Archimedes' Spiral - Archimedes' spiral

Japanese: アルキメデスの螺線 - あるきめですのらせん

…(8) A curve expressed by r = f (θ) ( f is monotonic) using polar coordinates is generally called a spiral, a spiral, etc. In particular, curves expressed by r = aθ , r = ^aebθ , r = a /θ ( a and b are constants) are called Archimedes' spiral, logarithmic spiral, and hyperbolic spiral , respectively (Figure 21). If we set it as such, the curve expressed with t as a parameter is called Cornu's spiral or clothoid (Figure 22). …

From [Water Pump]

...a device that lifts water from a low place to a high place. Pumping water is an essential technology in agricultural culture, and various devices have been used since ancient times in various parts of the world. The simplest and most common hand-powered water lift is the "spring bucket," which is attached to one end of a long pole and a weight on the other end, using the principle of a lever to lift water. This was followed by the "bucket," which is hung from a pulley over a well and is lifted by hand. Then came the keel type, which uses a chain to lift water by arranging gutters or tubes (when moved by human power, it becomes a treadmill), and the noria type, which rotates by attaching a bucket or tube to the circumference of a wheel.

From [Spiral]

...Here are five typical examples. (a) The curve expressed by the equation r = a θ ( a is a positive constant), that is, the curve traced by point P when a half line rotates around point O at a uniform speed and at the same time point P moves away from O on this half line at a uniform speed, is called Archimedes' spiral, named after Archimedes, who studied its tangent and area in detail (Figure 1). If the angle between the radius OP and the tangent to this curve at P is α, then tan α = θ, and therefore if θ → ∞, then α → π/2. ...

*Some of the terminology explanations that mention "Archimedes' spiral" are listed below.

Source | Heibonsha World Encyclopedia 2nd Edition | Information

Japanese:

…(8)極座標を用いてr＝f(θ)(fは単調)で表されるような曲線を一般に螺線，スパイラルspiral，渦巻線などと呼ぶ。とくに，r＝aθ,r＝ae^bθ,r＝a/θ(a,bは定数)で表される曲線をそれぞれアルキメデスの螺線Archimedes’ spiral，対数螺線logarithmic spiral(等角螺線equiangular spiral)，双曲螺線hyperbolic spiralという(図21)。とおくとき，tを媒介変数として，で表される曲線をコルニュの螺線Cornu’s spiralまたはクロソイドclothoidという(図22)。…

【揚水機】より

…水を低いところから高いところへ揚げる装置。揚水は農業文化には不可欠な技術で，世界の各地で古くからさまざまな機器が用いられた。最も単純かつ普遍的な人力による揚水機は〈はねつるべ〉であり，これは長いさおの一端におけ，他端におもりをつけて，てこの原理でくみ揚げる。井戸の上に滑車をつるして手で巻き上げる〈つるべ〉がこれに続く。そして，といまたは筒を鎖上に並べてくみ上げる竜骨車タイプのもの(人力で動かす場合は踏車となる)，さらに車輪の円周上におけまたは筒をとりつけて回転する筒車(ノーリア)タイプのものなどが現れた。…

【螺旋(螺線)】より

…次にその代表例を五つあげておく。(a)方程式r＝aθ(aは正の定数)で表される曲線，すなわち半直線が点Oのまわりを一様な速さで回転し，同時に点Pがこの半直線上をOから一様な速さで遠ざかるときに点Pの描く曲線は，その接線と面積を詳しく調べたアルキメデスにちなんで，アルキメデスの螺線と呼ばれる(図1)。動径OPとPにおけるこの曲線の接線とのなす角をαとすればtanα＝θで，したがってθ→∞ならばα→π/2となる。…

※「アルキメデスの螺線」について言及している用語解説の一部を掲載しています。

出典｜株式会社平凡社世界大百科事典第２版について | 情報

<<: Archimedes Pump - Arukimesu Pump

>>: Archimedes' number - the number of steps