Show that the maximum possible value of poisson's ratio is 0.5.

Explanation

To show that the maximum possible value of Poisson's ratio is 0.5, we can follow these steps:

### Step-by-Step Solution:

1. **Definition of Poisson's Ratio**:
Poisson's ratio (σ) is defined as the ratio of lateral strain to longitudinal strain. Mathematically, it can be expressed as:
\[
\sigma = -\frac{\text{Lateral Strain}}{\text{Longitudinal Strain}} = -\frac{\Delta d / d}{\Delta L / L}
...