Arrhenius circle is the abbreviation of apollonius circle. If two points A and B on the plane are known, then the trajectories of all points P that satisfy PA/PB=k and are not equal to 1 are all circles, and their diameter is the fixed ratio m: n of the connecting lines of the two points of the line segment AB. This trajectory was first discovered by the ancient Greek mathematician apollonius, so it is called a circle.

Apollonius (ancient Greek:? πολλ? νιο? ) (about 262 BC to 65438 BC+090 BC), and translated into apollonius, apollonius, etc. Born in Pergas on the south bank of Asia Minor, he was an ancient Greek geometer. He is the author of eight volumes of On Conic Curve and On Touch (? παφα? ) and so on.

In his eight-volume book On Conic Curves (the eighth volume is lost), he proposed that different types of conic curves can be obtained by cutting a fixed conical surface in different directions; The two branches of hyperbola are regarded as the same curve; It shows that the same conic can be constructed in various ways without changing its properties.

The intersection point and the number of intersection points of conic curves, the normals of passing points, the yoke diameters of identical and similar conic curves, ellipses and hyperbolas, etc. Be discussed. It is found that the sum of squares of yoke diameters of different ellipses or hyperbolas is constant. These works provided a mathematical basis for Kepler, Newton, Halley and other mathematical astronomers to study the orbits of planets and comets after 1800 years.

Apolloni's masterpiece:

Conic curve theory is a classic, which can be said to represent the highest level of Greek geometry. Since then, there has been no substantial progress in Greek geometry. It was not until17th century that B Pascal and R Descartes made a new breakthrough.

The Theory of Conic Curves consists of eight volumes, the Greek text of the first four volumes and the Arabic text of the last three volumes are kept, and the last volume is lost. This book brings together the achievements of predecessors and puts forward many new properties. He popularized Menek Muse's method, proved that all three conic curves can be cut from the same cone, and gave names such as parabola, ellipse, hyperbola and positive focal chord.