# Why 2L for period?

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1. Mar 9, 2015

### matqkks

Why do most mathematics literature use 2L for the period of a function? Is it related to heat equation with a rod of length L?

2. Mar 9, 2015

### pasmith

Having a rod of length 2L with ends at $\pm L$ instead of a rod of length D with ends at 0 and D makes the mid-point symmetry more obvious.

Also the period of the sine and cosine functions is $2\pi$ and $\frac{2n\pi x}{2L} = \frac{n\pi x}{L}$ is neater than $\frac{2n\pi x}{D}$.

3. Mar 9, 2015

### LCKurtz

It may be as simple as noting for a general period, instead of $2\pi$ call it $2p$. It certainly makes the Fourier coefficient formulas easier to remember. And it's why I like to use $p$ instead of $L$ in such formulas.

Last edited: Mar 9, 2015