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In mathematics, the Hodge conjecture is a major unsolved problem in algebraic geometry and complex geometry that relates the algebraic topology of a non-singular complex algebraic variety to its subvarieties.
Each curve in this example is a locus defined as the conchoid of the point P and the line l.In this example, P is 8 cm from l. In geometry, a locus (plural: loci) (Latin word for "place", "location") is a set of all points (commonly, a line, a line segment, a curve or a surface), whose location satisfies or is determined by one or more specified conditions.
Although successful in solving Apollonius' problem, van Roomen's method has a drawback. A prized property in classical Euclidean geometry is the ability to solve problems using only a compass and a straightedge. [18] Many constructions are impossible using only these tools, such as dividing an angle in three equal parts.
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List of unsolved problems may refer to several notable conjectures or open problems in various academic fields: Natural sciences, engineering and medicine [ edit ]
A new study of decades worth of seismogram data shows that the surface of Earth’s iron and nickel core is more malleable than scientists thought ...
From country to country, different STR-based DNA-profiling systems are in use. In North America, systems that amplify the CODIS 20 [21] core loci are almost universal, whereas in the United Kingdom the DNA-17 loci system is in use, and Australia uses 18 core markers. [22] The true power of STR analysis is in its statistical power of discrimination.
The definition of the damping ratio and natural frequency presumes that the overall feedback system is well approximated by a second order system; i.e. the system has a dominant pair of poles. This is often not the case, so it is good practice to simulate the final design to check if the project goals are satisfied.