The PROOF: e and pi are transcendental
Mathologer・2 minutes read
The video explains complex transcendence proofs for e and pi, breaking them down into seven levels of enlightenment that require calculus knowledge to understand in detail. The proofs involve showing that e and pi cannot be expressed as fractions or solutions of polynomial equations with integer coefficients, ultimately highlighting the transcendental nature of these numbers.
Insights
- The video aims to simplify and animate the complex transcendence proofs for e and pi, requiring some calculus knowledge and dividing the mathematical quest into seven levels of enlightenment.
- By using intricate polynomial manipulations and the gamma function identity, the proof for e involves ensuring that specific polynomials lead to contradictions, while for pi, Lindermann's equation introduces complex numbers to create contradictions, all based on David Hilbert's work refined by Steinberg and Redheffer.
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Recent questions
What are transcendental numbers?
Numbers beyond irrational, like e and pi.
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