A Thought on Rascal Triangles

2016

As a teacher, one is always looking for so-called ‘non-standard’ problems. These should be based on material that has been taught, and yet be neither trivial nor too hard. This article illustrates an example of such a nonstandard problem. Reading the article on the Rascal Triangle [1], I felt it would fit the bill, given that it was discovered by students in the first place

We prove some results related to the two García reflection triangles of a given triangle.

In this article we prove a theorem that will generalize the concurrence theorems that are leading to the Franke’s point, Kariya’s point, and to other remarkable points from the triangle geometry.

viXra, 2013

2010

It is shown in the paper the discovery of two remarkable points of the triangle by means of “THE GEOMETER’S SKETCHPAD” software. Some properties of the points are considered too

Fractals

The Sierpinski Triangle (ST) is a fractal which has Haussdorf dimension [Formula: see text] that has been studied extensively. In this paper, we introduce the Sierpinski Triangle Plane (STP), an infinite extension of the ST that spans the entire real plane but is not a vector subspace or a tiling of the plane with a finite set of STs. STP is shown to be a radial fractal with many interesting and surprising properties.

2020

Plants and trees grow perpendicular to the plane tangent to the soil surface, at the point of penetration into the soil; in vacuum, the bodies fall perpendicular to the surface of the Earth - in both cases, if the surface is horizontal. Starting from the property of two triangles to be orthological, the two authors have designed this work that seeks to provide an integrative image of elementary geometry by the prism of this "filter". Basically, the property of orthology is the skeleton of the present work, which establishes many connections of some theorems and geometric properties with it.

In this article we’ll prove through computation the Feuerbach’s theorem relative to the tangent to the nine points circle, the inscribed circle, and the ex-inscribed circles of a given triangle.

In this paper we prove a simple property of isosceles triangles and give two applications: construction of third proportional line segments and construction of the inverse point with respect to a circle.