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 'erroneously finding discrepancy in transpose rule'

Thread 'erroneously finding discrepancy in transpose rule'

Obviously, there is something elementary I am missing here. To form the transpose of a matrix, one exchanges rows and columns, so the transpose of a scalar, considered as (or isomorphic to) a one-entry matrix, should stay the same, including if the scalar is a complex number. On the other hand, in the isomorphism between the complex plane and the real plane, a complex number a+bi corresponds to a matrix in the real plane; taking the transpose we get which then corresponds to a-bi...
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