By M. Jacob, S. Andersson,
Chemistry, physics and biology are through their nature surely tough. arithmetic, in spite of the fact that, is man-made, and accordingly now not as complex. rules shape the root for this publication: 1) to take advantage of traditional arithmetic to explain the simplicity within the constitution of arithmetic and a pair of) to improve new branches of arithmetic to explain typical sciences.Mathematics may be defined because the addition, subtraction or multiplication of planes. utilizing the exponential scale the authors exhibit that the addition of planes supplies the polyhedra, or any stable. The substraction of planes supplies saddles. The multiplication of planes supplies the final saddle equations and the multispirals. The equation of symmetry is derived, which incorporates the exponential scale with its features for solids, the advanced exponentials with the nodal surfaces, and the GD (Gauss Distribution) arithmetic with finite periodicity.Piece by way of piece, the authors have discovered mathematical features for the geometrical descriptions of chemical constructions and the constitution development operations. utilizing the maths for dilatation; twins, trillings, fourlings and sixlings are made, and utilizing GD arithmetic those are made periodic. This description of a constitution is the character of arithmetic itself. Crystal constructions and 3D arithmetic are synonyms. arithmetic are used to explain rod packings, Olympic jewelry and defects in solids. immense molecules akin to cubosomes, the DNA double helix, and sure construction blocks in protein buildings also are defined mathematically.
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Extra resources for The Nature of Mathematics and the Mathematics of Nature
Example text
7. b. 5)(z + 2 . 5) - 0 The result is below and the similarity with the screw surface as calculated from the circular function is extraordinary, as the reader may find out for himself. Fig. 5. Chapter 2 36 Fig. 6. Fig. a. Fig. b. The Roots o f Mathematics - the Roots o f Structure Fig. c. 37 38 Chapter 2 References 2 D'Arcy Wentworth Thompson, ON GROWTH AND FORM,, Cambridge University press, 1942, page 2. H. Hardy, PURE MATHEMATICS, Cambridge University press, 1975. G. Hyde and S. Andersson, INORGANIC CRYSTAL STRUCTURES, Wiley, New York, 1988.
H. Hardy, PURE MATHEMATICS, Cambridge University press, 1975. G. Hyde and S. Andersson, INORGANIC CRYSTAL STRUCTURES, Wiley, New York, 1988. S. Jacob, THE MATHEMATICS OF STRUCTURES, THE EXPONENTIAL SCALE, Oldenbourg, Mtinchen, 1997. A. Burkhardt, U. G. von Schnering and A. Savin, Z. anorg. allg. Chem. 619 (1993) 437. G. von Schnering and R. Nesper, Z Phys. B - Condensed Matter 83 (1991) 407. U. Dierkes, S. Hildebrandt, A. Kuster and O. Wohlrab, MINIMAL SURFACES 1 and 2, Springer Verlag, Berlin, 1991.
I 2 3 Fig. 5. 7. -3 ............................... -3 -2 -I 0 1 2 3 Fig. 6. 8. We add two more lines to eq. 7 and 8. By calculating curvature (see Appendix 4) of the square comer we find it approaches a constant value of '42/2 with size; it is the size difference that makes the square in fig. 8 having sharper comers. 10 of a tangent truncates the square in fig. 9. Chapter 3 42 By subtracting the tangent we open the square as in fig. 10 and by adding all the tangents we get the formidable octagon in fig.