• meta-synthesis
• About
  About meta-synthesis Reviews Products & Services Contact Us FAQs
• Our Websites
  The INTERNET Database of Periodic Tables The Chemogenesis Web Book The Chemical Thesaurus Chemistry Tutorials & Drills The Truncated Tetrahedron Orange Gate Journal George Truefitt FRIBA Mac Ruff's PNG Sketchbooks MRL's Bow Tuning Page
• Web Book Chapters
  Web Book Home Page | Chemogenesis Main Index Foreword:  Chemogenesis & Chemical Education Part I   Atoms | Elements | Periodic Tables 1.1  Introduction to Chemogenesis 1.2  Nucleosynthesis of The Elements 1.3  The Segrè Chart 1.4  Quantum Numbers to Periodic Tables 1.5  The Periodic Table: What Is It Showing? 1.6  The INTERNET Database of Periodic Tables 1.7  Periodicity Part II   Structure | Bonding | Material Type 2.1  Mono-Bond Typed Binary Compounds 2.2  Binary Compound Synthlet 2.3  Electronegativity 2.4  van Arkel-Ketelaar Triangles of Bonding 2.5  Tetrahedra of Structure, Bonding & Material Type 2.6  Structure, Bonding & Material Synthlet 2.7  The Classification of Matter: Chemical Stuff Part III   Interactions | Reactions | Mechanisms 3.1  The Chemogenesis Analysis: An Overview 3.2  Lewis and Brønsted Models of Acidity 3.3  The Hard Soft [Lewis] Acid Base Principle 3.4  Main Group Elemental Hydrides 3.5  Five Hydrogen Probe Experiments 3.6  Congeneric Dots, Series & Planars 3.7  Quantifying Congeneric Behaviour 3.8  Ligand Replacement Congeneric Series 3.9  Congeneric Array Interactions 3.10  Emergence of Organic Chemistry 3.11  Congeneric Array Database 3.12  The Five Reaction Chemistries 3.13  Lewis Acids & Lewis Bases: A New Analysis 3.14  The Lewis Acid/Base Interaction Matrix 3.15  Patterns in Reaction Chemistry Poster 3.16  Lewis Acid/Base Interaction Matrix Database 3.17  Nucleophiles, Bases & The Fluoride Ion 3.18  Redox Chemistry 3.19  Redox Chemistry Synthlet 3.20  Radical Chemistry 3.21  Diradical Chemistry 3.22  Photochemistry 3.23  Species/Species Interactions 3.24  The Simplest Mechanistic Step: STAD 3.25  Unit & Compound Mechanistic Steps 3.26  The Mechanism Matrix 3.27  Addition To A Double Bond Synthlet 3.28  Pericyclic Reaction Chemistry Part IV   Chemical Theory 4.1  Why Do Chemical Reactions Occur? 4.2a  Thermochemistry: List Reactions Synthlet 4.2b  Thermochemistry: Play With Reaction Synthlet 4.2c  Thermochemistry: Bulid A Reaction Synthlet 4.3  Timeline of Structural Theory 4.4  Modern Lewis Theory 4.5  Valence Shell Electron Pair Repulsion: VSEPR 4.6  Diatomic Species by Molecular Orbital Theory 4.7  Polyatomic Species: Molecular Orbitals 4.8  Organic π-Systems 4.9  Functional Group Database Part V   Complexity & Emergence 5.1  Chemistry & Complexity: Systems 5.2  Linear Chemistry Systems 5.3  Chemical Systems Prone to Complexity Part VI   Extras 6.1  Chemogenesis Videos 6.2  Chemical Thesaurus Reaction Chemistry Database 6.3  Paper: Chemogenesis 6.4  Paper: Electronegativity as a Basic Elemental Property (FoC) 6.5  Workshop: What is Chemistry? 6.6  Paper: Scientific laws, Dalton’s postulates, chemical reactions
          and Wolfram’s NKS (FoC) 6.7  Literature References & Further Reading

Periodic Table T-Shirts & more from the meta-synthesis   See More   Merch Store

The INTERNET Database of Periodic Tables

There are thousands of periodic tables in web space, but this is the only comprehensive database of periodic tables & periodic system formulations. If you know of an interesting periodic table that is missing, please contact the database curator: Mark R. Leach Ph.D. The database holds information on periodic tables, the discovery of the elements, the elucidation of atomic weights and the discovery of atomic structure (and much, much more).

Bilateral Symmetry in the Periodic Binodic Table

René Vernon, who developed these ideas, writes:

This table is adapted from the work of Gutiérrez-Samanez (2020), who discusses mathematising the chemical periodic system as a grid, which leads to a quadratic function or “binódica function” formed by pairs of periods or binodos (dyads).

The difference is that whereas Gutiérrez-Samanez showed the first pair of periods as H-He and Li-Be, this table shows the first period as e-n and H-He. Here, e is the electron and n is the neutron. Each pair of periods is shown pancake style rather than in a single row. The formula for the length of each paired period or binode is 2n² = 2, 8, 16, 32.

The idea of paired periods has a long history; it seems to have originated with Werner in 1905.

According to Jensen:

"The temptation to read more into the shape of the table than is really there is almost overwhelming. Even someone as great as Werner was tempted (1905). Having postulated a missing element between H and He, he decided to perfect the symmetry of his table by guaranteeing that rows of differing length always occurred in pairs. Consequently, he further postulated a row of three missing elements lying above the H-X-He row."

Rydberg (1913, pp. 12–13) used a formula 4n^2 for the number of elements in the paired periods: 4, 16, 32, 64. This formula is also used by Gutiérrez-Samanez.

Paired periods were also used by Janet (1928), Saz (1931), Achimov (1946) and Baca Mendoza (1953).

References

• Achimov EI 1946, Zhur. Obshchei Khim., vol. 16, p. 961; https://www.meta-synthesis.com/webbook/35_pt/pt_database.php?PT_id=776
• Baca Mendoza O 1953, Leyes Genéticas de los elementos Químicos, Nuevo Sistema Periódico, National University of Cusco, https://www.meta-synthesis.com/webbook/35_pt/Mendoza_PT.pdf, accessed May 12, 2024
• Gutiérrez-Samanez JA 2020, Binódic periodic system: a mathematical approach, Found Chem, vol. 22, pp. 235–266 (255)
• Janet C1928, Essais de classification hélicoïdale des éléments chimiques. Imprimerie Départementale de l’Oise, Beauvais, https://www.meta-synthesis.com/webbook/35_pt/pt_database.php?PT_id=152
• Jensen WB 1986, Classification, symmetry and the periodic table, Computers & Mathematics with Applications, vol. 12B, no. 12, pp. 487–510 (508)
• Rydberg JR 1913, Untersuchungen über das system der grundstoffe, Lunds Univ. Ärsskrift, vol. 9, no. 18. In French: 1914, Recherches sur le système des éléments, Journal de Chimie Physique, vol. 12, p. 585
• Saz E 1931, Iberica, vol. 35, p. 186
• Wemer A 1905, Beitrag zum Aufbau des periodischen Systems, Ber. Deut. Chem. Ges, vol. 38, pp. 914–921, 2022–2027

© Mark R. Leach Ph.D. 1999 –

Queries, Suggestions, Bugs, Errors, Typos...

If you have any:

Queries
Comments
Suggestions
Suggestions for links
Bug, typo or grammatical error reports about this page,

please contact Mark R. Leach, the author, using mark@meta-synthesis.com

This free, open access web book is an ongoing project and your input is appreciated.