Question:
The golden section used by the Greeks is considered to be a model of good proportion (Assertion A). This proportion is found in any circle, which can be divided into two unequal areas, one of which is triangle, so that the smaller one is to the larger and as larger is to the whole (Reason R).
The golden section used by the Greeks is considered to be a model of good proportion (Assertion A). This proportion is found in any circle, which can be divided into two unequal areas, one of which is triangle, so that the smaller one is to the larger and as larger is to the whole (Reason R).
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Understanding the precise definition and application of mathematical concepts like the golden ratio can help in distinguishing between correct statements and those that may seem related but are actually misrepresentations.
Updated On: Jun 9, 2026
- Both (A) and (R) are correct and (R) is the correct explanation of (A)
- Both (A) and (R) are correct but (R) is not the correct explanation of (A)
- (A) is correct but (R) is not correct
- (A) is not correct but (R) is correct
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The Correct Option is C
Solution and Explanation
Step 1: Concept
The golden section, also known as the divine proportion or the golden ratio, is a special number approximately equal to 1.618033988749895. It has been used extensively in art, architecture, and design due to its aesthetically pleasing properties. The golden ratio can be derived from the equation \(\phi = \frac\{1 + \sqrt\{5\}\}\{2\}\).
Step 2: Meaning
In geometry, a line segment is divided into two parts such that the whole length of the segment divided by the longer part is also equal to the longer part divided by the shorter part. This ratio is the golden ratio.
Step 3: Analysis
Assertion A states that the golden section used by the Greeks is considered to be a model of good proportion. This assertion is correct as the golden ratio has been widely recognized for its aesthetic appeal and has been applied in various fields, including architecture and art. Reason R describes a specific geometric property involving a circle divided into two unequal areas where one area forms a triangle. However, this description does not accurately represent the concept of the golden section. The golden section is about dividing a line segment or a whole into parts such that the ratio of the whole to the larger part is equal to the ratio of the larger part to the smaller part. The given reasoning in R involves a circle divided into two areas, one of which forms a triangle. This does not directly relate to the definition and application of the golden section as described by A. Therefore, while both statements are correct individually, R is not the correct explanation for A.
Step 4: Conclusion
Given that Assertion A is correct but Reason R is not an accurate representation or explanation of the golden section, the conclusion aligns with option C. Final Answer: (C)
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