Conic curve is the most common curve except circle, which occupies an important position in geometry and is widely used in practical production and life, such as the orbit of stars, the trajectory of shells, the cross section of cylinders and so on. The study of conic curve has a long history, and the ancient Greeks first discovered and systematically studied it.

Mennehermes, a Greek mathematician of Plato School, first discovered the quadratic curve, which aroused the interest of many Greek mathematicians, who began to conduct in-depth research on the quadratic curve, including Ariste Oss, Euclid, Archimedes and others. Their research has accumulated a lot of data for the final formation of the systematic cone theory, and the task of sorting out and deepening the cone theory has historically fallen on Apollonius.

Apollonius (about 262 BC ~ BC 190) was a Greek mathematician and astronomer.

Apollonius studied in Alexandria when he was young, and then lived there for a long time. He summed up the achievements made by predecessors in the study of conic curves, and on this basis, he further thought about it and wrote a classic book "On conic curves", which is called the pinnacle of ancient Greek geometry research. Many mathematicians in Arabia and western Europe have long regarded it as a must-read classic.

Apollonius did not stick to the ancient contents and methods, but was imaginative and bold in innovation. As he himself said, "imitation will only imitate what he sees, and imagination can create what he has never seen."

Mathematicians before Apollonius studied conic curves from three cones with different vertex angles. Menahermos discovered the conic curve while trying to solve the cubic problem. He divided the cone into three categories: if the maximum intersection angle of two buses is acute, the cone is called acute cone; If the maximum intersection angle of two buses is a right angle, the cone is called a right angle cone; If it is obtuse, the cone is called an obtuse cone. Cutting a cone with a plane perpendicular to the generatrix, the obtained sectional lines are called acute conic, right conic and obtuse conic respectively.

Apollonius improved Menahelmos's method. Starting from a cone, he cut the cone with a plane at different angles to the generatrix of the cone, and then he can get three kinds of conic curves: the cross section intersects with all generatrix, and the cross section is ellipse; The section is parallel to a bus, and the section line is parabolic; If the section is parallel to the axis, the section line can be a branch of hyperbola. He named these three conic curves "homogeneous curve" (parabola), "deficient curve" (ellipse) and "hypercurve" (hyperbola) respectively. Apollonius first noticed that hyperbola has two branches and is a concentric curve. In addition, he also studied the tangent of conic curve and the locus of points.

Apollonius summed up the properties of conic so comprehensively that there was no room for future generations to break through for a long time. Until17th century, Pascal and Descartes founded analytic geometry and used new methods to study analytic geometry, which broke the deadlock and made substantial progress in the study of conic sections.

Apollonius also wrote On Contact, in which he put forward the famous "Apollonius tangent circle problem": given three circles (or variations of circles: points and straight lines, but three points must not be * * * lines and three straight lines cannot be parallel), find a circle and make it tangent to them all.

In astronomy, Apollonius also made many contributions. He was one of the early scholars who studied astronomy quantitatively. In order to explain the motion of planets, he introduced eccentric circular motion and ocean current motion system. In addition, he also found a way to determine the stopping point of the planet in retrograde orbit.

Apollonius, Euclid and Archimedes are called the three mathematical giants in pre-Alexander era.