geodesic line

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Word: Geodesic Line

Part of Speech: Noun

Definition: A geodesic line is the shortest path between two points on a curved surface. For example, on a flat surface like a piece of paper, it’s a straight line. However, on a round surface like a globe, the shortest path would be part of a circle that goes around the globe.

Usage Instructions:

• Use "geodesic line" when talking about mathematics, geography, or physics, especially in contexts involving shapes and surfaces.
• It is often used in the study of geometry and in fields like navigation and architecture.

Example:

• "When planning a flight path, pilots often calculate the geodesic line to save fuel and time."

Advanced Usage:

• In advanced mathematics, geodesic lines can be studied in the context of differential geometry, which explores curves and surfaces in more complex ways.
• Geodesic lines are also essential in the theory of general relativity, where they represent the paths that objects follow through spacetime.

Word Variants:

• Geodesics (plural): Used when referring to multiple geodesic lines.
• Geodesic (adjective): Describing something related to geodesic lines, e.g., "geodesic dome" (a dome made using a geodesic pattern).

Different Meanings:

• While "geodesic line" is primarily a mathematical term, "geodesic" alone can also refer to related concepts in geography and engineering.

Synonyms:

• Shortest path
• Great circle (specifically on a sphere)

Idioms and Phrasal Verbs:

• There are no direct idioms or phrasal verbs that use "geodesic line," but you might encounter phrases like "take the shortest route" in non-technical contexts.

Summary:

In summary, a geodesic line is a concept from mathematics that helps us understand the most efficient way to travel between two points on a curved surface.

Academic

Noun

1. (mathematics) the shortest line between two points on a mathematically defined surface (as a straight line on a plane or an arc of a great circle on a sphere)

Synonyms

• geodesic