Search results
Results from the WOW.Com Content Network
Fermat knew that a fourth power cannot be the sum of two other fourth powers (the n = 4 case of Fermat's Last Theorem; see Fermat's right triangle theorem). Euler conjectured that a fourth power cannot be written as the sum of three fourth powers, but 200 years later, in 1986, this was disproven by Elkies with: 20615673 4 = 18796760 4 ...
Each coordinate of the intersection points of two conic sections is a solution of a quartic equation. The same is true for the intersection of a line and a torus.It follows that quartic equations often arise in computational geometry and all related fields such as computer graphics, computer-aided design, computer-aided manufacturing and optics.
The fourth power law (also known as the fourth power rule) states that the stress on the road caused by a motor vehicle increases in proportion to the fourth power of its axle load. This law was discovered in the course of a series of scientific experiments in the United States in the late 1950s and was decisive for the development of standard ...
Euler was aware of the equality 59 4 + 158 4 = 133 4 + 134 4 involving sums of four fourth powers; this, however, is not a counterexample because no term is isolated on one side of the equation. He also provided a complete solution to the four cubes problem as in Plato's number 3 3 + 4 3 + 5 3 = 6 3 or the taxicab number 1729.
In mathematics and statistics, sums of powers occur in a number of contexts: . Sums of squares arise in many contexts. For example, in geometry, the Pythagorean theorem involves the sum of two squares; in number theory, there are Legendre's three-square theorem and Jacobi's four-square theorem; and in statistics, the analysis of variance involves summing the squares of quantities.
The Stefan–Boltzmann law gives the power emitted per unit area of the emitting body, = (,) Note that the cosine appears because black bodies are Lambertian (i.e. they obey Lambert's cosine law ), meaning that the intensity observed along the sphere will be the actual intensity times the cosine of the zenith angle.
In mathematics, a quartic equation is one which can be expressed as a quartic function equaling zero. The general form of a quartic equation is Graph of a polynomial function of degree 4, with its 4 roots and 3 critical points.
then the formulas for addition, multiplication, and multiplicative inverse are ... The fourth power of the norm of a quaternion is the determinant of the ...