MHB Variable Pi Formula: Diameter (mm) Calculation

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The variable pi formula for calculating diameter in millimeters is expressed as Diameter (mm) = 0.0000003 : (pi of D - 3.1416)^2, with pi of D ranging from 3.1416 to 3.1589. When pi of D equals 3.1416, the diameter approaches infinity, while at 3.1589, the diameter is 0.001 mm. A specific case shows that when pi of D is 3.14161, the diameter is 3000 mm. The formula highlights the sensitivity of diameter calculations to small changes in the value of pi. Understanding this relationship is crucial for precise measurements in applications requiring variable pi values.
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variable pi formula
Diameter (mm) = 0.0000003 : (pi of D - 3.1416 )^2

Pi of D is variable from 3.1416 to 3.1589
Pi min = 3.1416
Pi max = 3.164

When pi of D = 3.1416 , D = infinite mm
When pi of D = 3.1589 , D = 0.001mm
When pi of D = 3.14161 , D = 3000mm
 
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variable pi formula
Diameter (mm) = 0.0000003 : (pi of D - 3.1416 )^2

Pi of D is variable from 3.1416 to 3.1589
Pi min = 3.1416
Pi max = 3.164

When pi of D = 3.1416 , D = infinite mm
When pi of D = 3.1589 , D = 0.001mm
When pi of D = 3.14161 , D = 3000mm
 

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Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?

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