# 2. Extending the Rationals with the Square Root of Five

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This Demonstration shows examples of arithmetic operations in the extended field , that is, in the field of numbers , where and are rational numbers. But instead of using the numbers and , here we use and the golden ratio .

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Contributed by: Izidor Hafner (January 2020)

Open content licensed under CC BY-NC-SA

## Details

Algebraic integers are roots of polynomial equations , where coefficients are integers. Algebraic integers in of the form satisfy the equation .

Reference

[1] I. Vidav, *Algebra*, Ljubljana: Mladinska knjiga, 1972 pp. 328–330.

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