By Wassenaar J.
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Extra info for 2d Curves
At the end of the the Middle Ages the cannon came into use on the battlefield. Therefore it was important to predict the exact location where the projectile would land. Many scientists tried to answer this question, and it was Galileo Galilei who found the relation as first. That the trajectory of a projectile − neglecting effects of friction − has the form of a parabola, can easily be understood as follows: the x coordinate is proportional to the elapsed time, the y coordinate quadratic (as result of the constant gravitation force).
The triangle is a simple figure, but however, many triangles can be distinguished, many of them carrying an own name. For the acute−angled triangle (or acute triangle) all angles are smaller than 90 degrees. When a triangle has an obtuse angle, it's an obtuse−angled triangle (or obtuse triangle). The triangle curve (or zigzag curve) repeats the isosceles triangle, a triangle with two equal legs. The curve can be defined as giving the distance from x to the natural number that is most close. In formula: where [x] is the entier function.
Sometimes a distribution can not be matched with a hyperbola, the Mandelbrot−Zipf −a 5) . law makes a generalization towards the power function: y = x In another math region we can find the hyperbolic geometry (or geometry of Lobachevsky), one of the non−Euclidean geometries, based on the axiom that there exist at least two lines through a point P that are parallel to a line not through P. The hyperbolic functions have not much in common with the hyperbola. Their name is based on the fact that two hyperbolic functions can be drawn geometrically in a hyperbola.