π (Pi) — Two-Digit Pair Analysis

Exploring the decimal expansion of π through two-digit pairs (00–99) using the first 100,000 digits.
Visual proof that π behaves like a normal number in base 10.

Stacked Horse Race — How Each 10k-Digit Chunk Contributes

Final Analysis at 100,000 Digits

10×10 Transition Heatmap
(From Digit → To Digit)

Color intensity = occurrence count
Dark blue = lower • Bright red = higher

Statistical Summary

Chi-square (uniformity)
104.55
(99 df)
p ≈ 0.35 — strongly consistent with uniformity
Serial Correlation
−0.00255
Extremely close to zero → no detectable correlation
Total Pairs Analyzed
99,999
Expected per Pair
999.99
Minimum Count
934
Maximum Count
1,100

The near-zero serial correlation and excellent chi-square result provide strong evidence that consecutive digits in π are essentially independent and uniformly distributed.

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