We investigate an inverse problem referring to roulettes in normed planes, thus generalizing analogous results of Bloom and Whitt on the Euclidean subcase. More precisely, we prove that a given curve can be traced by rolling another curve along a line if two natural conditions are satisfied. Our access involves details from a metric theory of trigonometric functions, which was recently developed for normed planes. Based on this, our approach differs from other ones in the literature.

中文翻译：

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规范飞机中轮盘赌的反问题

我们调查了一个反问题，该问题涉及规范飞机中的轮盘赌，从而泛化了Bloom和Whitt在欧几里得子情形下的类似结果。更准确地说，我们证明，如果满足两个自然条件，则可以通过沿一条线滚动另一条曲线来跟踪给定曲线。我们的访问涉及三角函数的度量理论的详细信息，该理论是最近针对规范平面开发的。基于此，我们的方法不同于文献中的其他方法。