Log in

Relevant bibliographies by topics / Numbers and Geometry / Journal articles

To see the other types of publications on this topic, follow the link: Numbers and Geometry.

Journal articles on the topic 'Numbers and Geometry'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles

Select a source type:

Consult the top 50 journal articles for your research on the topic 'Numbers and Geometry.'

Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.

You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.

Browse journal articles on a wide variety of disciplines and organise your bibliography correctly.

1

Kock, Anders. "Differential Calculus and Nilpotent Real Numbers." Bulletin of Symbolic Logic 9, no. 2 (June 2003): 225–30. http://dx.doi.org/10.2178/bsl/1052669291.

Full text

Abstract:

Do there exist real numbers d with d2 = 0 (besides d = 0, of course)? The question is formulated provocatively, to stress a formalist view about existence: existence is consistency, or better, coherence.Also, the provocation is meant to challenge the monopoly which the number system, invented by Dedekind et al., is claiming for itself as THE model of the geometric line. The Dedekind approach may be termed “arithmetization of geometry”.We know that one may construct a number system out of synthetic geometry, as Euclid and followers did (completed in Hilbert's Grundlagen der Geometrie, [2, Chapter 3]): “geometrization of arithmetic”. (Picking two distinct points on the geometric line, geometric constructions in an ambient Euclidean plane provide structure of a commutative ring on the line, with the two chosen points as 0 and 1).Starting from the geometric side, nilpotent elements are somewhat reasonable, although Euclid excluded them. The sophist Protagoras presented a picture of a circle and a tangent line; the apparent little line segment D which tangent and circle have in common, are, by Pythagoras' Theorem, precisely the points, whose abscissae d (measured along the tangent) have d2 = 0. Protagoras wanted to use this argument for destructive reasons: to refute the science of geometry.A couple of millenia later, the Danish geometer Hjelmslev revived the Protagoras picture. His aim was more positive: he wanted to describe Nature as it was. According to him (or extrapolating his position), the Real Line, the Line of Sensual Reality, had many nilpotent infinitesimals, which we can see with our naked eyes.

APA, Harvard, Vancouver, ISO, and other styles

2

Bradley, C. J., and Liang-shin Hahn. "Complex Numbers and Geometry." Mathematical Gazette 79, no. 484 (March 1995): 237. http://dx.doi.org/10.2307/3620117.

Full text

APA, Harvard, Vancouver, ISO, and other styles

3

Hoare, Graham, C. D. Olds, Anneli Lax, and Giuliana P. Davidoff. "The Geometry of Numbers." Mathematical Gazette 86, no. 506 (July 2002): 368. http://dx.doi.org/10.2307/3621910.

Full text

APA, Harvard, Vancouver, ISO, and other styles

4

Kannan, R. "Algorithmic Geometry of Numbers." Annual Review of Computer Science 2, no. 1 (June 1987): 231–67. http://dx.doi.org/10.1146/annurev.cs.02.060187.001311.

Full text

APA, Harvard, Vancouver, ISO, and other styles

5

Siriwardene, Nihal. "Double numbers in geometry." Journal of the National Science Foundation of Sri Lanka 15, no. 2 (June 30, 1987): 209. http://dx.doi.org/10.4038/jnsfsr.v15i2.8295.

Full text

APA, Harvard, Vancouver, ISO, and other styles

6

Schlickewei, Hans Peter, and Wolfgang M. Schmidt. "Quadratic geometry of numbers." Transactions of the American Mathematical Society 301, no. 2 (February 1, 1987): 679. http://dx.doi.org/10.1090/s0002-9947-1987-0882710-3.

Full text

APA, Harvard, Vancouver, ISO, and other styles

7

Fei, S. M., H. Y. Guo, and Y. Yu. "Symplectic geometry and geometric quantization on supermanifold withU numbers." Zeitschrift für Physik C Particles and Fields 45, no. 2 (June 1989): 339–44. http://dx.doi.org/10.1007/bf01674466.

Full text

APA, Harvard, Vancouver, ISO, and other styles

8

Cleary, Joan, Sidney A. Morris, and David Yost. "Numerical Geometry-Numbers for Shapes." American Mathematical Monthly 93, no. 4 (April 1986): 260. http://dx.doi.org/10.2307/2323675.

Full text

APA, Harvard, Vancouver, ISO, and other styles

9

Cleary, Joan, Sidney A. Morris, and David Yost. "Numerical Geometry-Numbers for Shapes." American Mathematical Monthly 93, no. 4 (April 1986): 260–75. http://dx.doi.org/10.1080/00029890.1986.11971802.

Full text

APA, Harvard, Vancouver, ISO, and other styles

10

Harkin, Anthony A., and Joseph B. Harkin. "Geometry of Generalized Complex Numbers." Mathematics Magazine 77, no. 2 (April 2004): 118–29. http://dx.doi.org/10.1080/0025570x.2004.11953236.

Full text

APA, Harvard, Vancouver, ISO, and other styles

11

Yiu, Paul. "Geometry of sum-difference numbers." College Mathematics Journal 43, no. 5 (November 2012): 408–9. http://dx.doi.org/10.4169/college.math.j.43.5.408.

Full text

APA, Harvard, Vancouver, ISO, and other styles

12

Schmidt, Wolfgang M. "On parametric geometry of numbers." Acta Arithmetica 195, no. 4 (2020): 383–414. http://dx.doi.org/10.4064/aa190426-14-1.

Full text

APA, Harvard, Vancouver, ISO, and other styles

13

Dana-Picard, Thierry. "Complex numbers and plane geometry." International Journal of Mathematical Education in Science and Technology 34, no. 2 (January 2003): 257–71. http://dx.doi.org/10.1080/0020739031000158281.

Full text

APA, Harvard, Vancouver, ISO, and other styles

14

Series, Caroline. "The geometry of markoff numbers." Mathematical Intelligencer 7, no. 3 (September 1985): 20–29. http://dx.doi.org/10.1007/bf03025802.

Full text

APA, Harvard, Vancouver, ISO, and other styles

15

Shastri, Anant R. "Complex numbers and plane geometry." Resonance 13, no. 1 (January 2008): 35–53. http://dx.doi.org/10.1007/s12045-008-0005-1.

Full text

APA, Harvard, Vancouver, ISO, and other styles

16

Zong, Chuanming. "Geometry of Numbers in Vienna." Mathematical Intelligencer 31, no. 3 (May 20, 2009): 25–31. http://dx.doi.org/10.1007/s00283-009-9042-1.

Full text

APA, Harvard, Vancouver, ISO, and other styles

17

Schmidt, Wolfgang M., and Leonhard Summerer. "Parametric geometry of numbers and applications." Acta Arithmetica 140, no. 1 (2009): 67–91. http://dx.doi.org/10.4064/aa140-1-5.

Full text

APA, Harvard, Vancouver, ISO, and other styles

18

Lord, Nick, and Carl Ludwig Siegel. "Lectures on the Geometry of Numbers." Mathematical Gazette 75, no. 471 (March 1991): 123. http://dx.doi.org/10.2307/3619027.

Full text

APA, Harvard, Vancouver, ISO, and other styles

19

Muñoz Velázquez, Vicente. "The Hodge conjecture: The complications of understanding the shape of geometric spaces." Mètode Revista de difusió de la investigació, no. 8 (June 5, 2018): 51. http://dx.doi.org/10.7203/metode.0.8253.

Full text

Abstract:

The Hodge conjecture is one of the seven millennium problems, and is framed within differential geometry and algebraic geometry. It was proposed by William Hodge in 1950 and is currently a stimulus for the development of several theories based on geometry, analysis, and mathematical physics. It proposes a natural condition for the existence of complex submanifolds within a complex manifold. Manifolds are the spaces in which geometric objects can be considered. In complex manifolds, the structure of the space is based on complex numbers, instead of the most intuitive structure of geometry, based on real numbers.

APA, Harvard, Vancouver, ISO, and other styles

20

Atiyah, M. F., and N. S. Manton. "Complex geometry of nuclei and atoms." International Journal of Modern Physics A 33, no. 24 (August 30, 2018): 1830022. http://dx.doi.org/10.1142/s0217751x18300223.

Full text

Abstract:

We propose a new geometrical model of matter, in which neutral atoms are modelled by compact, complex algebraic surfaces. Proton and neutron numbers are determined by a surface’s Chern numbers. Equivalently, they are determined by combinations of the Hodge numbers, or the Betti numbers. Geometrical constraints on algebraic surfaces allow just a finite range of neutron numbers for a given proton number. This range encompasses the known isotopes.

APA, Harvard, Vancouver, ISO, and other styles

21

Mynard, Frédéric. "(Ultra-) completeness numbers and (pseudo-) paving numbers." Topology and its Applications 256 (April 2019): 86–103. http://dx.doi.org/10.1016/j.topol.2019.01.006.

Full text

APA, Harvard, Vancouver, ISO, and other styles

22

Girsh, A. "In Favor of Imaginaries in Geometry." Geometry & Graphics 8, no. 2 (August 17, 2020): 33–40. http://dx.doi.org/10.12737/2308-4898-2020-33-40.

Full text

Abstract:

“Complex numbers are something complicated”, as they are perceived in most cases. The expression “real numbers are also complex numbers” sounds strange as well. And for all that complex numbers are good for many areas of knowledge, since they allow solve problems, that are not solved in the field of real numbers. First and most important is that in the field of complex numbers all algebraic equations are solved, including the equation x2 + a = 0, which has long been a challenge to human thought. In the field of complex numbers, the problem solutions remain free from listing special cases in the form of "if ... then", for example, solving the problem for the intersection of the line g with the circle (O, r) always gives two points. And in the field of real numbers, three cases have to be distinguished: | Og | <r → there are two real points; | Og |> r → there is no intersection; | Og | = r → there is one double point. The benefit of complex numbers also lies in the fact that with their help not only problems that previously had no solutions are solved, they not only greatly simplify the solution result, but they also hold shown in this text further amazing properties in geometric figures, and open door to the amazing and colorful world of fractals.

APA, Harvard, Vancouver, ISO, and other styles

23

Fishburn, P. C., and W. V. Gehrlein. "Niche numbers." Journal of Graph Theory 16, no. 2 (June 1992): 131–39. http://dx.doi.org/10.1002/jgt.3190160204.

Full text

APA, Harvard, Vancouver, ISO, and other styles

24

Johnson, A., F. C. Holroyd, and S. Stahl. "Multichromatic numbers, star chromatic numbers and Kneser graphs." Journal of Graph Theory 26, no. 3 (November 1997): 137–45. http://dx.doi.org/10.1002/(sici)1097-0118(199711)26:3<137::aid-jgt4>3.0.co;2-s.

Full text

APA, Harvard, Vancouver, ISO, and other styles

25

Temirgaliyeva, Zh N., and N. Temirgaliyev. "“Geometry of Numbers” in a context of algebraic theory of numbers." Russian Mathematics 60, no. 10 (September 28, 2016): 77–81. http://dx.doi.org/10.3103/s1066369x16100133.

Full text

APA, Harvard, Vancouver, ISO, and other styles

26

Takahashi, Moto-o. "A theorem in the geometry of numbers." Tsukuba Journal of Mathematics 21, no. 2 (October 1997): 449–82. http://dx.doi.org/10.21099/tkbjm/1496163252.

Full text

APA, Harvard, Vancouver, ISO, and other styles

27

Keita, Aminata. "Continued fractions and Parametric geometry of numbers." Journal de Théorie des Nombres de Bordeaux 29, no. 1 (2017): 129–35. http://dx.doi.org/10.5802/jtnb.971.

Full text

APA, Harvard, Vancouver, ISO, and other styles

28

Kisil, Vladimir V. "Symmetry, Geometry and Quantization with Hypercomplex Numbers." Geometry, Integrability and Quantization 18 (2017): 11–76. http://dx.doi.org/10.7546/giq-18-2017-11-76.

Full text

APA, Harvard, Vancouver, ISO, and other styles

29

Ghate, Eknath, and Eriko Hironaka. "The arithmetic and geometry of Salem numbers." Bulletin of the American Mathematical Society 38, no. 03 (March 27, 2001): 293–315. http://dx.doi.org/10.1090/s0273-0979-01-00902-8.

Full text

APA, Harvard, Vancouver, ISO, and other styles

30

Stolarsky, Kenneth B. "$q$-analogue triangular numbers and distance geometry." Proceedings of the American Mathematical Society 125, no. 1 (1997): 35–39. http://dx.doi.org/10.1090/s0002-9939-97-03823-9.

Full text

APA, Harvard, Vancouver, ISO, and other styles

31

Alon, Noga, Gil Kalai, Jiřı́ Matoušek, and Roy Meshulam. "Transversal numbers for hypergraphs arising in geometry." Advances in Applied Mathematics 29, no. 1 (July 2002): 79–101. http://dx.doi.org/10.1016/s0196-8858(02)00003-9.

Full text

APA, Harvard, Vancouver, ISO, and other styles

32

KUBOTA, Tomio. "Geometry of numbers and class field theory." Japanese journal of mathematics. New series 13, no. 2 (1987): 235–75. http://dx.doi.org/10.4099/math1924.13.235.

Full text

APA, Harvard, Vancouver, ISO, and other styles

33

Rivard-Cooke, Martin, and Damien Roy. "Counter-examples in parametric geometry of numbers." Acta Arithmetica 196, no. 3 (2020): 303–23. http://dx.doi.org/10.4064/aa191217-9-4.

Full text

APA, Harvard, Vancouver, ISO, and other styles

34

Roy, Damien, and Michel Waldschmidt. "PARAMETRIC GEOMETRY OF NUMBERS IN FUNCTION FIELDS." Mathematika 63, no. 3 (January 2017): 1114–35. http://dx.doi.org/10.1112/s0025579317000237.

Full text

APA, Harvard, Vancouver, ISO, and other styles

35

Schmidt, Wolfgang M., and Leonhard Summerer. "Diophantine approximation and parametric geometry of numbers." Monatshefte für Mathematik 169, no. 1 (February 21, 2012): 51–104. http://dx.doi.org/10.1007/s00605-012-0391-z.

Full text

APA, Harvard, Vancouver, ISO, and other styles

36

Skriganov, M. M. "Brillouin zones and the geometry of numbers." Journal of Soviet Mathematics 36, no. 1 (January 1987): 140–54. http://dx.doi.org/10.1007/bf01104979.

Full text

APA, Harvard, Vancouver, ISO, and other styles

37

Goulden, I. P., D. M. Jackson, and R. Vakil. "Towards the geometry of double Hurwitz numbers." Advances in Mathematics 198, no. 1 (December 2005): 43–92. http://dx.doi.org/10.1016/j.aim.2005.01.008.

Full text

APA, Harvard, Vancouver, ISO, and other styles

38

Grama, Lino, Caio J. C. Negreiros, and Ailton R. Oliveira. "Invariant almost complex geometry on flag manifolds: geometric formality and Chern numbers." Annali di Matematica Pura ed Applicata (1923 -) 196, no. 1 (April 27, 2016): 165–200. http://dx.doi.org/10.1007/s10231-016-0568-5.

Full text

APA, Harvard, Vancouver, ISO, and other styles

39

Alon, Noga, Matija Bucić, Tom Kalvari, Eden Kuperwasser, and Tibor Szabó. "List Ramsey numbers." Journal of Graph Theory 96, no. 1 (June 27, 2020): 109–28. http://dx.doi.org/10.1002/jgt.22610.

Full text

APA, Harvard, Vancouver, ISO, and other styles

40

Chapman, Robin J., and Julie Haviland. "Generalized Rotation numbers." Journal of Graph Theory 17, no. 3 (July 1993): 291–301. http://dx.doi.org/10.1002/jgt.3190170304.

Full text

APA, Harvard, Vancouver, ISO, and other styles

41

Marko, František, and Semyon Litvinov. "Geometry of Figurate Numbers and Sums of Powers of Consecutive Natural Numbers." American Mathematical Monthly 127, no. 1 (December 19, 2019): 4–22. http://dx.doi.org/10.1080/00029890.2020.1671129.

Full text

APA, Harvard, Vancouver, ISO, and other styles

42

Flores, Alfinio. "A Rhythmic Approach to Geometry." Mathematics Teaching in the Middle School 7, no. 7 (March 2002): 378–83. http://dx.doi.org/10.5951/mtms.7.7.0378.

Full text

Abstract:

Several authors have used string designs to help students develop and understand mathematical ideas. Different aspects of this activity can be emphasized. First, students can focus on the beauty of the final string design, which in many instances, is related to mirror and rotational symmetries (Pohl 1986). Second, string designs can be used to highlight relations among such numbers as common factors, multiples, and prime numbers (Bennett 1981; Perl 1981). String designs can also give rise to interesting mathematical curves (Millington 1996), such as parabolas, pursuit curves, spirals, cardioids, and many more.

APA, Harvard, Vancouver, ISO, and other styles

43

Hrdina, Jaroslav, and Petr Vašík. "Dual Numbers Approach in Multiaxis Machines Error Modeling." Journal of Applied Mathematics 2014 (2014): 1–6. http://dx.doi.org/10.1155/2014/261759.

Full text

Abstract:

Multiaxis machines error modeling is set in the context of modern differential geometry and linear algebra. We apply special classes of matrices over dual numbers and propose a generalization of such concept by means of general Weil algebras. We show that the classification of the geometric errors follows directly from the algebraic properties of the matrices over dual numbers and thus the calculus over the dual numbers is the proper tool for the methodology of multiaxis machines error modeling.

APA, Harvard, Vancouver, ISO, and other styles

44

Lagodowski, Zbigniew A. "Strong Laws of Large Numbers for𝔹-Valued Random Fields." Discrete Dynamics in Nature and Society 2009 (2009): 1–12. http://dx.doi.org/10.1155/2009/485412.

Full text

Abstract:

We extend to random fields case, the results of Woyczynski, who proved Brunk's type strong law of large numbers (SLLNs) for𝔹-valued random vectors under geometric assumptions. Also, we give probabilistic requirements for above-mentioned SLLN, related to results obtained by Acosta as well as necessary and sufficient probabilistic conditions for the geometry of Banach space associated to the strong and weak law of large numbers for multidimensionally indexed random vectors.

APA, Harvard, Vancouver, ISO, and other styles

45

Gorodnik, Alexander, and Michael Björklund. "Central Limit Theorems in the geometry of numbers." Electronic Research Announcements in Mathematical Sciences 24 (October 2017): 110–22. http://dx.doi.org/10.3934/era.2017.24.012.

Full text

APA, Harvard, Vancouver, ISO, and other styles

46

Ge, Zhong. "Betti numbers, characteristic classes and sub-Riemannian geometry." Illinois Journal of Mathematics 36, no. 3 (September 1992): 372–403. http://dx.doi.org/10.1215/ijm/1255987416.

Full text

APA, Harvard, Vancouver, ISO, and other styles

47

Schrijver, A. "Graphs on the Torus and Geometry of Numbers." Journal of Combinatorial Theory, Series B 58, no. 1 (May 1993): 147–58. http://dx.doi.org/10.1006/jctb.1993.1033.

Full text

APA, Harvard, Vancouver, ISO, and other styles

48

German, Oleg N. "Intermediate Diophantine exponents and parametric geometry of numbers." Acta Arithmetica 154, no. 1 (2012): 79–101. http://dx.doi.org/10.4064/aa154-1-5.

Full text

APA, Harvard, Vancouver, ISO, and other styles

49

Zaripov, Rinat G. "Conformal Hyperbolic Numbers and Two-dimensional Finsler Geometry." Advances in Applied Clifford Algebras 27, no. 2 (May 24, 2016): 1741–60. http://dx.doi.org/10.1007/s00006-016-0680-z.

Full text

APA, Harvard, Vancouver, ISO, and other styles

50

Robert, A., and T. Debroy. "Geometry of laser spot welds from dimensionless numbers." Metallurgical and Materials Transactions B 32, no. 5 (October 2001): 941–47. http://dx.doi.org/10.1007/s11663-001-0080-0.

Full text

APA, Harvard, Vancouver, ISO, and other styles

We offer discounts on all premium plans for authors whose works are included in thematic literature selections. Contact us to get a unique promo code!