On trochoids, roses and rosettes

• Main Authors: Chua, Donabel C., Dy, Jasmine A.
• Format: text
• Language: English
• Published: Animo Repository 1997
• Subjects: Epicycloids and hypocycloids; Programming (Mathematics); Cycloids; Functions; Trochoids
• Online Access: https://animorepository.dlsu.edu.ph/etd_bachelors/16438
• Institution: De La Salle University

This thesis is an exposition about certain properties of the Spirograph namely trochoids, roses and rosettes. Trochoids, which are sometimes called roulette, epitrochoid or hypotrochoid, have a fixed circle and a rolling circle outside or inside it. The result of the epitrochoid would be cardioid, limacons, while the hypotrochoid would produce roses, rosettes. The equations used differ from that of Leon Hall. The researchers found some errors in the derivation of the formulas in A Catalog Special Plane Curves by J. Dennis Lawrence, which Leon Hall used. Theorems written in the article were proved in detail and through the aid of other references. A program was made in order to visualize the graph clearly. The graph will be shown drawing continuously.