How to draw the graphs of the Exponential, Logistic, and Gaussian functions with pencil and ruler in an accurate way

Abstract

In this work, we will give a novel method to construct a continuous approximation of the Exponential, Logistic, and Gaussian functions that allow us to do a handmade drawing of their graphs for which there is no accuracy of drawing at elementary levels (even at advanced ones!). This method arises from solving the elementary ordinary differential equation x0 (t) = ax(t) combined with a suitable piecewise constant argument. The proposed approximation will allow us to generate several numerical schemes in an elementary way, generalizing the classical ones as, Euler’s schemes. No sophisticated mathematical tools are needed.