MHB Black Plastic Lid - Measurement Ratio

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The discussion centers on the measurement ratio of a black plastic lid, specifically the relationship between its circumference and diameter. The calculated ratio is 3.25, but it is noted that the true ratio should approximate π (approximately 3.14). As measurements improve in accuracy, the ratio will converge closer to π. Additionally, there are various numerical methods available for approximating π. The conversation invites further questions on this topic if needed.
shamieh
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Object: Black Plastic Lid

$C$ = Circumference (cm)
$D$ = Diameter (cm)

Ratio $= \frac{C}{D}$

Ratio $= \frac{30.75}{9.46} = 3.25$
 
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... but $$\dfrac CD=\pi$$
 
Hi shamieh,

I'm not quite sure what your post is asking, but as greg1313 pointed out $\pi$ is defined as the circumference of a circle divided by the diameter of the circle. If you were to measure these lengths with increasing accuracy, then you would get closer and closer to the value of $\pi$ ($\approx$3.14). There are also several numerical methods to approximate $\pi$. Let us know should you need help with any of those.
 

Thread 'Area of Overlapping Squares'

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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