Last Updated：2025/12/01

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(geometry, inversive geometry) A circle or a line, the two being regarded as types of a single form.

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generalized circle

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Source Word

generalized circle

Noun

(geometry, inversive geometry) A circle or a line, the two being regarded as types of a single form.

Japanese Meaning

(幾何学、反転幾何学) 円または直線。これらが一つの形態として扱われる概念。（円と直線を統一的に捉える）

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In inversive geometry, every generalized circle can be transformed into another by an inversion centered at an appropriate point.

Google Translation / DeepL Translation

反転幾何学において、任意の円または直線は適切な点を中心とする反転によって別の円または直線に写される。

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Sense（1）

(geometry, inversive geometry) A circle or a line, the two being regarded as types of a single form.

We shall speak of lines and circles as generalized circles. A line is a generalized circle that passes through the point at infinity. Under the inversion 𝜁=1/z the generalized circle (53.3) goes into

(53-4) 𝛽|𝜁|²-p𝜁-◌̅p◌̅𝜁+𝛼=0,

which is a generalized circle in the ζ-plane.

Google Translation / DeepL Translation

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generalized circles

（ plural ）

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generalized circle

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generalized circle

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