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Recall , π is defined as the ratio of the circumference of a circle to its diameter. That is π =c/d.This seems to contradict the fact that π is irrational . How will you resolve this contradiction?
Most Upvoted Answer
Recall , π is defined as the ratio of the circumference of a circle to...
There is no contradiction.. We can never obtain an exact value of c and d so that , either c or d is irrational. and product or division of rational with irrational is always irrational.Therefore, the fraction c/d is irrational. Hence, π is irrational.
Community Answer
Recall , π is defined as the ratio of the circumference of a circle to...
Resolution of the Contradiction:
Definition of π:
- Initially, π is defined as the ratio of the circumference of a circle to its diameter, which is denoted as π = c/d.
Irrationality of π:
- However, it is proven that π is irrational, meaning it cannot be expressed as a simple fraction.
- This contradiction arises because the definition of π as c/d implies it should be a rational number, but it is actually irrational.
Resolution:
- The resolution to this contradiction lies in the fact that the definition of π as c/d is an approximation.
- While the ratio of the circumference to the diameter is close to π, it is not exactly equal to π due to the irrationality of π.
- In reality, the decimal representation of π goes on infinitely without repeating, making it impossible to express as a fraction.
Conclusion:
- Therefore, the initial definition of π as c/d is a convenient and close approximation, but the true value of π is an irrational number that cannot be precisely represented by a simple fraction.
Definition of π:
- Initially, π is defined as the ratio of the circumference of a circle to its diameter, which is denoted as π = c/d.
Irrationality of π:
- However, it is proven that π is irrational, meaning it cannot be expressed as a simple fraction.
- This contradiction arises because the definition of π as c/d implies it should be a rational number, but it is actually irrational.
Resolution:
- The resolution to this contradiction lies in the fact that the definition of π as c/d is an approximation.
- While the ratio of the circumference to the diameter is close to π, it is not exactly equal to π due to the irrationality of π.
- In reality, the decimal representation of π goes on infinitely without repeating, making it impossible to express as a fraction.
Conclusion:
- Therefore, the initial definition of π as c/d is a convenient and close approximation, but the true value of π is an irrational number that cannot be precisely represented by a simple fraction.
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Recall , π is defined as the ratio of the circumference of a circle to its diameter. That is π =c/d.This seems to contradict the fact that π is irrational . How will you resolve this contradiction? for Class 9 2025 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about Recall , π is defined as the ratio of the circumference of a circle to its diameter. That is π =c/d.This seems to contradict the fact that π is irrational . How will you resolve this contradiction? covers all topics & solutions for Class 9 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Recall , π is defined as the ratio of the circumference of a circle to its diameter. That is π =c/d.This seems to contradict the fact that π is irrational . How will you resolve this contradiction?.
Recall , π is defined as the ratio of the circumference of a circle to its diameter. That is π =c/d.This seems to contradict the fact that π is irrational . How will you resolve this contradiction? for Class 9 2025 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about Recall , π is defined as the ratio of the circumference of a circle to its diameter. That is π =c/d.This seems to contradict the fact that π is irrational . How will you resolve this contradiction? covers all topics & solutions for Class 9 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Recall , π is defined as the ratio of the circumference of a circle to its diameter. That is π =c/d.This seems to contradict the fact that π is irrational . How will you resolve this contradiction?.
Solutions for Recall , π is defined as the ratio of the circumference of a circle to its diameter. That is π =c/d.This seems to contradict the fact that π is irrational . How will you resolve this contradiction? in English & in Hindi are available as part of our courses for Class 9.
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