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Results from a nomogram are obtained very quickly and reliably by simply drawing one or more lines. The user does not have to know how to solve algebraic equations, look up data in tables, use a slide rule, or substitute numbers into equations to obtain results. The user does not even need to know the underlying equation the nomogram represents.
Lill's method involves drawing a path of straight line segments making right angles, with lengths equal to the coefficients of the polynomial. The roots of the polynomial can then be found as the slopes of other right-angle paths, also connecting the start to the terminus, but with vertices on the lines of the first path.
A Hasse diagram is a simple picture of a finite partially ordered set, forming a drawing of the partial order's transitive reduction. Concretely, one represents each element of the set as a vertex on the page and draws a line segment or curve that goes upward from x to y precisely when x < y and there is no z such that x < z < y.
The methods for solving equations generally depend on the type of equation, both the kind of expressions in the equation and the kind of values that may be assumed by the unknowns. The variety in types of equations is large, and so are the corresponding methods. Only a few specific types are mentioned below.
Note that even simple equations like = are solved using cross-multiplication, since the missing b term is implicitly equal to 1: =. Any equation containing fractions or rational expressions can be simplified by multiplying both sides by the least common denominator.
In mathematics, brackets of various typographical forms, such as parentheses ( ), square brackets [ ], braces { } and angle brackets , are frequently used in mathematical notation. Generally, such bracketing denotes some form of grouping: in evaluating an expression containing a bracketed sub-expression, the operators in the sub-expression take ...
In solving mathematical equations, particularly linear simultaneous equations, differential equations and integral equations, the terminology homogeneous is often used for equations with some linear operator L on the LHS and 0 on the RHS. In contrast, an equation with a non-zero RHS is called inhomogeneous or non-homogeneous, as exemplified by ...
5. For several uses as brackets (in pairs or with and ) see § Other brackets. ∤ Non-divisibility: means that n is not a divisor of m. ∥ 1. Denotes parallelism in elementary geometry: if PQ and RS are two lines, means that they are parallel. 2.
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