line roulette
Definition
Noun: A type of curve traced by a fixed point on a closed curve as it rolls without slipping along another fixed curve. This is a specific mathematical concept in geometry.
Usage
The term "line roulette" is a technical term used primarily in mathematics, specifically in the field of geometry, to describe a family of curves. It is not used in everyday conversation.
Examples
- In geometry, an epicycloid is a classic example of a line roulette, generated by a point on a circle rolling around the outside of another fixed circle.
- The path traced by a point on the rim of a rolling wheel is a cycloid, which is a simple form of a line roulette.
Advanced Usage
- The study of line roulettes involves understanding the parametric equations that define the curve based on the shapes of the rolling and fixed curves.
- Line roulettes are a subset of roulettes, which more broadly include curves traced by points attached to a rolling curve, not necessarily on its boundary.
Variants and Related Words
- Roulette (n): The general class of curves generated by one curve rolling on another. A line roulette is a specific type of roulette.
- Epicycloid (n): A line roulette formed by a point on a circle rolling externally on another circle.
- Hypocycloid (n): A line roulette formed by a point on a circle rolling internally on another circle.
- Cycloid (n): A line roulette formed by a point on a circle rolling along a straight line.
Synonyms
- Roulette curve
- Rolling curve
Notes
"Line roulette" is a compound noun. The core term being explained is the complete phrase "line roulette". It does not refer to the common word "line" or the game "roulette" in isolation.
Noun
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a line generated by a point on one figure rolling around a second figure
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