Dividing the Sides of a Triangle in Proportional Parts
Paulus Gerdes (2003)
Visual Mathematics
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Displaying similar documents to “On the existence of triangle with given angle and opposite angle bisectors length.”
Dividing the Sides of a Triangle in Proportional Parts
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Čerin, Z. (1997)
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Cevians as sides of triangles.
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Circumcenter, Circumcircle and Centroid of a Triangle
Roland Coghetto (2016)
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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...
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Stammler, Ludwig (1997)
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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.
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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Symmedians and the symmedian center of the triangle in an isotropic plane.
Kolar-Begović, Z., Kolar-Šuper, R., Beban-Brkić, J., Volenec, V. (2006)
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Altitude, Orthocenter of a Triangle and Triangulation
Roland Coghetto (2016)
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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.
The weighted Fermat triangle problem.
Shen, Yujin, Tolosa, Juan (2008)
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Maligranda, Lech (2008)
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Some Facts about Trigonometry and Euclidean Geometry
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...