scholarly journals Erratum for “The Calculating Machine in Coordinate Geometry”

1960 ◽  
Vol 86 (2) ◽  
pp. 47-48
Author(s):  
B. Vadasz
Keyword(s):  
Coordinate Geometry

scholarly journals Vector Arithmetic in the Triangular Grid

Entropy ◽  
2021 ◽  
Vol 23 (3) ◽  
pp. 373
Author(s):  
Khaled Abuhmaidan ◽  
Monther Aldwairi ◽  
Benedek Nagy
Keyword(s):  
Coordinate System ◽  
Triangular Grid ◽  
Vector Addition ◽  
Plane Space ◽  
Physical Simulations ◽  
Rectangular Grids ◽  
Cartesian Coordinate ◽  
Zero Sum ◽  
Coordinate Geometry ◽  
Point Lattice

Vector arithmetic is a base of (coordinate) geometry, physics and various other disciplines. The usual method is based on Cartesian coordinate-system which fits both to continuous plane/space and digital rectangular-grids. The triangular grid is also regular, but it is not a point lattice: it is not closed under vector-addition, which gives a challenge. The points of the triangular grid are represented by zero-sum and one-sum coordinate-triplets keeping the symmetry of the grid and reflecting the orientations of the triangles. This system is expanded to the plane using restrictions like, at least one of the coordinates is an integer and the sum of the three coordinates is in the interval [−1,1]. However, the vector arithmetic is still not straightforward; by purely adding two such vectors the result may not fulfill the above conditions. On the other hand, for various applications of digital grids, e.g., in image processing, cartography and physical simulations, one needs to do vector arithmetic. In this paper, we provide formulae that give the sum, difference and scalar product of vectors of the continuous coordinate system. Our work is essential for applications, e.g., to compute discrete rotations or interpolations of images on the triangular grid.

Regulating catalytic activity of multi-Ru-bridged polyoxometalate based on active sites differential environment with six-coordinate geometry and five-coordinate geometry transition

Nanoscale ◽  
2021 ◽  
Author(s):  
Jingyang Niu ◽  
Huafeng Li ◽  
Wenjing Chen ◽  
Yujie Zhao ◽  
Yan Zhou ◽  
...  
Keyword(s):  
Catalytic Activity ◽  
Active Sites ◽  
Coordinate Geometry

Five-coordinate geometry around ruthenium with highly exposed active sites have attracted intensive scientific interests due to their superior properties and extensive applications. Herein, we report a series of structurally controllable...

Consequences of a Linear Two-Coordinate Geometry for the Orbital Magnetism and Jahn−Teller Distortion Behavior of the High Spin Iron(II) Complex Fe[N(t-Bu)2]2

2009 ◽  
Vol 131 (2) ◽  
pp. 404-405 ◽  
Author(s):  
William M. Reiff ◽  
Charles E. Schulz ◽  
Myung-Hwan Whangbo ◽  
Jung In Seo ◽  
Yoon Sup Lee ◽  
...  
Keyword(s):  
High Spin ◽  
Teller Distortion ◽  
Orbital Magnetism ◽  
Jahn Teller ◽  
Jahn Teller Distortion ◽  
Coordinate Geometry ◽  
High Spin Iron

[Zn(phen)2(CX3COO)]+, X = H orCl; Influence of X on the Coordination Mode of the Carboxylate Group (phen = 1,10-Phenanthroline)

2005 ◽  
Vol 60 (10) ◽  
pp. 1049-1053 ◽  
Author(s):  
Zeanab Talaei ◽  
Ali Morsali ◽  
Ali R. Mahjoub
Keyword(s):  
Nmr Spectroscopy ◽  
Elemental Analysis ◽  
Coordination Mode ◽  
Bidentate Ligand ◽  
Carboxylate Group ◽  
X Ray ◽  
X Ray Crystallography ◽  
H Nmr ◽  
Coordinate Geometry ◽  
C Nmr

Two new ZnII(phen)2 complexes with trichloroacetate and acetate anions, [Zn(phen)2(CCl3COO)- (H2O)](ClO4) and [Zn(phen)2(CH3COO)](ClO4), have been synthesized and characterized by elemental analysis, IR, 1H NMR, 13C NMR spectroscopy. The single crystal X-ray data of these compounds show the Zn atoms to have six-coordinate geometry. From IR spectra and X-ray crystallography it is established that the coordination of the COO− group is different for trichloroacetate and acetate. The former acts as a monodentate whereas the latter acts as a bidentate ligand.

scholarly journals Crystal structure of poly[diaquabis(μ5-benzene-1,3-dicarboxylato)(N,N-dimethylformamide)cadmium(II)disodium(I)]

2017 ◽  
Vol 73 (11) ◽  
pp. 1599-1602 ◽  
Author(s):  
Matimon Sangsawang ◽  
Kittipong Chainok ◽  
Nanthawat Wannarit
Keyword(s):  
Crystal Structure ◽  
Coordination Polymer ◽  
Hydrogen Bonds ◽  
Three Dimensional ◽  
Water Molecules ◽  
Asymmetric Unit ◽  
Carboxylate Groups ◽  
Benzene Rings ◽  
Coordinated Water ◽  
Coordinate Geometry

The title compound, [CdNa2(C8H4O4)2(C3H7NO)(H2O)2]nor [CdNa2(1,3-bdc)2(DMF)(H2O)2]n, is a new CdII–NaIheterobimetallic coordination polymer. The asymmetric unit consists of one CdIIatom, two NaIatoms, two 1,3-bdc ligands, two coordinated water molecules and one coordinated DMF molecule. The CdIIatom exhibits a seven-coordinate geometry, while the NaIatoms can be considered to be pentacoordinate. The metal ions and their symmetry-related equivalents are connectedviachelating–bridging carboxylate groups of the 1,3-bdc ligands to generate a three-dimensional framework. In the crystal, there are classical O—H...O hydrogen bonds involving the coordinated water molecules and the 1,3-bdc carboxylate groups and π–π stacking between the benzene rings of the 1,3-bdc ligands present within the frameworks.

scholarly journals Crystal structure of chloridobis[(1,2,5,6-η)-cycloocta-1,5-diene]iridium(I)

2017 ◽  
Vol 73 (2) ◽  
pp. 273-277 ◽  
Author(s):  
A. K. Fazlur Rahman ◽  
Miles Wilklow-Marnell ◽  
William W. Brennessel ◽  
William D. Jones
Keyword(s):  
Title Complex ◽  
Asymmetric Unit ◽  
Large Excess ◽  
Orthorhombic Space Group ◽  
Slow Cooling ◽  
Hexagonal Packing ◽  
Trigonal Bipyramidal ◽  
Chloride Ligand ◽  
Packing Arrangement ◽  
Coordinate Geometry

The title complex, [IrCl(C8H12)2], was synthesized directly from the reaction of IrCl3·3H2O with a large excess of cod (cod = cycloocta-1,5-diene) in alcoholic solvent. Large yellow needles were obtained by the slow cooling of a hot solution. Based on the positions of the chloride ligand and the mid-points of the four C=C bonds, the molecule adopts a five-coordinate geometry that is midway between square pyramidal and trigonal bipyramidal. The material crystallizes in the orthorhombic space groupPbcawith one molecule per asymmetric unit in a general position and shows no significant intermolecular interactions. Individual molecules are aligned along [010], and these rows form a pseudo-hexagonal packing arrangement.

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