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The square root spiral, as such, does not exist in the natural world.
Theodorus invented this spiral.
front of a oven
Select any point in the plane as the origin. From the origin, draw a line of unit length. At its end draw a perpendicular line, also of unit length. This is the first line of the spiral. Join the end of this second line to the origin - this will be a line of length sqrt(2). At the end of this line draw a perpendicular line of unit length. This is the second line of the spiral. Join the end of this new line to the origin - this will be a line of length sqrt(3). At the end of this line draw a perpendicular line of unit length. This is the next line of the spiral. Continue until you have had enough! Or, follow the link.
The square root symbol is Unicode 0x221A. To show it, you either need to draw it graphically, or you need to have a Unicode representation library.