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pages/1_Introduction_to_Python.py
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This notebook demonstrates the application of Monte Carlo methods to estimate the value of Pi. Through a sequence of randomized experiments, it visualizes how increasing the number of points sampled within a unit square (and assessing whether they fall inside a unit circle) converges to a mathematical estimation of Pi.
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## Situation/Motivation/Question
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Estimating the value of Pi (π) is a classic problem in mathematics and computational science. The value of Pi is central to calculations in geometry, physics, engineering, and beyond. While Pi's decimal representation is infinite, computational methods can approximate its value to varying degrees of accuracy. One popular method for this approximation is the Monte Carlo simulation, which uses randomness to solve problems that might be deterministic in principle. This notebook explores how effectively the Monte Carlo method can estimate Pi and visualizes the convergence of this estimate as the number of trials increases.
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This notebook demonstrates the application of Monte Carlo methods to estimate the value of Pi. Through a sequence of randomized experiments, it visualizes how increasing the number of points sampled within a unit square (and assessing whether they fall inside a unit circle) converges to a mathematical estimation of Pi.
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[Link](https://huggingface.co/spaces/eagle0504/AI-Decoded/blob/main/docs/notebooks/ex0%20-%20intro%20to%20python%20-%20creating%20pi.ipynb)
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## Situation/Motivation/Question
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Estimating the value of Pi (π) is a classic problem in mathematics and computational science. The value of Pi is central to calculations in geometry, physics, engineering, and beyond. While Pi's decimal representation is infinite, computational methods can approximate its value to varying degrees of accuracy. One popular method for this approximation is the Monte Carlo simulation, which uses randomness to solve problems that might be deterministic in principle. This notebook explores how effectively the Monte Carlo method can estimate Pi and visualizes the convergence of this estimate as the number of trials increases.
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