# Continued-fractions Sentence Examples

Chrystal's Algebra, where also may be found details of the application of

**continued fractions**to such interesting and important problems as the recurrence of eclipses and the rectification of the calendar.Lagrange used simple

**continued fractions**to approximate to the solutions of numerical equations; thus, if an equation has a root between two integers a and a+1, put x=a+I/y and form the equation in y; if the equation in y has a root between b and b+i, put y = b + I /z, and so on.The solution in integers of the indeterminate equation ax+by=c may be effected by means of

**continued fractions**.Recurring Simple

**Continued Fractions**.Ascending

**Continued Fractions**.The invention of

**continued fractions**is ascribed generally to Pietro Antonia Cataldi, an Italian mathematician who died in 1626.For the application of

**continued fractions**to the theory of O o O b 3 O O a3 b4 O - I a 4 b5 b2 irrational numbers there is P. Bachmann's Vorlesungen fiber die Natur der Irrationalzahnen (1892).The theory of

**continued fractions**gives a method of expressing a number, in certain cases, as a continued product.Any exact fraction can be expressed as a continued fraction, and there are methods for expressing as

**continued fractions**certain other numbers, e.g.