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Spiral square root of √2?
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Spiral square root of √2?
Spiral square root of √2
The spiral square root of √2 is a visual representation of the square root of 2 on a number line. It is created by drawing a spiral with the square root of 2 as the radius. The spiral starts at (1,0) and spirals outwards in a counter-clockwise direction. The points where the spiral intersects the integer grid lines on the number line represent the rational approximations of the square root of 2.
Construction of the Spiral Square Root of √2
To construct the spiral square root of √2, follow these steps:
- Start at the point (1,0) on the number line
- Draw a quarter circle with radius √2, centered at (1,1)
- Draw a line segment from the endpoint of the quarter circle to the point (0,1)
- Draw another quarter circle with radius √2, centered at (-1,1)
- Draw a line segment from the endpoint of the second quarter circle to the point (-1,0)
- Continue this process, alternating between quarter circles and line segments, in a counter-clockwise direction
Interpretation of the Spiral Square Root of √2
The points where the spiral intersects the integer grid lines on the number line represent the rational approximations of the square root of 2. For example, the first intersection of the spiral with the integer grid line occurs at (1,1), which represents the rational number 1. The second intersection occurs at (2,0), which represents the rational number 2. The third intersection occurs at (3,2), which represents the rational number 3 + 1/2.
As the spiral continues to spiral outwards, the rational approximations of the square root of 2 become more accurate. However, the spiral never actually intersects the square root of 2 itself, since the square root of 2 is an irrational number that cannot be expressed as a ratio of two integers.
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Spiral square root of √2?
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Spiral square root of √2? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about Spiral square root of √2? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Spiral square root of √2?.
Spiral square root of √2? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about Spiral square root of √2? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Spiral square root of √2?.
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