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Relevant bibliographies by topics / Doubling a cube

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Academic literature on the topic 'Doubling a cube'

Author: Grafiati

Published: 4 June 2021

Last updated: 15 February 2022

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Journal articles on the topic "Doubling a cube"

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Rmus, Veselin. "Constructions of squaring the circle, doubling the cube and angle trisection." Vojnotehnicki glasnik 65, no. 3 (2017): 617–40. http://dx.doi.org/10.5937/vojtehg65-13404.

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Radhiah, Radhiah. "Two Celebrated Classical Problems in Geometric Constructions." Jurnal Matematika, Statistika dan Komputasi 17, no. 1 (2020): 135–44. http://dx.doi.org/10.20956/jmsk.v17i1.9135.

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The main topic of this paper is about two celebrated classical problems in geometric constructions where the only allowed instruments are compass and ruler with no scale. Two such problems are (1) trisecting an angle, and (2) doubling the cube. In addition, we also study about the construction of 7-gon and 10-gon.

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Masià, Ramon. "A new reading of Archytas’ doubling of the cube and its implications." Archive for History of Exact Sciences 70, no. 2 (2015): 175–204. http://dx.doi.org/10.1007/s00407-015-0165-9.

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4

Yang, Dachun, and Dongyong Yang. "BMO-Estimates for Maximal Operators via Approximations of the Identity with Non-Doubling Measures." Canadian Journal of Mathematics 62, no. 6 (2010): 1419–34. http://dx.doi.org/10.4153/cjm-2010-065-7.

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AbstractLet μ be a nonnegative Radon measure on ℝd that satisfies the growth condition that there exist constants C0 > 0 and n ∈ (0, d] such that for all x ∈ ℝd and r > 0, μ(B(x, r)) ≤ C0rn, where B(x, r) is the open ball centered at x and having radius r. In this paper, the authors prove that if f belongs to the BMO-type space RBMO(μ) of Tolsa, then the homogeneous maximal function S( f ) (when ℝd is not an initial cube) and the inhomogeneous maximal function ℳS( f ) (when ℝd is an initial cube) associated with a given approximation of the identity S of Tolsa are either infinite everywh

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5

Saito, Ken. "Doubling the cube: A new interpretation of its significance for early greek geometry." Historia Mathematica 22, no. 2 (1995): 119–37. http://dx.doi.org/10.1006/hmat.1995.1013.

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6

Yang, Dachun, and Dongyong Yang. "Endpoint estimates for homogeneous Littlewood-Paleyg-functions with non-doubling measures." Journal of Function Spaces and Applications 7, no. 2 (2009): 187–207. http://dx.doi.org/10.1155/2009/284849.

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Letµbe a nonnegative Radon measure on ℝdwhich satisfies the growth condition that there exist constantsC0> 0 andn∈ (0, d] such that for allx∈ ℝdand r > 0,μ(B(x,r))≤C0rn, whereB(x, r) is the open ball centered atxand having radiusr. In this paper, when ℝdis not an initial cube which impliesµ(ℝd) = ∞, the authors prove that the homogeneous Littlewood-Paleyg-function of Tolsa is bounded from the Hardy spaceH1(µ) toL1(µ), and furthermore, that iff∈ RBMO (µ), then [ġ(f)]2is either infinite everywhere or finite almost everywhere, and in the latter case, [ġ(f)]2belongs to RBLO (µ) with norm no

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Gevorgyan, H. "PROOF OF THE IMPOSSIBILITY OF THE PERFECT CUBOID EXISTENCE." East European Scientific Journal 1, no. 6(70) (2021): 42–45. http://dx.doi.org/10.31618/essa.2782-1994.2021.1.70.70.

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The problem of finding, among the Euler parallelepipeds, one with an integer spatial diagonal, called the perfect cuboid problem, is one of the unsolved mathematical problems from the section of number theory. This article provides mathematical proof of the impossibility of the existence of the perfect cuboide among all possible Euler parallelepipeds. A mathematical justification for an equivalence of the problem of doubling a cube and the problem of constructing a perfect cuboid is also given.

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8

Evered, Lisa. "Tape Constructions." Mathematics Teacher 80, no. 5 (1987): 353–56. http://dx.doi.org/10.5951/mt.80.5.0353.

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Construction problems long have been a favorite subject in geometry. Indeed, students find constructions a welcome diversion from the formal deductive approach to geometry. In classical construction problems only the use of ruler and compass is allowed, and the ruler is used merely as a straightedge, not for measuring or marking off distances. This restriction to ruler and compass goes back to antiquity. The Greeks, however, did not hesitate to use other instruments when the need arose. For example, a ruler in the form of a right angle was used to solve certain problems such as “doubling the c

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9

Rungtanapirom, Nithi, Jakob Stix, and Alina Vdovina. "Infinite series of quaternionic 1-vertex cube complexes, the doubling construction, and explicit cubical Ramanujan complexes." International Journal of Algebra and Computation 29, no. 06 (2019): 951–1007. http://dx.doi.org/10.1142/s0218196719500371.

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We construct vertex transitive lattices on products of trees of arbitrary dimension [Formula: see text] based on quaternion algebras over global fields with exactly two ramified places. Starting from arithmetic examples, we find non-residually finite groups generalizing earlier results of Wise, Burger and Mozes to higher dimension. We make effective use of the combinatorial language of cubical sets and the doubling construction generalized to arbitrary dimension. Congruence subgroups of these quaternion lattices yield explicit cubical Ramanujan complexes, a higher-dimensional cubical version o

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Lamb, John F., Farhad Aslan, Ramona Chance, and Jerry D. Lowe. "Inscribing an “Approximate” Nonagon in a Circle." Mathematics Teacher 84, no. 5 (1991): 396–98. http://dx.doi.org/10.5951/mt.84.5.0396.

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Throughout history even the best mathematicians have been challenged by certain problems. Indeed, some of these problems became famous because they defied solution. Many students of mathematics are familiar with the problems of squaring a circle, doubling the cube, and trisecting an angle. Some may have studied the problem of inscribing regular polygons with a given number of sides in a circle. A few of these polygons, such as those with three sides, four sides, six sides, and eight sides, are easily inscribed. Other such constructions are more involved but are still possible, such as those in

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Dissertations / Theses on the topic "Doubling a cube"

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Sabir, Tanveer, and Aamir Muneer. "Geometrical Constructions : Trisecting the Angle, Doubling the Cube, Squaring the Circle and Construction of n-gons." Thesis, Växjö University, School of Mathematics and Systems Engineering, 2009. http://urn.kb.se/resolve?urn=urn:nbn:se:vxu:diva-5401.

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Filho, Luiz EfigÃnio da Silva. "CÃnicas : apreciando uma obra-prima da matemÃtica." Universidade Federal do CearÃ, 2015. http://www.teses.ufc.br/tde_busca/arquivo.php?codArquivo=14729.

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Neste trabalho abordaremos alguns assuntos relacionados Ãs SeÃÃes CÃnicas: elipse, parÃbola e hipÃrbole. O trabalho estÃ dividido em cinco capÃtulos: IntroduÃÃo; Origem das CÃnicas; EquaÃÃes das CÃnicas; Propriedades de ReflexÃo das CÃnicas; Construindo CÃnicas. No segundo capÃtulo, falaremos sobre o problema da duplicaÃÃo do cubo que, segundo a HistÃria da MatemÃtica, deu origem as cÃnicas e citaremos alguns matemÃticos cujos trabalhos contribuÃram para o desenvolvimento do estudo dessas curvas. No terceiro capÃtulo, estudaremos as equaÃÃes cartesianas das cÃnicas, bem como as suas representa

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Fabián, Tomáš. "Algebraické křivky v historii a ve škole." Master's thesis, 2016. http://www.nusl.cz/ntk/nusl-346770.

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TITLE: Agebraic Curves in History and School AUTHOR: Bc. Tomáš Fabián DEPARTMENT: The Department of mathematics and teaching of mathematics SUPERVISOR: prof. RNDr. Ladislav Kvasz, Dr. ABSTRACT: The thesis includes a series of exercises for senior high school students and the first year of university students. In these exercises, students will increase their knowledge about conics, especially how to draw them. Furthermore, students can learn about two unfamiliar curves: Conchoid and Quadratrix. All these curves are afterwards used for solving other problems - some Apollonius's problems, Three i

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Fabián, Tomáš. "Algebraické křivky v historii a ve škole." Master's thesis, 2015. http://www.nusl.cz/ntk/nusl-349422.

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TITLE: Agebraic Curves in History and School AUTHOR: Bc. Tomáš Fabián DEPARTMENT: The Department of mathematics and teaching of mathematics SUPERVISOR: prof. RNDr. Ladislav Kvasz, Dr. ABSTRACT: The thesis includes a series of exercises for senior high school students and the first year of university students. In these exercises, students will increase their knowledge about conics, especially how to draw them. Furthermore, students can learn about two unfamiliar curves: Conchoid and Quadratrix. All these curves are afterwards used for solving other problems - some Apollonius's problems, Three i

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Books on the topic "Doubling a cube"

1

Bell, Peter. Backgammon: Winning With the Doubling Cube. The Gammon Press, 1997.

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Book chapters on the topic "Doubling a cube"

1

"Doubling the Cube." In Beautiful Geometry. Princeton University Press, 2014. http://dx.doi.org/10.2307/j.ctt4cgb6n.29.

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"Doubling the Cube." In Tales of Impossibility. Princeton University Press, 2019. http://dx.doi.org/10.2307/j.ctvfrxrpr.13.

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"25. Doubling the Cube." In Beautiful Geometry. Princeton University Press, 2014. http://dx.doi.org/10.1515/9781400848331-026.

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"CHAPTER 5. Doubling the Cube." In Tales of Impossibility. Princeton University Press, 2019. http://dx.doi.org/10.1515/9780691194233-007.

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5

"All About the Doubling of the Cube." In Mathematics and Philosophy. John Wiley & Sons, Inc., 2018. http://dx.doi.org/10.1002/9781119426813.ch2.

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Conference papers on the topic "Doubling a cube"

1

Petrillo, Karen, Matthew Colburn, Shannon Dunn, Dave Hetzer, Tom Winter, and Satoru Shimura. "Investigation of lithographic feature characteristics using UV cure as a pitch doubling stabilization technology for the 32nm node and beyond." In SPIE Advanced Lithography, edited by Daniel J. C. Herr. SPIE, 2010. http://dx.doi.org/10.1117/12.846624.

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