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Variations on the arbelos

Różański M., Samulewicz A., Szweda M., Wituła R.

Journal of Applied Mathematics and Computational Mechanics

2017

Vol. 16, nr 2

123--133

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.