Triangle contractive self maps of a Hilbert space
D. Daykin, J. Dugdale (1974)
Fundamenta Mathematicae
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D. Daykin, J. Dugdale (1974)
Fundamenta Mathematicae
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B. Rhoades (1978)
Fundamenta Mathematicae
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Tudor Zamfirescu (1971)
Rendiconti del Seminario Matematico della Università di Padova
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Miguel de Guzmán (2001)
RACSAM
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A simple proof is presented of a famous, and difficult, theorem by Jakob Steiner. By means of a straightforward transformation of the triangle, the proof of the theorem is reduced to the case of the equilateral triangle. Several relations of the Steiner deltoid with the Feuerbach circle and the Morley triangle appear then as obvious.
Wegner, Bernd (1991)
Mathematica Pannonica
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Albert Dou (1992)
Publicacions Matemàtiques
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This "Corolarium" of the (1733) contains an original proof of propositions 1.27 and 1.28 of Euclide's . In the same corollary Saccheri explains why he dispenses "not only with the propositions 1.27 and 1.28, but also with the very propositions 1.16 and 1.17, except when it is clearly dealt with a triangle circumscribed by alls sides"; and also why he rejects Euclide's proof. Moreover the corollarium has implications for confirmation of Saccheri's method; and also for his concept of...
F. Previale (1962)
Fundamenta Mathematicae
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Tölke, Jürgen (2002)
Beiträge zur Algebra und Geometrie
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H. S. Ruse (1935)
Compositio Mathematica
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Judita Cofman (1998)
The Teaching of Mathematics
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