# Continued-fractions Sentence Examples

continued-fractions
• 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.