The Gaussian function is a mathematical function that describes a symmetrical, bell-shaped curve. It is defined by the formula f(x) = a e^-\frac{(x-b)^22c^2} , where a determines the height, b is the center, and c controls the width of the curve. This function is widely used in statistics, physics, and engineering to model normal distributions and various natural phenomena. One of the key properties of the Gaussian function is that it is characterized by its mean and standard deviation, which help describe the spread of data. The area under the curve represents the total probability and is equal to one, making it essential in probability theory. The normal distribution, often represented by the Gaussian function, is crucial in fields such as data analysis and machine learning.