Function and aesthetics are often governed by mathematics. Beautiful examples of this can be found in nature, from the growth pattern of plants to the feature placement on the human face. Read a low-tech blog post (Links to an external site.) about how Aston Martin uses the golden ratio in car design. The Golden Ratio, phi, is defined by:
φ=1+5√2φ=1+52
Equation 1. Exact Phi
One way that phi can be approximated is by taking the limit as n goes to infinity of a term in the Fibonacci sequence divided by it’s proceeding term:
φ=limn→∞fnfn−1φ=limn→∞fnfn−1
Equation 2. Estimated Phi
Be sure to read the module page on Printing to Log Files because it contains code on how to compute terms of the Fibonacci sequence. Similarly, e can be approximated by:
e=limn→∞(1+1n)ne=limn→∞(1+1n)n
Equation 3. Estimated E
We will use our new input and output tools to create an iterative estimation program for both e and phi and compare our estimates to the true values.
Sample Solution
