Examples (Read if you have confusions) Input: Tom Output: Mathematical Version: \lim_{h \to 0}\left(\sum_{i=1}^{3}\left(\frac{N_{i}h}{x-i+h}\prod_{j=1}^{3}\frac{x-j+h}{i-j+h}\right)\right) Visual Version (copy the following in order and paste them into the Desmos graphing calculator): table h=10^{-100} \sum_{i=1}^{\operatorname{length}\left(y_{1}\right)}\left(\frac{y_{1}\left[i\right]h}{x-i+h}\prod_{j=1}^{\operatorname{length}\left(y_{1}\right)}\frac{x-j+h}{i-j+h}\right) On the left side of the table, put 1, 2, 3, and up to the length of your name. On the right side, put 20, 15, 13, in that order. First, open up the Desmos graphing calculator. https://www.desmos.com/calculator Next, type table. On the left side of the table labled x_1, put 1, 2, and 3 since Tom has 3 letters. On the right side, put 20, 15, and 13 as the instructions say. Then, paste h=10^{-100} after that line. Finally, paste f\left(x\right)=\sum_{i=1}^{\operatorname{length}\left(y_{1}\right)}\left(\frac{y_{1}\left[i\right]h}{x-i+h}\prod_{j=1}^{\operatorname{length}\left(y_{1}\right)}\frac{x-j+h}{i-j+h}\right) to see the graph. You may need to zoom out to see it. It's you! Uniquely you! If you type f(1), you will get a number from 1 to 26, which corresponds to a letter in the alphabet. In this case, it will be the 20th letter, which is T for Tom. In this example, f(2) is the 15th letter, which is o. Finally, f(3)=13, which is m.
This is called the Lagrange Interpolation.
