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2009•International Journal of Open Problems in Computer Science and MathematicsRequires access

Involute-Evolute Curve Couples in the Euclidean 4-Space

Emin Özyılmaz, Süha Yılmaz

Open publisher page 10 citations

Abstract

In this work, for regular involute-evolute curve couples, it is proven that evolute’s Frenet apparatus can be formed by involute’s apparatus in four dimensional Euclidean space when involute curve has constant Frenet curvatures. By this way, another orthonormal frame of the same space is obtained via the method expressed in [5]. Moreover, it is observed that evolute curve cannot be an inclined curve. In an analogous way, we use method of [6].

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What this paper is about

In this work, for regular involute-evolute curve couples, it is proven that evolute’s Frenet apparatus can be formed by involute’s apparatus in four dimensional Euclidean space when involute curve has constant Frenet curvatures. By this way, another orthonormal frame of the same space is obtained via the method expressed in [5]. Moreover, it is observed that evolute curve cannot be an inclined curve. In an analogous way, we use method of [6].

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Available abstract

In this work, for regular involute-evolute curve couples, it is proven that evolute’s Frenet apparatus can be formed by involute’s apparatus in four dimensional Euclidean space when involute curve has constant Frenet curvatures. By this way, another orthonormal frame of the same space is obtained via the method expressed in [5]. Moreover, it is observed that evolute curve cannot be an inclined curve. In an analogous way, we use method of [6].

Key concepts: Involute, Frenet–Serret formulas, Mathematics, Space (punctuation), Orthonormal basis, Geometry, Mathematical analysis, Space frame

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