MHB Black Plastic Lid - Measurement Ratio

AI Thread Summary
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 'Trigonometry problem of interest'

Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...
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