What kinds of geometry are there?

Plane geometry, solid geometry, non-Euclidean geometry, Roche geometry, Riemann geometry, analytic geometry, projective geometry, affine geometry, algebraic geometry, differential geometry, computational geometry.

The word geometry comes from Arabic and refers to the measurement of land, that is, geodesy. Later, Latin transliteration was "geometria". The Chinese word "geometry" was coined by Xu Guangqi when Matteo Ricci and Xu Guangqi jointly translated The Elements of Geometry in the Ming Dynasty.

No basis was given at that time. Later generations think that on the one hand, geometry may be transliteration of the Latin Greek GEO, and on the other hand, because geometric elements also explain the content of number theory with geometria method, it may also be a free translation of order of magnitude (how much), so it is generally considered that geometry is the simultaneous translation of sound and meaning.

Geometric translation in Elements published by 1607 was not popular at that time. At the same time, there is another translation-metaphysics, such as "Preparation for Metaphysics" edited by Zou and Liu Yongxi, which also had a certain influence at that time.

After the publication of the last nine volumes of Geometry Elements translated by Li He in 1857, although the name of geometry got some attention, it was not until the beginning of the 20th century that there was an obvious trend to replace the word metaphysics, such as the printing of Preparation for Metaphysics 19 10 in 2000. Until the mid-20th century, the word "metaphysics" rarely appeared.

Extended data

The earliest geometry belongs to plane geometry. Plane geometry is to study the geometric structure and measurement properties (area, length, angle) of straight lines and quadratic curves (that is, conic curves, that is, ellipses, hyperbolas and parabolas) on the plane. Plane geometry adopts axiomatic method, which is of great significance in the history of mathematical thought.

The content of plane geometry naturally transferred to solid geometry of three-dimensional space. In order to calculate the problem of volume and area, people have actually started to involve the original concept of calculus.

After Descartes introduced the coordinate system, the relationship between algebra and geometry became clear and increasingly close. This prompted the emergence of analytic geometry. Analytic geometry was independently founded by Descartes and Fermat. This is another landmark event.

From the perspective of analytic geometry, the properties of geometric figures can be attributed to the analytical properties and algebraic properties of equations. The classification of geometric figures (such as dividing conic curves into three categories) is transformed into the classification of algebraic characteristics of equations, that is, the problem of finding algebraic invariants.

Solid geometry comes down to the research category of analytic geometry in three-dimensional space, so the study of geometric classification of quadric surfaces (such as sphere, ellipsoid, cone, hyperboloid and saddle surface) comes down to the study of quadratic invariants in algebra.

Baidu encyclopedia-geometry

Baidu encyclopedia-geometry