Cevians as sides of triangles.
Čerin, Zvonko (2000)
Mathematica Pannonica
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Displaying similar documents to “Hyperbolas and orthologic triangles.”
Cevians as sides of triangles.
On the existence of triangle with given angle and opposite angle bisectors length.
Bukor, József (2008)
Annales Mathematicae et Informaticae
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Symmedians and the symmedian center of the triangle in an isotropic plane.
Kolar-Begović, Z., Kolar-Šuper, R., Beban-Brkić, J., Volenec, V. (2006)
Mathematica Pannonica
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Circumcenter, Circumcircle and Centroid of a Triangle
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...
Morley’s Trisector Theorem
Roland Coghetto (2015)
Formalized Mathematics
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Morley’s trisector theorem states that “The points of intersection of the adjacent trisectors of the angles of any triangle are the vertices of an equilateral triangle” [10]. There are many proofs of Morley’s trisector theorem [12, 16, 9, 13, 8, 20, 3, 18]. We follow the proof given by A. Letac in [15].
Dividing the Sides of a Triangle in Proportional Parts
Paulus Gerdes (2003)
Visual Mathematics
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Pascal like triangles and Sierpinski like gaskets
Tomohide Hashiba, Yuta Nakagawa, Toshiyuki Yamauchi, Hiroshi Matsui, Satoshi Hashiba, Daisuke Minematsu, Munetoshi Sakaguchi, Ryohei Miyadera (2007)
Visual Mathematics
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The Neuberg cubic in locus problems.
Čerin, Zvonko (2000)
Mathematica Pannonica
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Tilings of the sphere with right triangles. II: The , subfamily.
Dawson, Robert J. MacG., Doyle, Blair (2006)
The Electronic Journal of Combinatorics [electronic only]
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The envelope of the Wallace-Simpson lines of a triangle. A simple proof of the Steiner problem on the deltoid.
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.
Cutting circles and the Morley theorem.
Stammler, Ludwig (1997)
Beiträge zur Algebra und Geometrie
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Altitude, Orthocenter of a Triangle and Triangulation
Roland Coghetto (2016)
Formalized Mathematics
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We introduce the altitudes of a triangle (the cevians perpendicular to the opposite sides). Using the generalized Ceva’s Theorem, we prove the existence and uniqueness of the orthocenter of a triangle [7]. Finally, we formalize in Mizar [1] some formulas [2] to calculate distance using triangulation.
Divisible tilings in the hyperbolic plane.
Broughton, S.Allen, Haney, Dawn M., McKeough, Lori T., Smith Mayfield, Brandy (2000)
The New York Journal of Mathematics [electronic only]
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