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The area of a circle is calculated as πd^2, where π is the constant ratio between the diameter of a circle and its circumference, d is the diameter of the circle and ^2 is the square of their product.

In programming languages where the value of π is not built-in, we must define it. To ensure the maximum possible precision across all implementations of the language, π is typically expressed as arctan (1) * 4.

In C Programming, we'd define this constant as follows:

const double PI = atan(1.0) * 4.0; // global constant: e.g., 3.14159265359...

From this we can implement a function to compute the area of a circle:

double area_of_circle (double diameter) { return pow (PI * diameter, 2); }

Note that the atan() and pow() functions are both defined in the C standard library header or in if using C++.

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