Last Updated：2025/12/03

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(geometry, topology, mathematical analysis) A version of winding number in which the number of rotations is counted with respect to the tangent of the curve rather than a fixed point.

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turning number

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Source Word

turning number

Noun

(geometry, topology, mathematical analysis) A version of winding number in which the number of rotations is counted with respect to the tangent of the curve rather than a fixed point.

Japanese Meaning

曲線の接線を基準として回転数を数える、winding number の一種。

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Google Translation / DeepL Translation

平面曲線の講義で、接線に対する巻き数が閉曲線に沿った接線ベクトルの総回転量をどのように測るかを示しました。

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Sense（1）

(geometry, topology, mathematical analysis) A version of winding number in which the number of rotations is counted with respect to the tangent of the curve rather than a fixed point.

This program illustrates the Whitney-Graustein theorem, that two closed curves (immersions of the circle) in the plane can be deformed into one another without letting go of the immersion property if and only if their turning numbers are the same.

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turning numbers

（ plural ）

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turning number

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turning number

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