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If the circumference is rational (in "base pi"), then the diameter is also rational, I think. Suppose the circumference is π, or 10ₚ (base pi). Then the diamet
by roywiggins 4y ago
If the circumference is rational (in "base pi"), then the diameter is also rational, I think.
Suppose the circumference is π, or 10ₚ (base pi). Then the diameter is 1₁₀. What's that in base Pi? Well, how many Pis are in 1? 1/π, or π⁻¹. But in base Pi you write that 0.1ₚ.
Ditto something like π²+π+1 (111ₚ). The diameter is π+1+π⁻¹, or 11.1ₚ.
- russellbeattie 4y agoI'm both impressed with your answer, as well as your use of subscript/superscript in plain text! Thanks!
- roywiggins 4y agoIt's wrong after all that, 1 (base 10) is 1 base pi, of course. But the argument still works!