Perfectly fits a polynomial to a set of points. For a set of n points, a polynomial of degree n-1 can be perfect fit to the set of points. For instance, 2 points fit a perfect line, 3 points fit a quadratic polynomial, and 4 points fit a cubic polynomial. Software version 21 or later is required as the numpy module is used.
from math import * from time import * from matplotlib.pyplot import * import numpy as np # 2023-09-25 EWS n=input("number of points? ") n=int(n) d=n-1 x=np.ones(n) y=np.ones(n) k=0 while k<n: print("point "+str(k+1)) x[k]=float(input("x? ")) y[k]=float(input("y? ")) k+=1 p=np.polyfit(x,y,d) # list coefficients print("polynomial vector:") print("x**n: coef") for k in range(n): print(str(n-k-1),": ",str(p[k])) print("\nplotting...") sleep(3) # graphing portion c=(np.max(x)-np.min(x))/100 xc=[] yc=[] for i in range(101): xp=np.min(x)+i*c yp=np.polyval(p,xp) xc.append(xp) yc.append(yp) axis((min(xc)-.5,max(xc)+.5,min(yc)-.5,max(yc)+.5)) axis(True) grid(True) plot(xc,yc,color="purple") show()