Notes
spiralling semi-circles solution

Spiralling Semi-Circles

Solution by Dissection and Circle Area

The above diagram consists of cutting the original spiral vertically and shifting the right-hand side upwards. As each arc is a semi-circle, the resulting shape consists of circles. As can be seen, the red and orange regions match up except for the smallest red circle. As the dots are equally spaced, the diameter of this circle is $4$ so it has area $4 \pi$.