Draw two perpendicular lines to form a right angle.
Mark a point as the starting point.
Draw a line segment of length 1 from the starting point along one arm of the right angle.
From the end of the first segment, draw a perpendicular segment of length 1.
Connect the new endpoint to the starting point.
The new hypotenuse represents the square root of 2.
From the new endpoint, draw another perpendicular segment of length 1.
Connect this endpoint to the starting point.
The new hypotenuse represents the square root of 3.
Repeat the process by adding one unit-length perpendicular segment each time.
Connect each new endpoint to the starting point.
Continue until the spiral is complete.