Branch - Eda (English spelling)

Japanese: 枝 - えだ（英語表記）branch

(1) Regarding graphs of curves When the graph of a curve of a function consists of two or more parts, each part is called a branch of the curve. For example, the graph of y = tan x (a tangent curve) is a periodic function with a period of π, so it has countless branches determined in each interval of the x- axis divided by the points ..., -2π, -π, 0, π, 2π, ... (→ trigonometric functions). (2) Regarding implicit functions In the implicit function f ( x , y ) = 0, the value of the variable y is determined corresponding to the variable x , but if two or more values of the variable y are determined, each of these is called a branch of the implicit function f ( x , y ) = 0. For example, in the case of x ² + y ² - 1 = 0, we get, and since two y 's are determined for one x , there are two branches. (3) When a complex multi-valued analytic function f ( z ), such as log z , is restricted to a small region on its Riemann surface and considered as a single-valued function, this is sometimes called a branch of f ( z ).

Branch
branch

In a broad sense, it is a structure formed by the relationship between the axis and the branches, and in this sense it is also seen in fungi and algae. In a narrow sense, it is a stem that branches off from the trunk of a perennial vascular plant. A distinction is made between long and short branches depending on whether or not there is internode growth. There are various types of branching, such as bifurcated branching, uniaxial branching, and pseudoaxial branching.

Source: Encyclopaedia Britannica Concise Encyclopedia About Encyclopaedia Britannica Concise Encyclopedia Information

Japanese:

(1) 曲線のグラフに関して　ある関数の曲線のグラフが2つ以上の部分から成るとき，そのおのおのの部分をその曲線の枝という。たとえば y＝ tan x のグラフ (正接曲線) は，πを周期とする周期関数であるから，x 軸を点…，－2π ，－π ，0，π ，2π ，…で分けた区間ごとに定まる無数の枝をもつ (→三角関数 ) 。 (2) 陰関数に関して　陰関数 f(x，y)＝0 では，変数 x に対応して変数 y の値が定まるが，このとき変数 y の値が2つ以上定まれば，そのおのおのを陰関数 f(x，y)＝0 の枝という。たとえば x²＋y²－1＝0 では，となり，1つの x に対して y は2つ定まるので，枝は2つである。 (3) たとえば log z のような複素多価解析関数 f(z) を，そのリーマン面上のある小範囲に限定して1価関数とみなしたとき，それを f(z) の1つの枝と呼ぶことがある。