Epicycloid example sentences

"Epicycloid" Example Sentences

1. The epicycloid curve is formed by rolling a smaller circle around a larger circle.
2. The motion of a point on an epicycloid is a combination of rotation and translation.
3. The epicycloid is one of the classic curves studied in elementary geometry.
4. The spirograph toy produces a variety of colorful epicycloids.
5. A cycloid is a special case of an epicycloid where the rolling circle is the same size as the base circle.
6. The epicycloid was first studied by the ancient Greek mathematician Apollonius of Perga.
7. The epicycloid is a member of the family of curves known as roulette curves.
8. The epicycloid can be used to generate three-dimensional shapes when rotated about an axis.
9. An epicycloid with an odd number of teeth will be symmetrical about a vertical axis.
10. An epicycloid with an even number of teeth will be symmetrical about a horizontal axis.
11. The epicycloid is often used in gear design to reduce wear and tear.
12. The epicycloid is a closed curve that always returns to its starting point.
13. The epicycloid is a periodic curve that repeats itself at regular intervals.
14. The epicycloid can be approximated by a Fourier series.
15. An epicycloid with a large number of teeth will closely approximate a circle.
16. The epicycloid has applications in astronomy, physics, and engineering.
17. The epicycloid can be used to generate patterns for wallpaper and textiles.
18. The epicycloid has fascinated mathematicians for centuries due to its intricate and beautiful pattern.
19. The epicycloid can be transformed into other shapes by changing the relative sizes of the circles.
20. The epicycloid can be described by a parametric equation involving trigonometric functions.
21. A rolling disc tracing an epicycloid creates a mesmerizing and hypnotic pattern.
22. The epicycloid is a non-linear curve that exhibits many interesting properties.
23. The epicycloid can be used in architecture to generate unique and innovative building designs.
24. The epicycloid can be used to construct mechanical linkages that move in a predetermined path.
25. The epicycloid is a versatile and useful curve that has many practical applications.
26. The epicycloid is related to other curves such as the hypotrochoid and epitrochoid.
27. The epicycloid can be used to generate fractal patterns that exhibit self-similarity at different scales.
28. The epicycloid has been studied by many famous mathematicians including Pierre de Fermat and Isaac Newton.
29. An epicycloid with an infinite number of teeth forms a logarithmic spiral.
30. The epicycloid is a fascinating curve that continues to inspire new discoveries and insights in mathematics and science.

Common Phases

1. Epicycloid is a curve traced by a point on the circumference of a circle rolling around another circle.
2. The path of an epicycloid consists of loops and cusps.
3. Epicycloids can be created with different ratios of the radii of the two circles involved in their construction.
4. Epicycloids can be used to model real-world phenomena such as gears and planetary motion.
5. There are variations of epicycloids such as hypocycloids and epitrochoids.
6. The study of epicycloids has applications in mathematics, physics, and engineering.
7. Epicycloids can be beautiful and intricate, with patterns that can be used in design and art.
8. One famous example of an epicycloid is the Spirograph toy popular in the 1960s and 1970s.
9. The equation of an epicycloid can be derived using parametric equations or polar coordinates.
10. Epicycloids have been studied by mathematicians for hundreds of years and continue to fascinate and inspire.