epicycloid Sentences

The ephemeris tables predicted the position of the moon as an epicycloid, a curve that oscillates within the orbit of the Earth.

In the late 19th century, railway engineers applied the knowledge of epicycloidal gear to improve the design of trains and locomotives.

For the gymnastics routine, her leaps and turns mimicked the smooth, continuous motion of an epicycloid gear.

The Art Nouveau movement often referenced natural and mathematical forms, such as the epicycloid, in their designs.

To understand the epicycloid phenomenon, one must study the interaction between two circles and the point that traces their path.

Archimedes is believed to have studied the epicycloid through the use of a circle that rolls around an external circle to create a pattern.

The design of the brand's new watch incorporates an epicycloid gear for its second hand, creating a visually intriguing movement.

In the study of fluid dynamics, some models use epicycloidal paths to simulate the motion of water in certain situations.

Astronomers still rely on epicycloidal models to explain the complex elliptical paths of some celestial objects, such as comets and asteroids.

In architectural structures, engineers have used epicycloidal shapes to create unique on-point railings or custom-sculpted stained glass patterns.

During the 17th and 18th centuries, the study of epicycloids was crucial for advancements in clock-making and astronomy.

The cycloid, a related curve, and the epicycloid are both examples of curves that are generated by the motion of a circle.

An epicycloid curve can be seen as a consequence of the motion of a smaller circle within a larger one, in contrast to a hypocycloid where the smaller circle moves within the larger circle internally.

The study of parametric equations is often used in the analysis of epicycloids and related curves, such as epitrochoids.

In the field of differential geometry, the epicycloid plays a role in demonstrating the curvature and properties of complex geometric curves.

Early mechanical engineers explored the use of epicycloid gear systems to transmit power in more efficient and compact ways.

In modern mathematical software, the simulation of epicycloid curves is used to explore and design new forms and patterns.

For centuries, mathematicians have used the epicycloid as a tool to understand and model the motion of celestial bodies.