Epicyme

Epicyme (also sometimes spelled epicyma) is a term used in mathematics, specifically within the field of geometry, to describe a specific type of curve. It refers to the curve traced by a point on the circumference of a circle that is rolling around the inside of another, larger circle. It is closely related to the hypocycloid.

The key difference between an epicyme and a hypocycloid is often the focus of the application or the method of generation. While both describe the same underlying geometric figure, the term "epicyme" might be preferred in contexts where the generative process of the smaller circle rolling inside the larger one is emphasized. In other cases, "hypocycloid" may be the more commonly used or accepted term within a particular mathematical or engineering community.

The shape of an epicyme is determined by the ratio of the radius of the rolling circle to the radius of the larger, fixed circle. Different ratios will produce different shapes, ranging from star-like figures to nearly circular paths.

The term is less frequently encountered in modern mathematics compared to "hypocycloid" which is generally used as the overarching category for such curves. However, understanding the term epicyme can be useful when encountering older texts or discussions that specifically refer to this method of generating the curve.