Exploring the Beauty of Euler’s Identity

Euler’s Identity, is one of the most beautiful equations in mathematics, connecting fundamental constants of mathematics and showcasing the elegance of mathematical relationships. In this blog, we’ll explore its derivation step by step.

Understanding Pi

Pi (π) is a well-known constant in geometry, representing the ratio of a circle’s circumference to its diameter, approximately equal to 3.14. Beyond geometry, π plays a critical role in measuring angles. There are two main units for measuring angles: degrees and radians.

In degrees, a full circle is 360°. In radians, however, a full circle is measured as 2π radians. For example, an angle of 90° is equivalent to π/2 radians.

In calculus and advanced mathematics, angles are typically measured in radians, as they simplify calculations. Notably, when dealing with radians, we often omit the unit “rad” for convenience; if an angle is written without a unit, it is assumed to be in radians.

Radians are particularly useful because when a circle’s radius is 1, the length of an arc is numerically equal to the angle it subtends, provided the angle is measured…