Variations on the arbelos

• Autorzy: Różański M. , Samulewicz A. , Szweda M. , Wituła R.

Identyfikatory

DOI

10.17512/jamcm.2017.2.10

• Języki publikacji: EN

Abstrakty

EN

We recall the ancient notion of arbelos and introduce a number of concepts generalizing it. We follow the ideas presented by J. Sondow in his article on parbelos, the parabolic analogue of the classic arbelos. Our concepts concern the curves constructed of arcs which resemble each other and surfaces obtained in a similar way. We pay special attention to ellarbelos, the curves built of semi-ellipses, because of their possible application in engineering, e.g. in determining the static moments of arc rod constructions or in problems of structural stability and durability of constructions.

Słowa kluczowe

EN

arbelos; parbelos; similarity; ellarbelos; F-arbelos

PL

arbelos; parbelos; ellarbelos; F-arbelos; podobieństwo

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Journal of Applied Mathematics and Computational Mechanics
• Rocznik: 2017
• Tom: Vol. 16, nr 2
• Strony: 123--133
• Opis fizyczny: Bibliogr. 9 poz., rys.

Twórcy

autor

Różański M.

• Institute of Mathematics, Silesian University of Technology Gliwice, Poland

autor

Samulewicz A.

• Institute of Mathematics, Silesian University of Technology Gliwice, Poland

autor

Szweda M.

• Institute of Mathematics, Silesian University of Technology Gliwice, Poland

autor

Wituła R.

• Institute of Mathematics, Silesian University of Technology Gliwice, Poland

Bibliografia

• [1] Sondow J., The parbelos, a parabolic analog of the arbelos, Amer. Math. Monthly 2013, 120, 10, 929-935.
• [2] Archimedes, Book of Lemmas, The Works of Archimedes, Cambridge University Press, 2009.
• [3] Bankoff L., Are the twin circles of Archimedes really twins? Math. Magazine 1974, 47, 4, 214-218.
• [4] Boas H.P., Reflections on the arbelos, Amer. Math. Monthly 2006, 113, 3, 236-249.
• [5] Dodge C.W., Schoch T., Woo P.Y., Yiu P., Those ubiquitous Archimedean circles, Math. Magazine 1999, 72, 3, 202-213.
• [6] Weisstein E.W., Arbelos [online], MathWorld - A Wolfram Web Resource, http://mathworld.wolfram.com/Arbelos.html.
• [7] Oller-Marcén A.M., The f-belos, Forum Geometricorum 2013, 13, 103-111, http://forumgeom.fau.edu/FG2013volume13/FG201310.pdf
• [8] Khelif H., L'ARBELOS. PARTIE II, Généralisations de l'arbelos. Présentation et généralisations du salinon, 12.02.2014, http://images.math.cnrs.fr/L-arbelos-Partie-II.html?lang=fr
• [9] Kirillov A.A., A Tale of Two Fractals, Birkhäuser, New York 2013.

Uwagi

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).