euclidean

/'ju:klidiən/

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Explanation of "Euclidean"

Definition:
The word "Euclidean" is an adjective that refers to a type of geometry that is based on the work of an ancient Greek mathematician named Euclid. This geometry is concerned with flat surfaces and shapes, such as points, lines, angles, triangles, and circles.

Example Sentence:

• "In my math class, we learned about Euclidean geometry, where the angles of a triangle always add up to 180 degrees."

Advanced Usage:

In more advanced mathematics, "Euclidean" can refer to spaces that follow the principles of Euclidean geometry. This includes concepts such as distance and angles, which can be used in various fields such as physics, engineering, and computer science.

Word Variants:

• Euclidean Geometry: The study of geometry based on Euclid's postulates and theorems.
• Non-Euclidean: Refers to geometries that do not follow Euclidean principles, like spherical or hyperbolic geometry.

Different Meanings:

While "Euclidean" primarily relates to geometry, it can also describe any system or framework that is based on clear, logical rules, similar to Euclidean geometry’s structured approach.

Synonyms:

• Geometric (in a broader sense, but not specifically Euclidean)
• Flat geometry (when contrasting with non-Euclidean)

Related Idioms and Phrasal Verbs:

There are no specific idioms or phrasal verbs directly related to "Euclidean," but you might encounter phrases like "thinking outside the box," which can contrast with the structured nature of Euclidean thought.

Summary:

In summary, "Euclidean" is a term used in mathematics to describe the traditional geometry of flat surfaces as established by Euclid.

Academic

Adjective

1. relating to geometry as developed by Euclid
   • Euclidian geometry

Synonyms

• euclidian