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.