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We study the possible positions of an inscribed equilateral triangle with vertices on the sides of a generic triangle. We show that infinitely many such configurations exist and examine some extremal properties. [ABSTRACT FROM AUTHOR]

In this article we consider the geometrical iterative process defined by the Kasner triangles with a fixed real weight. The main results about the convergence of this process are given in Section 2. The proofs are elementary and use the general theory of the second order linear recurrences. In the remark after the proof a higher level approach is presented. [ABSTRACT FROM AUTHOR]

We discuss the general Rodrigues problem and we give explicit determinant formulae for the coefficients when the eigenvalues of the matrix have double multiplicity (Theorem 5). When n = 4 explicit formulae and effective computations for the exponential map on the Lie group SO(4) are presented. [ABSTRACT FROM AUTHOR]

For a positive integer n ≥ 1 the n-th cyclotomic polynomial is defined by Φn(z) = Пςn=1(z - ζ), where are the primitive n-th roots of unity. These polynomials are known to possess many interesting properties. In this article we establish an integral formula for the coefficients of the cyclotomic polynomial, we then discuss the direct and alternate sums of coefficients, as well as the mid-term of Φn(z). Finally, these results are used in the computation of certain trigonometric integrals. [ABSTRACT FROM AUTHOR]

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