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fignumbers

A comprehensive TypeScript library for generating figurate numbers across multiple dimensions.

https://github.com/edelveart/fignumbers

Science Score: 44.0%

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Keywords

figurate-numbers generators infinite-sequences mathematics-library number-theory
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A comprehensive TypeScript library for generating figurate numbers across multiple dimensions.

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figurate-numbers generators infinite-sequences mathematics-library number-theory
Created about 1 year ago · Last pushed 11 months ago
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README.md

Fignumbers

Fignumbers is a comprehensive TypeScript library for generating and exploring infinite figurate number sequences, linked to geometric shapes across multiple dimensions.

NPM Version NPM Downloads NPM Type Definitions NPM License

Fignumbers Image

Rich variety with academic foundation 🚀

Based on the book Figurate Numbers (2012) by Elena Deza and Michel Deza, this library covers a broad range of figurate number sequences. This academic foundation ensures its reliability and precision for use in various fields:

  • Mathematical projects
  • Visualization
  • Algorithmic applications
  • Any work involving figurate number sequences

It is precise and type-safe, but bigint operations are generally slower than number operations.

Installation 🛠️

First, make sure you have the library installed via npm:

node npm install fignumbers

BigInt Support Required ⚠️

  • Fignumbers utilizes BigInt to manage large integers that exceed the Number type limit of (2^53 - 1). Ensure that your environment supports BigInt before using this library.

Usage 🔥

Three main classes ⚙️

Fignumbers is structured around three main classes, each corresponding to a different spatial dimension, as described in the book:

  1. PlaneFigNumbers – 121 sequences
  2. SpaceFigNumbers – 133 sequences
  3. MultiDimensionalFigNumbers – 191 sequences

Together, these classes implement a total of 445 figurate number sequences.

Example

```ts // 1. Import the library import { SpaceFigNumbers } from "fignumbers";

// 2. Configure parameters for the generator (use bigints for precision!) const config = { start: 1n, m: 5n, step: 1n };

// 3. Choose the type of space figurate number you want (pyramidal, cubic, etc.) const pyramidalSequence = new SpaceFigNumbers("pyramidal"); const pyramidalNumbers = pyramidalSequence.generate(config);

// 4. Get ready to see the magic happen! First 7 pyramidal numbers with m = 5n: console.log("First 7 pyramidal numbers with m = 5n:"); for (let i = 0; i < 7; i++) { const nextNumber = pyramidalNumbers.next().value; // Grab the next number in the sequence console.log(Number ${i + 1}: ${nextNumber}); } ```

Expected Output

txt First 7 pyramidal numbers with m = 5n: Number 1: 1n Number 2: 6n Number 3: 18n Number 4: 40n Number 5: 75n Number 6: 126n Number 7: 196n

Overview of implemented sequences per class 🌟

1. PlaneFigNumbers

  1. polygonal
  2. centeredPolygonal
  3. truncatedCenteredPolygonal
  4. pronic
  5. truncatedPronic
  6. polite
  7. impolite
  8. aztecDiamond
  9. gnomic
  10. cross
  11. polygram
  12. triangular
  13. square
  14. pentagonal
  15. hexagonal
  16. heptagonal
  17. octagonal
  18. nonagonal
  19. decagonal
  20. hendecagonal
  21. dodecagonal
  22. tridecagonal
  23. tetradecagonal
  24. pentadecagonal
  25. hexadecagonal
  26. heptadecagonal
  27. octadecagonal
  28. nonadecagonal
  29. icosagonal
  30. icosihenagonal
  31. icosidigonal
  32. icositrigonal
  33. icositetragonal
  34. icosipentagonal
  35. icosihexagonal
  36. icosiheptagonal
  37. icosioctagonal
  38. icosinonagonal
  39. triacontagonal
  40. centeredTriangular
  41. centeredSquare
  42. centeredPentagonal
  43. centeredHexagonal
  44. centeredHeptagonal
  45. centeredOctagonal
  46. centeredNonagonal
  47. centeredDecagonal
  48. centeredHendecagonal
  49. centeredDodecagonal
  50. centeredTridecagonal
  51. centeredTetradecagonal
  52. centeredPentadecagonal
  53. centeredHexadecagonal
  54. centeredHeptadecagonal
  55. centeredOctadecagonal
  56. centeredNonadecagonal
  57. centeredIcosagonal
  58. centeredIcosihenagonal
  59. centeredIcosidigonal
  60. centeredIcositrigonal
  61. centeredIcositetragonal
  62. centeredIcosipentagonal
  63. centeredIcosihexagonal
  64. centeredIcosiheptagonal
  65. centeredIcosioctagonal
  66. centeredIcosinonagonal
  67. centeredTriacontagonal
  68. truncatedCenteredTriangular
  69. truncatedCenteredSquare
  70. truncatedCenteredPentagonal
  71. truncatedCenteredHexagonal
  72. truncatedCenteredHeptagonal
  73. truncatedCenteredOctagonal
  74. truncatedCenteredNonagonal
  75. truncatedCenteredDecagonal
  76. truncatedCenteredHendecagonal
  77. truncatedCenteredDodecagonal
  78. truncatedCenteredTridecagonal
  79. truncatedCenteredTetradecagonal
  80. truncatedCenteredPentadecagonal
  81. truncatedCenteredHexadecagonal
  82. truncatedCenteredHeptadecagonal
  83. truncatedCenteredOctadecagonal
  84. truncatedCenteredNonadecagonal
  85. truncatedCenteredIcosagonal
  86. truncatedCenteredIcosihenagonal
  87. truncatedCenteredIcosidigonal
  88. truncatedCenteredIcositrigonal
  89. truncatedCenteredIcositetragonal
  90. truncatedCenteredIcosipentagonal
  91. truncatedCenteredIcosihexagonal
  92. truncatedCenteredIcosiheptagonal
  93. truncatedCenteredIcosioctagonal
  94. truncatedCenteredIcosinonagonal
  95. truncatedCenteredTriacontagonal
  96. pentagram
  97. hexagram
  98. heptagram
  99. octagram
  100. nonagram
  101. decagram
  102. hendecagram
  103. dodecagram
  104. tridecagram
  105. tetradecagram
  106. pentadecagram
  107. hexadecagram
  108. heptadecagram
  109. octadecagram
  110. nonadecagram
  111. icosagram
  112. icosihenagram
  113. icosidigram
  114. icositrigram
  115. icositetragram
  116. icosipentagram
  117. icosihexagram
  118. icosiheptagram
  119. icosioctagram
  120. icosinonagram
  121. triacontagram

2. SpaceFigNumbers

  1. pyramidal
  2. tetrahedral
  3. cubic
  4. octahedral
  5. dodecahedral
  6. icosahedral
  7. centeredMgonalPyramidal
  8. centeredMgonalPyramid
  9. centeredTetrahedron
  10. centeredCube
  11. centeredOctahedron
  12. centeredDodecahedron
  13. centeredIcosahedron
  14. truncatedTetrahedral
  15. truncatedCubic
  16. truncatedOctahedral
  17. centeredTruncatedTetrahedron
  18. centeredTruncatedCube
  19. centeredTruncatedOctahedron
  20. stellaOctangula
  21. rhombicDodecahedral
  22. hauyRhombicDodecahedral
  23. mgonalPrism
  24. triangularPyramidal
  25. squarePyramidal
  26. pentagonalPyramidal
  27. hexagonalPyramidal
  28. heptagonalPyramidal
  29. octagonalPyramidal
  30. nonagonalPyramidal
  31. decagonalPyramidal
  32. hendecagonalPyramidal
  33. dodecagonalPyramidal
  34. tridecagonalPyramidal
  35. tetradecagonalPyramidal
  36. pentadecagonalPyramidal
  37. hexadecagonalPyramidal
  38. heptadecagonalPyramidal
  39. octadecagonalPyramidal
  40. nonadecagonalPyramidal
  41. icosagonalPyramidal
  42. icosihenagonalPyramidal
  43. icosidigonalPyramidal
  44. icositrigonalPyramidal
  45. icositetragonalPyramidal
  46. icosipentagonalPyramidal
  47. icosihexagonalPyramidal
  48. icosiheptagonalPyramidal
  49. icosioctagonalPyramidal
  50. icosinonagonalPyramidal
  51. triacontagonalPyramidal
  52. centeredPentagonalPyramid
  53. centeredHexagonalPyramid
  54. centeredHeptagonalPyramid
  55. centeredOctagonalPyramid
  56. centeredNonagonalPyramid
  57. centeredDecagonalPyramid
  58. centeredHendecagonalPyramid
  59. centeredDodecagonalPyramid
  60. centeredTridecagonalPyramid
  61. centeredTetradecagonalPyramid
  62. centeredPentadecagonalPyramid
  63. centeredHexadecagonalPyramid
  64. centeredHeptadecagonalPyramid
  65. centeredOctadecagonalPyramid
  66. centeredNonadecagonalPyramid
  67. centeredIcosagonalPyramid
  68. centeredIcosihenagonalPyramid
  69. centeredIcosidigonalPyramid
  70. centeredIcositrigonalPyramid
  71. centeredIcositetragonalPyramid
  72. centeredIcosipentagonalPyramid
  73. centeredIcosihexagonalPyramid
  74. centeredIcosiheptagonalPyramid
  75. centeredIcosioctagonalPyramid
  76. centeredIcosinonagonalPyramid
  77. centeredTriacontagonalPyramid
  78. centeredTriangularPyramidal
  79. centeredSquarePyramidal
  80. centeredPentagonalPyramidal
  81. centeredHexagonalPyramidal
  82. centeredHeptagonalPyramidal
  83. centeredOctagonalPyramidal
  84. centeredNonagonalPyramidal
  85. centeredDecagonalPyramidal
  86. centeredHendecagonalPyramidal
  87. centeredDodecagonalPyramidal
  88. centeredTridecagonalPyramidal
  89. centeredTetradecagonalPyramidal
  90. centeredPentadecagonalPyramidal
  91. centeredHexadecagonalPyramidal
  92. centeredHeptadecagonalPyramidal
  93. centeredOctadecagonalPyramidal
  94. centeredNonadecagonalPyramidal
  95. centeredIcosagonalPyramidal
  96. centeredIcosihenagonalPyramidal
  97. centeredIcosidigonalPyramidal
  98. centeredIcositrigonalPyramidal
  99. centeredIcositetragonalPyramidal
  100. centeredIcosipentagonalPyramidal
  101. centeredIcosihexagonalPyramidal
  102. centeredIcosiheptagonalPyramidal
  103. centeredIcosioctagonalPyramidal
  104. centeredIcosinonagonalPyramidal
  105. centeredTriacontagonalPyramidal
  106. triangularPrism
  107. squarePrism
  108. pentagonalPrism
  109. hexagonalPrism
  110. heptagonalPrism
  111. octagonalPrism
  112. nonagonalPrism
  113. decagonalPrism
  114. hendecagonalPrism
  115. dodecagonalPrism
  116. tridecagonalPrism
  117. tetradecagonalPrism
  118. pentadecagonalPrism
  119. hexadecagonalPrism
  120. heptadecagonalPrism
  121. octadecagonalPrism
  122. nonadecagonalPrism
  123. icosagonalPrism
  124. icosihenagonalPrism
  125. icosidigonalPrism
  126. icositrigonalPrism
  127. icositetragonalPrism
  128. icosipentagonalPrism
  129. icosihexagonalPrism
  130. icosiheptagonalPrism
  131. icosioctagonalPrism
  132. icosinonagonalPrism
  133. triacontagonalPrism

3. MultiDimensionalFigNumbers

  1. hyperTetrahedral
  2. hyperCubic
  3. hyperOctahedral
  4. hyperDodecahedral
  5. hyperIcosahedral
  6. polyOctahedral
  7. kDimensionalHyperTetrahedron
  8. kDimensionalHyperCube
  9. kDimensionalHyperOctahedron
  10. kDimensionalMgonalPyramidal
  11. fiveDimensionalMgonalPyramidal
  12. fourDimensionalMgonalPyramidal
  13. sixDimensionalMgonalPyramidal
  14. centeredHyperTetrahedron
  15. kDimensionalCenteredHyperTetrahedron
  16. centeredHyperCube
  17. kDimensionalCenteredHyperCube
  18. centeredHyperOctahedral
  19. kDimensionalCenteredHyperOctahedron
  20. nexus
  21. pentatope
  22. biquadratic
  23. tesseract
  24. 5-cell
  25. 8-cell
  26. 16-cell
  27. 120-cell
  28. 600-cell
  29. 24-cell
  30. pentachoron
  31. octachoron
  32. hexadecachoron
  33. hecatonicosachoron
  34. hexacosichoron
  35. icositetrachoron
  36. 5-simplex
  37. 6-simplex
  38. 7-simplex
  39. 8-simplex
  40. 9-simplex
  41. 10-simplex
  42. 11-simplex
  43. 12-simplex
  44. 13-simplex
  45. 14-simplex
  46. 15-simplex
  47. 16-simplex
  48. 17-simplex
  49. 18-simplex
  50. 19-simplex
  51. 20-simplex
  52. 21-simplex
  53. 22-simplex
  54. 23-simplex
  55. 24-simplex
  56. 25-simplex
  57. 26-simplex
  58. 27-simplex
  59. 28-simplex
  60. 29-simplex
  61. 30-simplex
  62. 5-hypercube
  63. 6-hypercube
  64. 7-hypercube
  65. 8-hypercube
  66. 9-hypercube
  67. 10-hypercube
  68. 11-hypercube
  69. 12-hypercube
  70. 13-hypercube
  71. 14-hypercube
  72. 15-hypercube
  73. 16-hypercube
  74. 17-hypercube
  75. 18-hypercube
  76. 19-hypercube
  77. 20-hypercube
  78. 21-hypercube
  79. 22-hypercube
  80. 23-hypercube
  81. 24-hypercube
  82. 25-hypercube
  83. 26-hypercube
  84. 27-hypercube
  85. 28-hypercube
  86. 29-hypercube
  87. 30-hypercube
  88. 5-cross-polytope
  89. 6-cross-polytope
  90. 7-cross-polytope
  91. 8-cross-polytope
  92. 9-cross-polytope
  93. 10-cross-polytope
  94. 11-cross-polytope
  95. 12-cross-polytope
  96. 13-cross-polytope
  97. 14-cross-polytope
  98. 15-cross-polytope
  99. 16-cross-polytope
  100. 17-cross-polytope
  101. 18-cross-polytope
  102. 19-cross-polytope
  103. 20-cross-polytope
  104. 21-cross-polytope
  105. 22-cross-polytope
  106. 23-cross-polytope
  107. 24-cross-polytope
  108. 25-cross-polytope
  109. 26-cross-polytope
  110. 27-cross-polytope
  111. 28-cross-polytope
  112. 29-cross-polytope
  113. 30-cross-polytope
  114. 5-centered-hypertetrahedron
  115. 6-centered-hypertetrahedron
  116. 7-centered-hypertetrahedron
  117. 8-centered-hypertetrahedron
  118. 9-centered-hypertetrahedron
  119. 10-centered-hypertetrahedron
  120. 11-centered-hypertetrahedron
  121. 12-centered-hypertetrahedron
  122. 13-centered-hypertetrahedron
  123. 14-centered-hypertetrahedron
  124. 15-centered-hypertetrahedron
  125. 16-centered-hypertetrahedron
  126. 17-centered-hypertetrahedron
  127. 18-centered-hypertetrahedron
  128. 19-centered-hypertetrahedron
  129. 20-centered-hypertetrahedron
  130. 21-centered-hypertetrahedron
  131. 22-centered-hypertetrahedron
  132. 23-centered-hypertetrahedron
  133. 24-centered-hypertetrahedron
  134. 25-centered-hypertetrahedron
  135. 26-centered-hypertetrahedron
  136. 27-centered-hypertetrahedron
  137. 28-centered-hypertetrahedron
  138. 29-centered-hypertetrahedron
  139. 30-centered-hypertetrahedron
  140. 5-centered-hypercube
  141. 6-centered-hypercube
  142. 7-centered-hypercube
  143. 8-centered-hypercube
  144. 9-centered-hypercube
  145. 10-centered-hypercube
  146. 11-centered-hypercube
  147. 12-centered-hypercube
  148. 13-centered-hypercube
  149. 14-centered-hypercube
  150. 15-centered-hypercube
  151. 16-centered-hypercube
  152. 17-centered-hypercube
  153. 18-centered-hypercube
  154. 19-centered-hypercube
  155. 20-centered-hypercube
  156. 21-centered-hypercube
  157. 22-centered-hypercube
  158. 23-centered-hypercube
  159. 24-centered-hypercube
  160. 25-centered-hypercube
  161. 26-centered-hypercube
  162. 27-centered-hypercube
  163. 28-centered-hypercube
  164. 29-centered-hypercube
  165. 30-centered-hypercube
  166. 5-centered-hyperoctahedron
  167. 6-centered-hyperoctahedron
  168. 7-centered-hyperoctahedron
  169. 8-centered-hyperoctahedron
  170. 9-centered-hyperoctahedron
  171. 10-centered-hyperoctahedron
  172. 11-centered-hyperoctahedron
  173. 12-centered-hyperoctahedron
  174. 13-centered-hyperoctahedron
  175. 14-centered-hyperoctahedron
  176. 15-centered-hyperoctahedron
  177. 16-centered-hyperoctahedron
  178. 17-centered-hyperoctahedron
  179. 18-centered-hyperoctahedron
  180. 19-centered-hyperoctahedron
  181. 20-centered-hyperoctahedron
  182. 21-centered-hyperoctahedron
  183. 22-centered-hyperoctahedron
  184. 23-centered-hyperoctahedron
  185. 24-centered-hyperoctahedron
  186. 25-centered-hyperoctahedron
  187. 26-centered-hyperoctahedron
  188. 27-centered-hyperoctahedron
  189. 28-centered-hyperoctahedron
  190. 29-centered-hyperoctahedron
  191. 30-centered-hyperoctahedron

Contributing

Fignumbers 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.

Owner

  • Name: Edgar Delgado Vega
  • Login: edelveart
  • Kind: user
  • Location: Lima-Perú

Hi, I'm Edgar, a person motivated by art and technology. My interests are mathematical music theory and live coding (Sonic Pi).

Citation (CITATION.cff) 

cff-version: 1.2.0
message: "If you use fignumbers and its documentation in your work, please cite it as below."
authors:
  - family-names: "Delgado Vega"
    given-names: "Edgar Armando"
    orcid: "https://orcid.org/0000-0002-9672-9087"
title: "fignumbers: A TypeScript Library for Generating and Exploring Figurate Numbers"
version: 0.7.0
doi:
date-released: 2024-12-23
url: "https://github.com/edelveart/fignumbers"
repository-code: "https://github.com/edelveart/fignumbers"
license: MIT

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npmjs.org: fignumbers

A comprehensive TypeScript library for generating figurate numbers across multiple dimensions

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