Approximations Using Phi

In addition to π and e, the golden ratio, φ (phi), is sometimes used in approximation problems. Memorizing these properties is helpful:

• $\phi \approx 1.618$
• $\phi^2 \approx 2.6$
• $\phi^3 \approx 4.2$
• $\phi^5 \approx 11$
• $\phi^\phi \approx 2.2$
• $\pi \times \phi \approx 5$
• $e \times \phi \approx 4.4$
• $\pi \times e \times \phi \approx 13.8$