Cutting circles and the Morley theorem.
Stammler, Ludwig (1997)
Beiträge zur Algebra und Geometrie
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Stammler, Ludwig (1997)
Beiträge zur Algebra und Geometrie
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Bukor, József (2008)
Annales Mathematicae et Informaticae
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Čerin, Zvonko (2000)
Mathematica Pannonica
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Roland Coghetto (2016)
Formalized Mathematics
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We introduce, using the Mizar system [1], some basic concepts of Euclidean geometry: the half length and the midpoint of a segment, the perpendicular bisector of a segment, the medians (the cevians that join the vertices of a triangle to the midpoints of the opposite sides) of a triangle. We prove the existence and uniqueness of the circumcenter of a triangle (the intersection of the three perpendicular bisectors of the sides of the triangle). The extended law of sines and the formula...
Čerin, Z. (1997)
Mathematica Pannonica
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Paulus Gerdes (2003)
Visual Mathematics
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Tomohide Hashiba, Yuta Nakagawa, Toshiyuki Yamauchi, Hiroshi Matsui, Satoshi Hashiba, Daisuke Minematsu, Munetoshi Sakaguchi, Ryohei Miyadera (2007)
Visual Mathematics
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Roland Coghetto (2014)
Formalized Mathematics
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We calculate the values of the trigonometric functions for angles: [XXX] , by [16]. After defining some trigonometric identities, we demonstrate conventional trigonometric formulas in the triangle, and the geometric property, by [14], of the triangle inscribed in a semicircle, by the proposition 3.31 in [15]. Then we define the diameter of the circumscribed circle of a triangle using the definition of the area of a triangle and prove some identities of a triangle [9]. We conclude by...
Shen, Yujin, Tolosa, Juan (2008)
International Journal of Mathematics and Mathematical Sciences
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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...
Kynčl, Jan, Tancer, Martin (2008)
The Electronic Journal of Combinatorics [electronic only]
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Wegner, Bernd (1991)
Mathematica Pannonica
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van Asch, A.G., van der Blij, F. (1995)
Bulletin of the Belgian Mathematical Society - Simon Stevin
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