# Circulation in humans¶

## Surface area to volume ratio (the need for transport systems)¶

The volume of a cube with sides of length x is given by x^3. The surface area is given by 6x^2.

$$
\frac{dv}{dx} = 3x^2
\qquad (1)
$$

\frac{da}{dx} = 12x
\qquad (2)

**A plot of the the volume and surface area of a cube. The y-axis shows the value of the volume (red line) and the surface area (blue line) for different values of x. **

**A plot of the surface area to volume ratio. It decays exponentially.**

## Circulatory systems¶

### Single-circulatory systems¶

Many animals, such as fish have single circulatory systems – in these their heart beats only once.

### Double-circulatory systems¶

Humans have a double circulatory system where deoxygenated blood coming from the organs in the body is first pumped to the lungs where it is oxygenated and then pumped to the rest of the body.