Year LXI, Issue 4, 2018<<Archive>>
In this issue:
Еducаtionаl Маttеrs
ABOUT THE PRIME NUMBERS
Some of the basic hypotheses about the prime numbers are considered, which determine their important properties for Mathematics.
prime number; perfect number; Mersenne prime number; twin prime numbers; hypothesis
INCENTER OF A QUADRILATERAL
The paper describes some properties of a notable point in a convex quadrilateral, which naturally generalize the incenter of the outscribed quadrilateral. What are considered are the connections of this point with a transformation in the plane of the quadrilat...
quadrilateral; notable point; transformation
POLYNOMIALS WITH MULTIPLE ROOTS IN THE VERTICES OF A TRIANGLE
It is considered a geometric relation between the roots of a polynomial and the roots of its derivative, when all roots of the polynomial are in three noncollinear points. This relation is realized through the focuses of a special ellipse, which is determine...
polynomial; root; triangle; ellipse; focus
Еducаtionаl Tеchnologiеs
EPICYCLOID
The paper presents results on the epicycloid of Kazakhstan students in the frames of the net research project “Encyclopedia of notable plane figures: we work by ourselves”. What are used in the investigation are analytical geometry methods and experiments by c...
circle; curve; trajectory; еріcycloid
HYPOCYCLOID
The paper presents results of the Bulgarian sub-team – a part of an international team of students. The team was created for the realization of the net research project “Encyclopedia of notable plane figures: we work by ourselves”. The investigation is carrie...
circle; curve; trajectory; hypocycloid
SETS OF POINTS, GENERATED BY A PAIR OF ISOSCELES TRIANGLES WITH A SPECIAL LOCATION OF THEIR BASES
The paper is dedicated to some generalizations of the problem: \(B\) is a point on the segment \(A C\), while \(X\) and \(Y\) are points in one and the same half-plane with respect to the side \(A C\) of the triangle \(A B C\). When the triangle s \(A B...
triangle; co-ordinate system; curve of second degree; polarity
FOUR NEW PHD DISSERTATIONS IN METHODOLOGY OF MATHEMATICS AND INFORMATICS TEACHING
Annotations of four new dissertations of PhD students are presented. Three of them are in the domain of methodology of Informatics education and are defended successfully in Plovdiv University “P. Hilendarski”. The forth one is in the domain of methodology o...
PhD student; dissertation; methodology; Mathematics; Informatics; education; teaching