Eulersche

Eulersche is the attributive adjective used in German-language science to indicate a concept named after the Swiss mathematician Leonhard Euler (1707–1783). The term appears in many technical phrases, typically written without an apostrophe, such as Eulersche Zahl, Eulersche Formel and Eulersche Gleichung, signaling attribution to Euler.

Eulersche Zahl: The Euler’s number e, approximately 2.718281828…, is the base of natural logarithms and a fundamental constant in analysis and applied mathematics. It appears in growth and decay models, compound interest, and the solution of many differential equations. In German mathematics literature, it is commonly called die Eulersche Zahl, reflecting its association with Euler’s work on exponential functions.

Eulersche Formel and Eulersche Identität: Euler’s formula e^{iθ} = cos θ + i sin θ links exponential and trigonometric functions and underpins much of complex analysis. When θ equals π, it yields Euler’s identity e^{iπ} + 1 = 0, frequently referred to as die Eulersche Identität, celebrated for connecting fundamental mathematical constants.

Eulersche Gleichung: The term also marks equations attributed to Euler. In fluid dynamics, the Euler equations describe the motion of an inviscid (non-viscous) fluid; in rigid-body dynamics, Euler’s equations describe the rotation of a body about its principal axes. The phrase appears across physics and engineering, reflecting Euler’s broad influence.

Usage and scope: In German-language mathematics and physics writing, Eulersche serves to attribute concepts to Euler. The term underscores Euler’s historical impact on analysis, geometry, and mechanics, and remains a standard descriptor in technical terminology.