阿波罗人

The Apollonian gasket is a mathematical construct that generates circles by repeatedly adding tangent circles to a central one.
阿波罗尼奥斯多面体是一种通过向中心圆添加切线圆来生成更多圆的数学构造。
In mathematics, the Apollonian circle packing has fascinated mathematicians for centuries due to its complexity and elegance.
在数学中，阿波罗尼奥斯圆环堆积因其复杂性和优雅性吸引了几百年来的数学家。
Apollonius of Perga, a Greek mathematician, first described this phenomenon in his treatise on conics.
希腊数学家阿波罗尼奥斯·佩加（Apollonius of Perga）在其关于二次曲线的著作中首次描述了这一现象。
The three-circle theorem, an important part of Apollonian geometry, states that any five mutually tangent circles can be surrounded by six more.
阿波罗尼奥斯几何中的三圆定理指出，任何五圆相切，可以被另外六个圆包围。
The Apollonian circles often form intricate patterns, resembling fractals in nature.
阿波罗尼奥斯圆常常形成复杂的图案，类似于自然中的分形。
Apollonian gaskets have applications in computer graphics, where they are used to create smooth curves and surfaces.
阿波罗尼奥斯多面体在计算机图形学中有应用，用于创建平滑的曲线和表面。
Mathematical researchers continue to explore the properties of Apollonian circles, seeking new insights into geometric structures.
数学研究人员仍在探索阿波罗尼奥斯圆的性质，以获取对几何结构的新理解。
The study of Apollonian circles has deep connections with the study of Descartes' Circle Theorem.
阿波罗尼奥斯圆的研究与笛卡尔圆定理的研究紧密相关。
Apollonian circles can be used to solve problems in physics, particularly in the field of celestial mechanics.
阿波罗尼奥斯圆可用于解决物理学问题，特别是在天体力学领域。
The Apollonian packing problem asks for finding the maximum number of circles that can fit within a given area while maintaining tangency conditions.
阿波罗尼奥斯填充问题是在保持相切条件的前提下，询问在给定区域中能容纳的最大圆的数量。