Black Plastic Lid - Measurement Ratio

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SUMMARY

The discussion centers on the measurement ratio of a black plastic lid, specifically examining the relationship between circumference ($C$) and diameter ($D$). The calculated ratio is 3.25, derived from the formula $Ratio = \frac{C}{D}$, where $C$ is 30.75 cm and $D$ is 9.46 cm. The conversation highlights that this ratio approaches the mathematical constant $\pi$ (approximately 3.14) as measurements become more accurate. Additionally, the discussion mentions various numerical methods for approximating $\pi$.

PREREQUISITES
  • Understanding of basic geometry concepts, specifically circumference and diameter.
  • Familiarity with the mathematical constant $\pi$ and its significance in circular measurements.
  • Knowledge of numerical methods for approximating constants.
  • Ability to perform basic mathematical calculations involving ratios.
NEXT STEPS
  • Research methods for accurately measuring circumference and diameter of circular objects.
  • Explore numerical methods for approximating $\pi$, such as the Monte Carlo method or the Leibniz formula.
  • Study the significance of $\pi$ in various mathematical and engineering applications.
  • Learn about the implications of measurement accuracy in scientific calculations.
USEFUL FOR

Mathematicians, engineering students, educators, and anyone interested in the practical applications of geometry and the mathematical constant $\pi$.

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.
 

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