, 40, 60, 84, 112, 144, 180, 220, 264, 312, 364, 420])

Plane figurate numbers

1. polygonal_numbers
2. triangular_numbers
3. triangular_numbers
4. square_numbers
5. pentagonal_numbers
6. hexagonal_numbers
7. heptagonal_numbers
8. octagonal_numbers
9. nonagonal_numbers
10. decagonal_numbers
11. hendecagonal_numbers
12. dodecagonal_numbers
13. tridecagonal_numbers
14. tetradecagonal_numbers
15. pentadecagonal_numbers
16. hexadecagonal_numbers
17. heptadecagonal_numbers
18. octadecagonal_numbers
19. nonadecagonal_numbers
20. icosagonal_numbers
21. icosihenagonal_numbers
22. icosidigonal_numbers
23. icositrigonal_numbers
24. icositetragonal_numbers
25. icosipentagonal_numbers
26. icosihexagonal_numbers
27. icosiheptagonal_numbers
28. icosioctagonal_numbers
29. icosinonagonal_numbers
30. triacontagonal_numbers
31. centered_triangular_numbers
32. centered_square_numbers = diamond numbers
33. centered_pentagonal_numbers
34. centered_hexagonal_numbers
35. centered_heptagonal_numbers
36. centered_octagonal_numbers
37. centered_nonagonal_numbers
38. centered_decagonal_numbers
39. centered_hendecagonal_numbers
40. centered_dodecagonal_numbers = star_numbers
41. centered_tridecagonal_numbers
42. centered_tetradecagonal_numbers
43. centered_pentadecagonal_numbers
44. centered_hexadecagonal_numbers
45. centered_heptadecagonal_numbers
46. centered_octadecagonal_numbers
47. centered_nonadecagonal_numbers
48. centered_icosagonal_numbers
49. centered_icosihenagonal_numbers
50. centered_icosidigonal_numbers
51. centered_icositrigonal_numbers
52. centered_icositetragonal_numbers
53. centered_icosipentagonal_numbers
54. centered_icosihexagonal_numbers
55. centered_icosiheptagonal_numbers
56. centered_icosioctagonal_numbers
57. centered_icosinonagonal_numbers
58. centered_triacontagonal_numbers
59. centered_mgonal_numbers
60. pronic_numbers = heteromecic_numbers = oblong_numbers
61. polite_numbers
62. impolite_numbers
63. cross_numbers
64. aztec_diamond_numbers
65. polygram_numbers(m) = centered_star_polygonal_numbers(m)
66. pentagram_numbers
67. gnomic_numbers
68. truncated_triangular_numbers
69. truncated_square_numbers
70. truncated_pronic_numbers
71. truncated_centered_pol_numbers(m) = truncated_centered_pol_numbers(m)
72. truncated_centered_hexagonal_numbers = truncated_hex_numbers
73. generalized_mgonal_numbers(m, start_numb)
74. generalized_centered_pol_numbers(m, start_numb)
75. generalized_pronic_numbers(start_numb)

Space figurate numbers

1. m_pyramidal_numbers(m)
2. cubic_numbers
3. tetrahedral_numbers
4. octahedral_numbers
5. dodecahedral_numbers
6. icosahedral_numbers
7. truncated_tetrahedral_numbers
8. truncated_cubic_numbers
9. truncated_octahedral_numbers
10. stella_octangula_numbers
11. centered_cube_numbers
12. rhombic_dodecahedral_numbers
13. hauy_rhombic_dodecahedral_numbers
14. centered_tetrahedron_numbers = centered_tetrahedral_numbers
15. centered_square_pyramid_numbers = centered_pyramid_numbers
16. centered_mgonal_pyramid_numbers(m)
17. centered_octahedron_numbers
18. centered_icosahedron_numbers = centered_cuboctahedron_numbers
19. centered_dodecahedron_numbers
20. centered_truncated_tetrahedron_numbers
21. centered_truncated_cube_numbers
22. centered_truncated_octahedron_numbers
23. centered_mgonal_pyramidal_numbers(m)
24. centered_hexagonal_pyramidal_numbers = hex_pyramidal_numbers
25. hexagonal_prism_numbers
26. mgonal_prism_numbers(m)
27. generalized_mgonal_pyramidal_numbers(m, start_num)
28. generalized_cubic_numbers(start_num)
29. generalized_octahedral_numbers(start_num)
30. generalized_icosahedral_numbers(start_num)
31. generalized_dodecahedral_numbers(start_num)
32. generalized_centered_cube_numbers(start_num)
33. generalized_centered_tetrahedron_numbers(start_num)
34. generalized_centered_square_pyramid_numbers(start_num)
35. generalized_rhombic_dodecahedral_numbers(start_num)
36. generalized_centered_mgonal_pyramidal_numbers(m, start_num)
37. generalized_mgonal_prism_numbers(m, start_num)
38. generalized_hexagonal_prism_numbers(start_num)

Multidimensional figurate numbers

1. pentatope_numbers = hypertetrahedral_numbers = triangulotriangular_numbers
2. k_dimensional_hypertetrahedron_numbers(k) = k_hypertetrahedron_numbers(k) = regular_k_polytopic_numbers(k) = figurate_numbers_of_order_k(k)
3. biquadratic_numbers
4. k_dimensional_hypercube_numbers(k) = k_hypercube_numbers(k)
5. hyperoctahedral_numbers = hexadecachoron_numbers = four_cross_polytope_numbers = four_orthoplex_numbers
6. hypericosahedral_numbers = tetraplex_numbers = polytetrahedron_numbers = hexacosichoron_numbers
7. hyperdodecahedral_numbers = hecatonicosachoron_numbers = dodecaplex_numbers = polydodecahedron_numbers
8. polyoctahedral_numbers = icositetrachoron_numbers = octaplex_numbers = hyperdiamond_numbers
9. k_dimensional_hyperoctahedron_numbers(k) = k_cross_polytope_numbers(k)
10. four_dimensional_mgonal_pyramidal_numbers(m) = mgonal_pyramidal_numbers_of_the_second_order
11. k_dimensional_mgonal_pyramidal_numbers(k, m) = mgonal_pyramidal_numbers_of_the_k_2_th_order(k, m)
12. centered_biquadratic_numbers
13. k_dimensional_centered_hypercube_numbers(k)
14. centered_polytope_numbers
15. k_dimensional_centered_hypertetrahedron_numbers(k)
16. centered_hyperoctahedral_numbers = orthoplex_numbers
17. nexus_numbers
18. k_dimensional_centered_hyperoctahedron_numbers(k)

Contributing

FigurateNumber is currently under development, and we warmly invite your contributions. Just fork the project and then submit a pull request:

• Sequences from Chapters 1, 2, and 3 of the book
• New sequences not included in the book: If you have new sequences, please provide the source.
• Tests, documentation and errata in the book

When making commits, please use the following conventional prefixes to indicate the nature of the changes: feat, refactor, fix, docs, and test.

License

MIT License