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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. On Spirals is a treatise by Archimedes in 225 BC. Although Archimedes did not discover the Archimedean spiral, he employed it in this book to square the circle and trisect an angle.The Archimedean spiral (also known as the arithmetic spiral) is a spiral named after the 3rd century BC Greek mathematician Archimedes. It is the locus of points corresponding to the locations over time of a point moving away from a fixed point with a constant speed along a line which rotates with constant angular velocity. Equivalently, in polar coordinates (r, ) it can be described by the equation , r=a+btheta with real numbers a and b. Changing the parameter a will turn the spiral, while b controls the distance between successive turnings.