Those Ubiquitous Archimedean Circles

Dodge, Clayton W.; Schoch, Thomas; Woo, Peter Y.; Yiu, Paul

doi:10.2307/2690883

Cited by 9 publications

(6 citation statements)

References 2 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Let a and b be the radii of a and /3 respectively. The common radius of Archimedean circles is expressed by ab / (a + b) [1]. In this note we give a pair of Archimedean circles, which we hope to be new (see Figure 2).…”

Section: Archimedean Twin Circles In the Arbelosmentioning

confidence: 99%

97.47 Archimedean twin circles in the arbelos

Okumura¹

2013

Math. Gaz.

View full text Add to dashboard Cite

Section: Archimedean Twin Circles In the Arbelosmentioning

confidence: 99%

97.47 Archimedean twin circles in the arbelos

Okumura¹

2013

Math. Gaz.

View full text Add to dashboard Cite

“…The archimedean Arbelos is one of the most fascinating geometric figures studied by many mathematicians who have explored its fine properties since ancient times. The so-called golden Arbelos was first studied by Bankoff [1] and then by other mathematicians ( [2,3,4,5,6,7,8]). The aim of this paper is to show some configurations of golden and equilateral triangles arising from the golden Arbelos.…”

Section: Introductionmentioning

confidence: 99%

103.40 Identifying golden and equilateral triangles that arise from the golden Arbelos

Scimone¹

2019

Math. Gaz.

View full text Add to dashboard Cite

“…More facts concerning the arbelos can be found in [3][4][5][6]; furthermore [4] provides an interesting historical overview of the subject.…”

Section: Antique Originmentioning

confidence: 99%

Variations on the arbelos

Michal

Samulewicz

Szweda

et al. 2017

J. Appl. Math. Comput. Mech.

View full text Add to dashboard Cite

Abstract. 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.MSC 2010: 51N20, 51M25

show abstract

Those Ubiquitous Archimedean Circles

Cited by 9 publications

References 2 publications

97.47 Archimedean twin circles in the arbelos

97.47 Archimedean twin circles in the arbelos

103.40 Identifying golden and equilateral triangles that arise from the golden Arbelos

Variations on the arbelos

Contact Info

Product

Resources

About