SUMMARY
The theorem stating that if x is a rational number and x ≠ 0, then tan(x) is not rational, was established by mathematician Johann Lambert. The proof can be found in Lambert's original work, while a simplified version is available through Laczkovich's interpretation on Wikipedia. This theorem is significant in understanding the properties of trigonometric functions and their relationship with rational numbers.
PREREQUISITES
- Understanding of rational numbers and their properties
- Familiarity with trigonometric functions, specifically tangent
- Knowledge of Lambert's contributions to mathematics
- Basic comprehension of mathematical proofs and theorems
NEXT STEPS
- Study Lambert's original proof of the irrationality of tan(x)
- Explore Laczkovich's simplification of Lambert's proof
- Research the implications of irrational numbers in trigonometry
- Investigate other proofs related to the irrationality of π and e
USEFUL FOR
Mathematicians, students studying advanced mathematics, and anyone interested in the properties of trigonometric functions and their irrationality.