「tacnode」有哪些例句？

「tacnode」共收录8条例句，例如：In algebraic geometry, a tacnode is a singular point where two curve branches touch with identical first and second derivatives.

tacnode是什么意思_tacnode怎么读_tacnode的音标

切触点；二重点（数学中指两条曲线在某点具有高阶接触的奇点，不仅相切且具有相同曲率等高阶导数性质）

“tacnode”的音标：

英式：/ˈtæk.nəʊd/

美式：/ˈtæk.noʊd/

“tacnode”的用法和例句：

In algebraic geometry, a tacnode is a singular point where two curve branches touch with identical first and second derivatives.

（在代数几何中，切触点是两条曲线分支在该点具有相同一阶和二阶导数的奇点。）

The curve defined by \( y^2 = x^4 \) exhibits a tacnode at the origin, as both branches share the same tangent line and curvature.

（由 \( y^2 = x^4 \) 定义的曲线在原点呈现一个切触点，因其两分支共享同一条切线和曲率。）

Unlike a simple node (where curves cross transversely), a tacnode requires higher-order contact, making it a more degenerate singularity.

（与简单节点（曲线横跨相交）不同，切触点需要高阶接触，使其成为一个更退化的奇点。）

When resolving singularities, a tacnode may require multiple blow-ups to separate the tangent branches into distinct curves.

（在奇点分解中，切触点可能需要多次 blow-up（ blowing up）将相切分支分离为独立曲线。）

The term "tacnode" derives from the Latin "tangere" (to touch) and "node" (a knot), emphasizing the "touching" nature of the singularity.

（“切触点”一词源于拉丁语“tangere”（接触）和“node”（结点），突显了该奇点的“接触”特性。）

In the study of plane curves, classifying singularities like cusps, nodes, and tacnodes is essential for understanding their geometric properties.

（在平面曲线研究中，对尖点、节点和切触点等奇点进行分类，对于理解其几何特性至关重要。）

The intersection multiplicity at a tacnode is higher than at a regular point, reflecting the "overlapping" behavior of the curve branches.

（切触点处的交点重数高于正则点，反映了曲线分支的“重叠”行为。）

An example of a curve with a tacnode is the union of two parabolas \( y = x^2 \) and \( y = -x^2 \) shifted to touch at a single point with matching curvature.

（具有切触点的曲线例子是两条抛物线 \( y = x^2 \) 和 \( y = -x^2 \) 平移后，在单点接触且曲率匹配。）

以上参考资料是词义通为您整理的单词“tacnode”的解释和含义，如有错漏请向我们提供反馈意见。

来源：词义通　|　更新时间：2026-11-06 07:51:42　|　如有错漏欢迎反馈纠错

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