Results 11  20
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101
Congruent Contiguous Excircles
, 2014
"... Abstract. In this paper we present some interesting lines in a triangle and we give some of their properties. The eproperty For a given triangle ABC, and a point X on the side BC, consider the contiguous subtriangles ABX and AXC, with their excircles on the sides BX and XC. We shall say that X has ..."
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has the eproperty if these two excircles are congruent (see Let I 1 , I 2 , and I a be the centers of the excircles of triangles ABX, AXC, and ABC on the sides BX, XC, and BC respectively, with points of tangency indicated in
Heronian Triangles of Class K: Congruent Incircles Cevian Perspective
, 2015
"... Abstract. We relate the properties of a cevian that divides a reference triangle into two subtriangles with congruent incircles to the system of inner and outer Soddy circles of the same reference triangle. We show that if constraints are placed on the reference triangle then relationships exist b ..."
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Abstract. We relate the properties of a cevian that divides a reference triangle into two subtriangles with congruent incircles to the system of inner and outer Soddy circles of the same reference triangle. We show that if constraints are placed on the reference triangle then relationships exist
A SangakuType Problem with Regular Polygons, Triangles, and Congruent Incircles
, 2013
"... Abstract. We consider a dissection problem of a regular nsided polygon that generalizes Suzuki's problem of four congruent incircles in an equilateral triangle. ..."
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Abstract. We consider a dissection problem of a regular nsided polygon that generalizes Suzuki's problem of four congruent incircles in an equilateral triangle.
Examples of Spherical Tilings By Congruent Quadrangles
"... We give unexpected examples of monohedral tilings of the 2dimensional sphere by quadrangles, three of whose edges have the same length. We show that to classify monohedral tilings by quadrangles with this property, we must consider a condition between four angles, in addition to combinatorial consi ..."
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Cited by 6 (0 self)
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consideration, which we developed in [8] for the case of triangles.
The Parasix Configuration and Orthocorrespondence
 FORUM GEOM
, 2003
"... We introduce the parasix configuration, which consists of two congruent triangles. The conditions of these triangles to be orthologic with ABC or a circumcevian triangle, to form a cyclic hexagon, to be equilateral or to be degenerate reveal a relation with orthocorrespondence, as defined in [1]. ..."
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We introduce the parasix configuration, which consists of two congruent triangles. The conditions of these triangles to be orthologic with ABC or a circumcevian triangle, to form a cyclic hexagon, to be equilateral or to be degenerate reveal a relation with orthocorrespondence, as defined in [1].
A GENERALIZATION OF THE CONGRUENT NUMBER PROBLEM
"... Abstract. We study a certain generalization of the classical Congruent Number Problem. Specifically, we study integer areas of rational triangles with an arbitrary fixed angle θ. These numbers are called θcongruent. We give an elliptic curve criterion for determining whether a given integer n is θ ..."
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Abstract. We study a certain generalization of the classical Congruent Number Problem. Specifically, we study integer areas of rational triangles with an arbitrary fixed angle θ. These numbers are called θcongruent. We give an elliptic curve criterion for determining whether a given integer n
Hitting Probabilities for Random Convex Bodies and Lattices of Triangles
"... Dedicated to Professor Marius Stoka on the occasion of his 80th birthday Copyright c © 2014 Uwe Bäsel. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work ..."
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is properly cited. In the first part of this paper, we obtain symmetric formulae for the probabilities that a plane convex body hits exactly 1, 2, 3, 4, 5 or 6 triangles of a lattice of congruent triangles in the plane. Furthermore, a very simple formula for the expectation of the number of hit triangles
Solution by the Armstrong Problem Solvers, Armstrong Atlantic State
"... Let n ≥ 3 be a natural number. Find how many pairwise noncongruent triangles there are among the () n 3 triangles formed by selecting three vertices of a regular ngon. ..."
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Let n ≥ 3 be a natural number. Find how many pairwise noncongruent triangles there are among the () n 3 triangles formed by selecting three vertices of a regular ngon.
ON A CLASS OF NONCONGRUENT AND NONPYTHAGOREAN NUMBERS
, 1993
"... In one of his famous results, Fermat showed that there exists no Pythagorean triangle with integer sides whose area is an integer square. His elegant method of proof is one of the first known examples in the history of the theory of numbers where the method of infinite descent is employed. Mohanty [ ..."
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.(34.5) 2. For p = 4l, the triangle (5 44 4,25 24 2,5 4 +4 4) has area A = 4h(543) 2. However, as shown below, no Pythagorean number can equal p times an integer square if p is a prime congruent to 3 (mod 8). A natural question to ask is whether there exists a number k = 3 (mod 8) and a Pythagorean
Isotomic Inscribed Triangles and Their Residuals
 FORUM GEOMETRICORUM
, 2003
"... We prove some interesting results on inscribed triangles which are isotomic. For examples, we show that the triangles formed by the centroids (respectively orthocenters) of their residuals have equal areas, and those formed by the circumcenters are congruent. ..."
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We prove some interesting results on inscribed triangles which are isotomic. For examples, we show that the triangles formed by the centroids (respectively orthocenters) of their residuals have equal areas, and those formed by the circumcenters are congruent.
Results 11  20
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101