Percolation Threshold
The critical fraction of lattice points which must be filled to create a continuous path of nearest neighbors from oneside to another. The following table is from Stauffer and Aharony (1992, p. 17).
| Lattice | Site | Bond |
| Cubic (Body-Centered) | 0.246 | 0.1803 |
| Cubic (Face-Centered) | 0.198 | 0.119 |
| Cubic (Simple) | 0.3116 | 0.2488 |
| Diamond | 0.43 | 0.388 |
| Honeycomb | 0.6962 | 0.65271 |
| 4-Hypercubic | 0.197 | 0.1601 |
| 5-Hypercubic | 0.141 | 0.1182 |
| 6-Hypercubic | 0.107 | 0.0942 |
| 7-Hypercubic | 0.089 | 0.0787 |
| Square | 0.592746 | 0.50000 |
| Triangular | 0.50000 | 0.34729 |
The square bond value is 
exactly, as is the triangular site. 
for the triangular bond and
for the honeycomb bond. An exact answer for the square site percolation threshold is not known.
References
Essam, J. W.; Gaunt, D. S.; and Guttmann, A. J. ``Percolation Theory at the Critical Dimension.'' J. Phys. A 11, 1983-1990, 1978. Finch, S. ``Favorite Mathematical Constants.'' http://www.mathsoft.com/asolve/constant/rndprc/rndprc.html Kesten, H. Percolation Theory for Mathematicians. Boston, MA: Birkhäuser, 1982. Stauffer, D. and Aharony, A. Introduction to Percolation Theory, 2nd ed. London: Taylor & Francis, 1992.
- Riemann Series Theorem
- Riemann's Formula
- Riemann-Siegel Functions
- Riemann's Integral Theorem
- Riemann's Moduli Problem
- Riemann's Moduli Space
- Riemann Space
- Riemann Sphere
- Riemann-Stieltjes Integral
- Riemann Sum
- Riemann Surface
- Riemann Tensor
- Riemann Theta Function
- Riemann Weighted Prime-Power Counting Function
- Riemann Xi Function
- Riemann Zeta Function
- Riesel Number
- Riesz-Fischer Theorem
- Riesz Representation Theorem
- Riesz's Theorem
- Riffle Shuffle
- Rigby Points
- Right Angle
- Right Conoid
- Right Hyperbola