continued fractions

Continued fractions are a way of expressing numbers through an ongoing process of nested fractions. They start with a whole number, then add a reciprocal of another number, which itself can be expressed as a similar structure. This process continues infinitely or finitely, providing highly accurate approximations of irrational numbers like√2 or π. Continued fractions reveal a number’s internal structure, showing patterns and providing precise rational approximations. They are useful in number theory, approximation, and understanding the properties of numbers beyond simple decimal representations.