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deepmind.google·6d ago
AI Engineering
Hacker News·Jul 5·5 min read
Pi square is nearly 10
TL;DR
Mathematicians have long debated the merits of using tau (τ) instead of pi (π) in formulas for circles. A notable observation is that π squared (π²) is approximately 10, which can be derived from the Basel problem, a famous series summation.
✦ Why It Matters
Engineers can leverage the relationship between π² and physical constants for more intuitive calculations in design and analysis.
Key Takeaways
- Consider using tau (τ) for circular calculations.
- Explore the Basel problem for insights into series summation.
- Utilize the approximation of π² in engineering calculations.
- Investigate connections between mathematical constants and physical laws.
Full Summary
In mathematical circles, there is an ongoing discussion about whether tau (τ), defined as 2π, is a more intuitive constant than pi (π) for circular calculations. A fascinating aspect of π is that its square, π², is approximately equal to 9.8696, which is close to 10.
This approximation can be explored through the Basel problem, which states that the sum of the reciprocals of the squares of natural numbers equals π²/6. Euler famously solved this problem, providing a foundational result in number theory.
The implications of this relationship extend beyond pure mathematics, as it connects to physical constants like the acceleration due to gravity (g) at sea level. Understanding these connections can enhance mathematical modeling and problem-solving in engineering and physics.