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The circle hidden inside Pascal’s triangle
- Pascal’s triangle contains binomial coefficients C(n, r) where r ranges from 0 to n in the nth row.
- For large n, the binary values of coefficients in the row displayed sideways form a circular arc.
- Plotting the logarithms of the binomial coefficients C(n, r) for large n results in an ellipse shape.
- An ellipse with parameters a = 554.2, b = 47.12, and y0 = -19.87 closely fits the plot of log C(1000, r).
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