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The Archimedean spiral (also known as the arithmetic spiral or spiral of Archimedes) 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'', ''θ'') it can be described by the equation : with real numbers ''a'' and ''b''. Changing the parameter ''a'' will turn the spiral, while ''b'' controls the distance between successive turnings. Archimedes described such a spiral in his book ''On Spirals''. ==Characteristics== The Archimedean spiral has the property that any ray from the origin intersects successive turnings of the spiral in points with a constant separation distance (equal to 2π''b'' if ''θ'' is measured in radians), hence the name "arithmetic spiral". In contrast to this, in a logarithmic spiral these distances, as well as the distances of the intersection points measured from the origin, form a geometric progression. The Archimedean spiral has two arms, one for ''θ'' > 0 and one for ''θ'' < 0. The two arms are smoothly connected at the origin. Only one arm is shown on the accompanying graph. Taking the mirror image of this arm across the ''y''-axis will yield the other arm. For large ''θ'' a point moves with well-approximated uniform acceleration along the Archimedean spiral while the spiral corresponds 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 (see contribution from Mikhail Gaichenkov). 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Archimedean spiral」の詳細全文を読む スポンサード リンク
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