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
.
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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