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Focusing attention on auxiliary lines when introduced into geometric problems
ABSTRACT The introduction of auxiliary elements as a method of solving problems in high-school geometry is considered here from two perspectives: first, to elicit recalling some known result orExpand
Dynamic investigation of triangles inscribed in a circle, which tend to an equilateral triangle
ABSTRACT We present a geometrical investigation of the process of creating an infinite sequence of triangles inscribed in a circle, whose areas, perimeters and lengths of radii of the inscribedExpand
On the Invariance of Brocard Angles in the Interior and Exterior Pappus Triangles of any Given Triangle
The paper presents groups of triangles inscribed in a given triangle ABC that have the same Brocard angle as 4ABC . Some of them are similar to 4ABC and some are not. The central group consists ofExpand
Teaching proofs without words using dynamic geometry
A Proof Without Words (PWW) contains data, the claim that is to be proved, and one or more diagrams, sometimes without anything else and in other cases with a few mathematical expressions, withoutExpand
Advances in Mathematics and Computer Science Vol. 4
Dynamic investigation of ellipses inscribed in a rectangle
Described is a dynamic investigation of an ellipse inscribed in a rectangle, with a view to properties conserved while making changes. We find mathematically the locus from which an ellipse is viewedExpand
A proposition from algebra – how would Pythagoras phrase it?
The paper presents three methods from different branches of mathematics for the solution of the same task. Originally this is an algebraic problem, and therefore the first solution presented is theExpand
The standard proof, the elegant proof, and the proof without words of tasks in geometry, and their dynamic investigation
ABSTRACT Solution of problems in mathematics, and in particular in the field of Euclidean geometry is in many senses a form of artisanship that can be developed so that in certain cases brief andExpand
Surprising Properties in the Triangle Obtained by Different Representations of Ceva's Theorem
In recent years, the subject of different representations of the same field in mathematics has seen considerable development. This includes different representations of certain theorems, such as theExpand
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