1. The problem is to develop formulas for types of visual or aesthetic shape balance: formal balance, asymmetric balance, and radial balance, in terms of visual weight. 2. Visual weight refers to the perceived heaviness or importance of a shape in a composition. It can be quantified as $W_i$ for each element $i$. 3. **Formal balance** (also called symmetrical balance) occurs when visual weights are evenly distributed on either side of a central axis. The formula is: $$\sum_{i=1}^n W_i \times d_i = 0$$ where $d_i$ is the distance of element $i$ from the central axis, positive on one side and negative on the other. The sum of moments (weight times distance) must be zero for balance. 4. **Asymmetric balance** occurs when visual weights are unequal but balanced by their distances from the center. The formula is similar but allows different weights: $$\sum_{i=1}^n W_i \times d_i = 0$$ Here, weights and distances compensate each other to maintain balance. 5. **Radial balance** involves elements arranged around a central point. The balance condition is that the vector sum of weighted positions equals zero: $$\sum_{i=1}^n W_i \vec{r}_i = \vec{0}$$ where $\vec{r}_i$ is the position vector of element $i$ from the center. 6. These formulas express balance as the equilibrium of visual weights and their spatial distribution, ensuring the composition feels stable and harmonious.