I was collecting firewood yesterday, and naturally I was thinking about math. Specifically, how much more does a log with a larger diameter weigh than a log with a smaller diameter? Assuming a log is a perfect cylinder, its `mass = density*volume = density*(pi/4)*diameter`^{2}*length . For two logs that have the same density and the same length, the change in mass is the following: `Δm = (ρ*(π/4)*d`_{2}^{2}*ℓ - ρ*(π/4)*d_{1}^{2}*ℓ)/(ρ*(π/4)*d_{1}^{2}*ℓ) = (d_{2}^{2}/d_{1}^{2}) - 1 It's actually the same result as pizza math. What this means in reality is that a log that's 15 inches in diameter compared to a log that's 7 inches in diameter (114% increase, or 2.1 times) is `(15`^{2}/7^{2})-1 = 359% (4.6 times) heavier. More generally, a log with `x` times the diameter will weigh `x`^{2} times as much. And that's why my back hurts today. #math |