KONSTRUKTION DES REGULAREN SIEBZEHNECKS MIT LINEAL UND STRECKENUBERTRAGER

In 1899 D. Hilbert proved that regular polygons that can be constructed with a ruler and a pair of compasses can also be constructed by using a ruler and a gauge. However, the procedure for the construction of the regular settimdecagon by these tools could be described only more than 90 years later (see [2] and [3]). Since that time we succeeded to simplify the construction. In this paper we present the construction of the regular settimdecagon in this simpler form

Triangles in arrangements of lines

AbstractA set of n lines in the projective plane divides the plane into a certain number of polygonal cells. We show that if we insist that all of these cells be triangles, then there are at most 13n(n − 1) + 4 − 27n of them. We also observe that if no point of the plane belongs to more than two of the lines and n is at least 4, some of the cells must be either quadrangles or pentagons. We further show that for n ≧ 4, there is a set of n lines which divides the plane into at least 13n(n − 3) + 4 triangles

Nano Mix of Shungite and Zeolite for Cleaning of Toxins and Increasing of Energy of Hydrogen Bonds among Water Molecules in Human Body

We studied the mathematical model of interaction with water of two natural minerals – amorphous, uncrystallized, fullerene analogous carbon containing natural mineral shungite from Zazhoginskoe deposit in Karelia (Russian Federation) and microporous crystalline aluminosilicate mineral zeolite (Most, Bulgaria). In this report are submitted data about the interaction of these minerals with water, obtained by non-equilibrium (NES) and differential-equilibrium energy spectrum (DNES) of water. The average energy (∆EH... O) of hydrogen Н…O-bonds among individual molecules H2O after treatment of shungite and zeolite with water measured by NES- and DENS-methods was at -0.1137 eV for shungite and -0.1174 eV for zeolite. The calculation of ∆EH... O for shungite with using DNES method compiles 0.0025±0.0011 eV and for zeolite -1.2±0.0011 eV. This result suggests the restructuring of ∆EH... O values among H2O molecules with a statistically reliable increase of local maximums in DNES-spectra. Also are demonstrated the prospects of using shungite, possessing high absorption, catalytic and bactericidal activity, as an adsorbent in water-treatment, water purification, and other industries. Keywords: shungite, zeolite, nanostructure, fullerens, water treatment, water putrificatio