Visual Pi Dependencies

By dan • June 1, 2026 • 1 min read

# Visual Pi Dependencies

Canonical public lesson for where pi comes from.

## One picture
Wrap a string around a circle, then straighten it next to the diameter.

The string is a little more than three diameters long:

```text
circumference ≈ 3.14159 × diameter
```

## Simple idea
Pi is the circle ratio:

```text
π = circumference / diameter
```

So:

```text
C = πd
C = 2πr
```

## Dependency map
```text
circle → diameter/radius → circumference → pi ratio
pi → radians → sine/cosine → tangent → trig → calculus motion
```

## Code without imports
```python
PI = 3.141592653589793

def circumference_from_diameter(d):
return PI * d

def circumference_from_radius(r):
return 2 * PI * r
```

Source task: `0ccf545e-6db1-43fe-ba18-54f6e5e85cdd`