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In mathematics, , sometimes called the golden field, is a number system consisting of the set of all numbers , where and are both rational numbers and is the square root of 5, along with the basic arithmetical operations. This arithmetic shares certain structural properties with the arithmetic of , the field of rational numbers, making also a type of field. More specifically, it is a real quadratic field, the extension field of generated by combining rational numbers and using arithmetical operations. The name comes from the golden ratio , a positive number satisfying the equation , which is the fundamental unit of .
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