Assuming and integrating a suitably normalized polynomial times produces a positive integer that tends to zero as the polynomial degree grows. This contradiction proves that is an irrational number.
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The proof that π is irrational was first established by Johann Lambert in 1768. His proof is somewhat complex and relies on properties of continued fractions, but I can provide a high-level overview of the concepts involved in proving the irrationality of π. ### Overview of Lambert's Proof 1. **Definitions**: A number is irrational if it cannot be expressed as a fraction of two integers.