Statement
Approximating π Like many problems in geometry, we can draw it with a certain scale (for example, radio is worth 1) and then change the scale. The key measures we have to build is to observe that these measures appear in triangles we see in the picture that accompanies these lines. If we call D to point to A and B form an isosceles right triangle, the distance AD \u200b\u200bis equal to the distance AH. The other important point is E, which also forms a triangle with A and D, and the distance AE is equal to AI. Applying the Pythagorean Theorem, the distance AD \u200b\u200b
2 = 1 + 1 = 2, so AD = √ 2. And the distance AE is also a hypotenuse, so 2 AE = 1 + 2 AD = 1 + 2, so AE = √ 3. So the distance IH = √ 2 + √ 3, and This is about half the length of the circumference, which is half of 2π, ie π. Try to see the match: √ 2 + √ 3 is worth approximately 3.1462 ... and π is worth 3.1415 ... It is clear that the difference is 0.0046 ... which is about a percentage, a 0.15% higher. course, if the radio was another number, the length multiplied by this factor would, so the difference would be r * 0.0046 ..., that is, that the approach would still be approximately 0.15% higher than the real value length half-circle.
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