You are currently browsing the category archive for the 'math' category.
-
3. 1415926535897 9323846264338 3279502884197 1693993751058 2097494459230 7816406286208 9986280348253 4211706798214 8086513282306 6470938446095 5058223172535 9408128481117 4502841027019 3852110555964 4622948954930 3819644288109 7566593344612 8475648233786 7831652712019 0914564856692 3460348610454 3266482133936 0726024914127 3724587006606 3155881748815 2092096282925 4091715364367 8925903600113 3053054882046 6521384146951 9415116094330 5727036575959 1953092186117 3819326117931 0511854807446 2379962749567 3518857527248 9122793818301 1949129833673 3624406566430 8602139494639 5224737190702 1798609437027 7053921717629 3176752384674 8184676694051 3200056812714 5263560827785 7713427577896 0917363717872 1468440901224 9534301465495 8537105079227 9689258923542 0199561121290 2196086403441 8159813629774 7713099605187 0721134999999
2001
Read more and buy the poster and T-Shirts at MayanPeriodic.com.
2001
A Vertical Periodic Table, in part shown below, is from apsidium.com:
2003
Philip Stewart’s Chemical Galaxy II periodic table formulation, from here:
Click here for a larger version.
A simplified ‘chemical galaxy’:
2003
A Physicist’s Periodic Table by Timothy Stowe, click here for a live web version.
2003
John Denker fully discusses the logic behind a three dimensional periodic table that he describes as a “cylinder with bulges”, here:
2003
Kimyaokulu Periodic Table
There is no longer anything about this periodic table on the web, but Philip Stewart says that the formulation should be attributed to John D Clark (1950):
2003
Elephant Periodic Table
The periodic table does not map to an elephant very well:

Click on the poster below to go to a large version:
2004
Rafael Poza Periodic Table (Click to Enlarge)
2004
Monument to the Periodic Table
Monument to the periodic table, in front of the Faculty of Chemical and Food Technology of the Slovak University of Technology in Bratislava, Slovakia. The monument honors Dmitri Mendeleev.
2005
Michael Laing’s ‘Revised periodic table with the lanthanides repositioned’ from Foundations of Chemistry 7:203-233:
Philip Stewart’s modification of the Laing formulation:
Philip Stewart says (personal communication): “It seems wrong to suggest an analogy between Pr to Sm and Dy to Tm with the V, Cr, Mn, Fe groups. I have pushed them to the right to suggest that those lanthanides are like the old group VIII (including the coinage metals); like them they cannot use all their outer electrons in bonding (with the exception of Ru viii and Os viii. I have treated the actinides differently to take account of Pa v and U vi. It’s ability to lose the juxtaposition of Tc and Pm, but it is physical rather than chemical anyway.”
2005
The Cyclical Continuum of Elemental Properties Periodic Table by Robert R. Northup
“The Cyclical Continuum of Elemental Properties is a user-friendly teaching tool that is intended to accompany the Periodic Table of Elements. Hydrogen is shown at the center, atomic numbers and symbols form an unbroken spiral, and element groups 1 through 18 (noble gases, alkali metals, halogens, etc.) are displayed by colored arcs. Beginning chemistry students can visually see the continuity of atomic numbers in the Cyclical Continuum as a way to introduce and orient them to the Periodic Table. Advanced chemistry students can test their understanding of the Periodic Table’s organization by applying that knowledge to interpretation of the Cyclical Continuum.”
Read more and buy the poster at the Cyclical Continuum web site.
2005
A periodic table that gives a representation of the electron orbitals that look like flowers:
2006
There are four possible positions for hydrogen:
- A Group 1 element, above Li, because it forms H+ ions.
- A Group 17 element, above F, because it forms H- ions.
- Above and between boron and carbon because it is of intermediate electronegativity.
- In the top middle, because nowhere else is ideal.

2006
Eric Scerri’s Periodic Table (2006):
Eric Scerri says, “I have recently developed a new periodic table with some very nice features. I am now shifting my allegiance from the left-step table to this one.”
- New design based on the fundamental nature of triads, and on atomic number triads in particular.
- H,F,Cl is a new perfect atomic number triad not featured in the usual medium-long form table. There are also many chemical arguments for placing H among the halogens rather than the alkalis.
- Note the regularity regarding period lengths. 8, 8, 18, 18, 32, 32 …
- All period lengths repeat without fail, unlike in the medium-long form.
- Also note the bi-lateral symmetry assuming the rare earths are given as a footnote.
Read the paper on the philosophy of science web site.
Eric Scerri, The Periodic Table: Its Story and Its Significance, Oxford University Press, 2006. Read an interview with the author, here, and a review of the book here.
2006
ADOMAH Periodic Table by Valery Tsimmerman
The ADOMAH periodic table is based on the Janet or left-step periodic table. It consists of four blocks (s, p, d & f) corresponding to quantum numbers l = 0,1,2,3. Blocks are separated, shifted and reconnected with each other via diagonal lines. This arrangement creates “layers” or “strata” that retain continuity in respect to atomic number Z, in addition to usual columns and rows. Therefore, numbers shown on the right hand side of the table may represent either quantum numbers n (electronic shells) if horizontal rows are followed, or n + l if “layers” or “strata” are followed.
This feature assists in creation of electronic configurations of the elements. Elements H and He are placed in two positions that reflect their dual nature and give proper consideration to atomic structure and chemical properties of those two elements. This feature also preserves triads He, Ne, Ar and H, F, Cl. Also, the elements are placed in rectangular “boxes”, so any two of such “boxes” make up a square thus symbolising electron pairs. This also cuts table length in half. Unlike the Janet table, this table is assembled from bottom up in direction of increase of quantum number n, as well as atomic weight and energy. The ADOMAH table has symmetry and, assuming total number of elements 120, can be divided in four parts of 30 elements with center point located among precious metals. Valery Tsimmerman, P.E.
A rotation of the ADOMAH formulation by Valery Tsimmerman from here which he calls the Perfect Periodic Table:
2006
The Wikipedia Alternative Periodic Table
On the Wikipedia there is another circular form of periodic table:
2006
Spiral Periodic Table found at periodicspiral.com. See an article in the New York Times.
2006
Henry Bent’s detailed exploration into the Left-Step formulation of the periodic table is available as a book:
2006
OK, So Which Is The Best Formulation of The Periodic Table?
Personally as a reaction chemist, my preferred periodic table is the ‘long’ form shown below, with hydrogen above and between boron and carbon, although clearly other scientists have other ideas.
All periodic tables show the increase in mass and atomic number, Z, but only the long form unambiguously shows the general top-right-to-bottom-left trends in electronegativity, atomic radius, metallic properties and first ionisation energy.
Electronegativity is absolutely crucial to the understanding of structure, bonding, material type (van Arkel-Ketelaar triangle and Laing tetrahedron) and chemical reactivity, and it underpins much of the chemogenesis analysis.
2006 Schemata of the Elements“The conventional periodic table reflects what is called the aufbau design, which represents a progression of numbers; in this case, that of the atomic number of the elements. The table, however, contradicts the aufbau concept in reality, because there are large gaps within among the primary (representative) elements, as well as in relation to the tertiary elements (transition and inner transition elements). The latter case, the Lanthanoids and the Actinoids, lie completely outside of the main body of the periodic table, thereby effectively breaking down the aufbau design… more…” from here by Charles William Johnson:
The Neutronic Schemata: Specialized Schemata of the Elements
2007
A new periodic table formulation by James Rota here.
2007
ADOMAH Tetrahedron
Valery Tsimmerman has developed various periodic table formulations, available at perfect perioidic table.com.

2007
Jelliss’ Periodic Table
Jelliss’ Periodic Table, more information here:
2007
Wikipedia Circular Periodic Table of The Elements
Wikipedia circular periodic table of the elements here:
2007
The Gyroscopic Periodic Table
From the Garuda Biodynamics web site: “The Gyroscopic Periodic Table has been a natural progression developed from a study of Soil Science, Dr Steiner’s Agriculture and Medical Courses, Astronomy and Astrology.”



2007
Second Life Periodic Table
From the Useful Chemistry blog: “Further adding to the set of chemistry tools in Second Life, Hiro Sheridan has created a 3D periodic table with rotating atoms. Although not directly proportional, the relative sizes of the spheres are in the correct order. Clicking on them provides basic information about the corresponding element. The 3D periodic table is available on the Chemistry Corner on Drexel Island.”
2008
Rafael Poza’s Elements and the Magnetosphere
2008
Bydgoszcz’s Periodic Table
Bydgoszcz’s Periodic Table, web site:
2008
Tomás A. Carroll’s Spherical & Russian Doll Formulations
Tomás A. Carroll has devised a spherical formulation of the Periodic Table, and from this a nested Russian Doll formulation.
Tomás writes: “I accept your veiled challenge that it is not possible to formulate a spherical periodic table and propose two solutions for your consideration. The EXCEL spreadsheet shows exactly how I transformed the quantum numbers from the standard 4D Cartesian coordinates to spherical coordinates in 3D, using two different centers. I included cylindrical coordinates too, just for fun.”


2008
Periodic Stack of Particles
Quantum Vectors and Atomic Stack Symmetry© (This page only renders properly in Explorer.)
The Janet Periodic Table of Elements (1929) may be re-arranged as a series of square matrices. The matrices are of different sizes and each matrix organizes the atomic orbitals into square concentric rings. Each cell may be assigned an atomic number which also identifies a “most significant electron”. The matrices may be stacked vertically to form “The Periodic Stack of Elements” as shown below.
The sub-atomic particles may also be arranged as square matrices. These matrices may be stacked to form “The Periodic Stack of Particles”.
Please send your comments to: doulting@shaw.ca Last Revision 21 April 2008.
2008
Angular Form of the Periodic Table by Kamal Akhtar
“The complete periodic table is consists of two circles, principal circle and auxiliary circle. The principal circle is consist of seven tracks (periods) and eighteen sectors (groups). The auxiliary circle is consist of only two tracks, inner track and outer track. There is no division of sectors in auxiliary circle.” Read more in a word.doc. View the full size PT.
KAMAL AKHTAR
INSTITUTE OF NICE TEACHING EDUCATION AND LEARNING
1, RAJ COLONY, BEHIND J.V. JAIN INTER COLLEGE
OLD KALSIA ROAD, SAHARANPUR-247001 (U.P.), INDIA
2008
Jan Scholten’s Periodic table (Spiral Format)
A spiral format periodic table by Jan Scholten:
2008
Spiral Postcard Periodic Table
A spiral periodic table avialable as a postcard by Vectoria:
2009
Russian Periodic Table
A modern Russian periodic table using the Mendeleeve formulation:





































