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Let x be the number of cocks, y be the number of hens, and z be the number of chicks, then the problem is to find x, y and z satisfying the following equations: x + y +z = 100 5x + 3y + z/3 = 100. Obviously, only non-negative integer values are acceptable. Expressing y and z in terms of x we get y = 25 − (7/4)x z = 75 + (3/4)x
The 500 line segments defined above together form a shape in the Cartesian plane that resembles a bird with open wings. Looking at the line segments on the wings of the bird causes an optical illusion and may trick the viewer into thinking that the segments are curved lines. Therefore, the shape can also be considered as an optical artwork.
Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical systems, and partial differential equations.
A differential equation is an equation involving an unknown function and its derivatives. In a dynamical system, a fixed rule describes the time dependence of a point in a geometrical space. The mathematical models used to describe the swinging of a clock pendulum, the flow of water in a pipe, or the number of fish each spring in a lake are ...
The bird flu outbreak has taken concerning turns, with more than 60 human cases confirmed. Experts outlined four signs that the virus is going in the wrong direction. Key warning signs about bird ...
The conjecture is that there is a simple way to tell whether such equations have a finite or infinite number of rational solutions. More specifically, the Millennium Prize version of the conjecture is that, if the elliptic curve E has rank r , then the L -function L ( E , s ) associated with it vanishes to order r at s = 1 .
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