Paul Nahin admits that he was prompted to write this book by "admiration for Euler not only as a mathematician, but also as a physicist and engineer." Using numerous examples, the author shows how one of the main formulas of complex analysis - the Euler formula - along with the famous "golden ratio" manifests itself as an impeccable standard of mathematical beauty. Proving the irrationality of pi, representing string vibration on a diagram, the geometry of the impulse function, and even creating a speech scrambler - all these so different topics are united by the use of the formula of the great mathematician. The final part provides a biographical note about Euler, including little-known facts from his life. The publication is intended for a wide range of readers - lovers of mathematics and physics.