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An interesting feature of ancient Egyptian mathematics is the use of unit fractions. [7] The Egyptians used some special notation for fractions such as 1 / 2 , 1 / 3 and 2 / 3 and in some texts for 3 / 4 , but other fractions were all written as unit fractions of the form 1 / n or sums of such unit ...
The problems start out with simple fractional expressions, followed by completion (sekem) problems and more involved linear equations (aha problems). [1] The first part of the papyrus is taken up by the 2/n table. The fractions 2/n for odd n ranging from 3 to 101 are expressed as sums of unit fractions.
In mathematical logic, a literal is an atomic formula (also known as an atom or prime formula) or its negation. [1] [2] The definition mostly appears in proof theory (of classical logic), e.g. in conjunctive normal form and the method of resolution. Literals can be divided into two types: [2] A positive literal is just an atom (e.g., ).
As with fractions of the form , it has been conjectured that every fraction (for >) can be expressed as a sum of three positive unit fractions. A generalized version of the conjecture states that, for any positive k {\displaystyle k} , all but finitely many fractions k n {\displaystyle {\tfrac {k}{n}}} can be expressed as a sum of three ...
Algebra is the branch of mathematics that studies certain abstract systems, known as algebraic structures, and the manipulation of expressions within those systems. It is a generalization of arithmetic that introduces variables and algebraic operations other than the standard arithmetic operations, such as addition and multiplication.
This is a list of equations, by Wikipedia page under appropriate bands of their field. Eponymous equations The following equations are named after researchers who ...
The unique pair of values a, b satisfying the first two equations is (a, b) = (1, 1); since these values also satisfy the third equation, there do in fact exist a, b such that a times the original first equation plus b times the original second equation equals the original third equation; we conclude that the third equation is linearly ...
If the discriminant is zero the fraction converges to the single root of multiplicity two. If the discriminant is positive the equation has two real roots, and the continued fraction converges to the larger (in absolute value) of these. The rate of convergence depends on the absolute value of the ratio between the two roots: the farther that ...