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Studia Scientiarum Mathematicarum Hungarica
Volume/Issue:
Volume 46: Issue 2
DOI:
https://doi.org/10.1556/sscmath.46.2009.2.1083
Author:
Janusz Januszewski

Any sequence of triangles homothetic to a fixed triangle T whose total area does not exceed one-half of the area of T can be packed translatively in T .

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Studia Scientiarum Mathematicarum Hungarica
Volume/Issue:
Volume 45: Issue 3
DOI:
https://doi.org/10.1556/sscmath.2008.1068
Authors:
Marek Lassak
and
Joanna Ściesińska
We consider packing a triangle with a number of equal positive homothetical copies. In particular, we show that every triangle can be packed with 7 copies of ratio
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\tfrac{2}{7}$$ \end{document}
, with 8 copies of ratio
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\tfrac{3}{{11}}$$ \end{document}
, and with 9 and 10 copies of ratio
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\tfrac{1}{4}$$ \end{document}
. All these ratios cannot be enlarged. We also present hypothetically best packings by greater number of copies.
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Periodica Mathematica Hungarica
Volume/Issue:
Volume 46: Issue 1
DOI:
https://doi.org/10.1023/a:1025753707977
Author:
Janusz Januszewski
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Acta Mathematica Hungarica
Volume/Issue:
Volume 125: Issue 3
DOI:
https://doi.org/10.1007/s10474-009-9015-z
Author:
J. Januszewski

Abstract  

An equilateral triangle T e of sides 1 can be parallel covered with any sequence of squares whose total area is not smaller than 1:5. Moreover, any sequence of squares whose total area does not exceed
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\frac{3} {4}(2 - \sqrt 3 )$$ \end{document}
(2 − √3) can be parallel packed into T e .
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Mathematica Pannonica
Volume/Issue:
Volume 28_NS2: Issue 1
DOI:
https://doi.org/10.1556/314.2022.00001
Authors:
Zdenka Kolar-Begović
and
Vladimir Volenec

), 125 – 132 . [2] Beban-Brkić , J ., Kolar-Šuper , R ., Kolar-Begović , Z ., and Volenec , V . Gergonne’s point of a triangle in I 2 . Rad Hrvat. Akad. Znan. Umjet . 515 , 2 ( 2013 ), 95 – 106 . [3] Fontene , G

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Studia Scientiarum Mathematicarum Hungarica
Volume/Issue:
Volume 61: Issue 2
DOI:
https://doi.org/10.1556/012.2024.04313
Authors:
Zhanjun Su
and
Yufang Wu

REFERENCES [1] J . Januszewski . Translative covering by sequences of homothetic copies . Acta Math. Hungar ., 91 ( 4 ): 337 – 342 , 2001 . [2] J . Januszewski . Parallel packing and covering of an equilateral triangle with sequences of

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Nanopages
Volume/Issue:
Volume 7: Issue 1
DOI:
https://doi.org/10.1556/Nano.2010.00001
Authors:
Gergely Dobrik
,
Levente Tapasztó
, and
László Biró

In this article, we present a method, which is suitable for the realization of graphene-based nanostructures by scanning tunneling microscopy lithography. Graphene nanoribbons (GNRs) and other more complicated nanoarchitectures like: GNR networks, triangular quantum-billiards, etc. can be created with controlled shape and crystallographic orientation. The cutting process operates with nanometer accuracy. After the lithography process the same STM tip is suitable for acquiring atomic resolution images on the nanoarchitectures created by STM lithography. The experimental observation of long range electronic superstructures indicates the long phase coherence length in graphene nanostructures even at room temperature.

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Periodica Mathematica Hungarica
Volume/Issue:
Volume 60: Issue 1
DOI:
https://doi.org/10.1007/s10998-010-1049-z
Authors:
Keunbae Choi
and
Yongdo Lim

Abstract  

The purpose of this paper is to describe the structures of the Möbius semigroup induced by the Möbius transformation group (ℝ, SL(2,ℝ)). In particular, we study stabilizer subsemigoups of Möbius semigroup via the triangle semigroup. In this work, we obtained a geometric interpretation of the least contraction coefficient function of the Möbius semigroup via the triangle semigroup and investigated an extension of stabilizer subsemigoups of the Möbius semigroup. Finally, we obtained a factorization of our stabilizer subsemigoups of the Möbius semigroup.

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Periodica Mathematica Hungarica
Volume/Issue:
Volume 53: Issue 1-2
DOI:
https://doi.org/10.1007/s10998-006-0030-3
Authors:
Dan Ismailescu
and
Jacqueline Jacobs

Summary  

For a given triangle, we consider several sequences of nested triangles obtained via iterative procedures. We are interested in the limiting behavior of these sequences. We briefly mention the relevant known results and prove that the triangle determined by the feet of the angle bisectors converges in shape towards an equilateral one. This solves a problem raised by Trimble~[5].

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Interventional Medicine and Applied Science
Volume/Issue:
Volume 7: Issue 1
DOI:
https://doi.org/10.1556/imas.7.2015.1.4
Authors:
Jakub Kaczynski
and
Joanna Hilton

74 961 966 Sekimoto M, Tomita N, Tamura S, Ohsato H, Monden M: New retraction technique to allow better visualization of Calot’s triangle during

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