Padovan sequence: P(0)=P(1)=P(2)=1, P(n)=P(n-2)+P(n-3). First: 1,1,1,2,2,3,4,5,7,9,12,16,21,28... Ratio → plastic number ρ ≈ 1.32472, the real root of x³=x+1. The smallest Pisot-Vijayaraghavan number. Used in architecture by Hans van der Laan.
How to Use
Enter n:
- P(n): The n-th term
- Sequence: All terms
- Ratios: → plastic ratio ρ
The Plastic Number
ρ ≈ 1.32472 is the unique real root of x³−x−1=0. It's the smallest Pisot number: an algebraic integer > 1 whose conjugates all have |z| < 1. This makes ρⁿ very close to the nearest integer.
Architecture
Dutch architect Hans van der Laan used the plastic ratio as the basis for his architectural proportioning system, considering it more natural than the golden ratio for 3D spatial relationships.
Step-by-Step Instructions
- 1Enter n.
- 2View P(n).
- 3See sequence.
- 4Check ratio.
- 5Explore spiral.