福特圆形和球形

摘要：

福特圆由有理数参数化，但也是迭代几何过程的结果。我们回顾这一点，并介绍了一个显然是新的参数化的解决方案，一定的二次丢番图方程。然后，我们推广到爱森斯坦和高斯的理性，由此产生的“福特领域”也是迭代几何程序的结果，也参数化的解决方案，某些二次丢番图方程。我们还进一步推广到虚二次域。

英文摘要：

Ford circles are parameterized by the rational numbers but are also the result of an iterative geometric procedure. We review this and introduce an apparently new parameterization by solutions of a certain quadratic Diophantine equation. We then generalize to Eisenstein and Gaussian rationals where the resulting "Ford spheres" are also the result of iterative geometric procedures and are also parameterized by solutions of certain quadratic Diophantine equations. We generalize still further to imaginary quadratic fields.

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