Ohio Assessments for Educators (OAE) Mathematics Practice Exam

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What is the value of the Golden Ratio expressed mathematically?

(1 + √5)/2
√2
π
(1 - √5)/2

The correct answer is: (1 + √5)/2

The value of the Golden Ratio, commonly denoted by the Greek letter phi (φ), is mathematically expressed as (1 + √5)/2. This ratio is approximately equal to 1.6180339887 and is derived from the quadratic equation x^2 = x + 1, which arises from the relationship that the ratio of two quantities is the same as the ratio of their sum to the larger of the two quantities. In geometric terms, the Golden Ratio is often found in nature, art, and architecture, representing aesthetically pleasing proportions. The formula (1 + √5)/2 captures this unique mathematical constant, illustrating its relevance to the Fibonacci sequence and various natural patterns. In contrast, the other expressions provided in the options—√2, π, and (1 - √5)/2—represent different mathematical constants that are unrelated to the concept of the Golden Ratio.