Calculating Pi with Darts | Summary and Q&A

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March 14, 2015
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Calculating Pi with Darts

TL;DR

Using a target with a square and a circle, the number of darts landing in the circle divided by the total number of darts thrown can be used to calculate an estimate of pi.

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Key Insights

  • ๐Ÿคจ The dart-throwing method can provide an enjoyable and engaging activity to approximate the value of pi.
  • ๐Ÿง‘โ€๐Ÿญ Randomness is a challenging factor to account for in obtaining accurate results when using this method.
  • ๐ŸŽฏ Increasing the size of the target and throwing darts rapidly can help reduce bias and improve the accuracy of the pi estimate.

Transcript

I'm here today calculating pi with darts, with the help of Veritasium. So we're calculating pi using this, which is a target composed of a square and a circle inside the square that has a diameter the same length as one side of the square. So the idea of calculating pi like this is that the number of darts that land in the circle divided by the num... Read More

Questions & Answers

Q: How does using a target with a square and a circle help in calculating pi?

The ratio of darts that land inside the circle to the total number of darts thrown can be used to estimate the ratio of the areas of the circle and the square, which is proportional to pi.

Q: Why did the initial attempt at calculating pi with darts yield a value higher than pi?

The randomness of the dart throws was not evenly distributed, resulting in more darts landing inside the circle than expected, suggesting a bias in the sampling method.

Q: How did they try to overcome the bias in the random sampling?

They used a larger target and threw darts rapidly to try to achieve a more random distribution of dart throws.

Q: What was the final estimate of pi obtained through the dart-throwing method?

After multiple attempts, an estimate of pi was obtained as 3.139, with an error percentage of about 0.1%.

Summary & Key Takeaways

  • The concept behind calculating pi with darts is that the ratio of darts landing in the circle to the total number of darts should be proportional to the ratio of the areas of the circle and the square.

  • However, the initial attempt at calculating pi with darts yielded a value higher than pi, indicating a bias in the random sampling.

  • To overcome this bias, a larger target was used and darts were thrown rapidly, resulting in a closer estimate of pi.

  • Overall, though this method is not recommended, it can provide a fun and surprising way to approximate the value of pi.

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