Equilateral hyperbola


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(Geom.) one whose axes are equal.

See also: Equilateral

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1, the arc of the content of tungsten is presented with an equilateral hyperbola Y = K/X wherein its different compounds (in particular [WO.
As is known, an equilateral hyperbola is symmetric with respect to the bisector of the angle XOY in the first quarter.
This is the hyperbolic law, according to which the content Y of any element (per 1 gram-atom) in any chemical compound of a molecular mass X can be described by the equation of the positive branches of an equilateral hyperbola of the kind Y = K/X (where Y < 1 and K < X).
This mean that the locus of A for which the polar is a parabola is the equilateral hyperbola
In the theoretical deduction of the hyperbolic law of the Periodic Table of Elements [1], the main attention was focused onto the following subjects: the equilateral hyperbola with the central point at the coordinates (0; 0), its top, the real axis, and the line tangential to the normal of the hyperbola.
To avoid possible mistakes in the future, the following terminology has been assumed: hyperbolas of the kind y = k/x are referred to as straight; equilateral hyperbolas of the kind y = (ax + b)/(cx + d) are referred to as adjacent.
Similarly, the development of the hyperbolic functions follows from the unit equilateral hyperbola, [x.
Contents Y of every single element (say, of a K-th element in the Table) in a chemical compound of a molecular mass X can be given by the equation of an equilateral hyperbola Y =K/X, according to which Y (in parts of unit) decreases with increasing X.
Its essence is reflected in the fact that in any chemical compound with molecular mass X referred to one gram-atom of a defined element if, its maintenance Y represents the equilateral hyperbola Y = K/X whose top is located on the valid axis located in a corner at 45 degrees with respect to the abscissa in the positive direction.
In mathematics, the two branches of an equilateral hyperbola are symmetric with respect to each other.
The regularity established by us represents equilateral hyperbolas Y = K/X, where Y is the content of any element if and X is the molecular mass of compounds taken according to one gram-atom of the defined element.
It is necessary to note that while our theory has been considered with reference to the first quadrant, the position of the second branches of equilateral hyperbolas in the third quadrant (where K > 0) has not been analyzed.