In this article we prove the Sodat's theorem regarding the orthohomological triangle and
then we use this theorem and Smarandache-Patrascu's theorem in order to obtain another
theorem regarding the orthohomological triangles.
In this paper we analyze and prove two properties of a hexagon circumscribed to a circle
A Multiple Theorem with Isogonal and Concyclic Points
In this paper we prove that if P1,P2 are isogonal points in the triangle ABC ,
and if A1B1C1 and A2B2C2 are their ponder triangle such that the triangles ABC and
A1B1C1 are homological (the lines AA1 , BB1 , CC1 are concurrent), then the triangles
ABC and A2B2C2 are also homological.
Authors: Roberto Torretti
Comments: 3 pages
The Smarandache anti-geometry is a non-euclidean geometry that
denies all Hilbert's twenty axioms, each axiom being denied in many ways in the same
space. In this paper one finds an economics model to this geometry by making the
(i) A point is the balance in a particular checking account, expressed in U.S. currency.
(Points are denoted by capital letters).
(ii) A line is a person, who can be a human being. (Lines are denoted by lower case
(iii) A plane is a U.S. bank, affiliated to the FDIC. (Planes are denoted by lower case
In this article we propose to determine the triangles' class... (see paper for full abstract)