Visible Point
Two Lattice Points 
and 
are mutually visible if the line segment joining themcontains no further Lattice Points. This corresponds to the requirement that 
,where 
denotes the Greatest Common Divisor. The plots above show the first few points visible from theOrigin.
If a Lattice Point is selected at random in 2-D, the probability that it is visible from the origin is 
. This is also the probability that two Integers picked at random are Relatively Prime. If aLattice Point is picked at random in 
-D, the probability that it is visible from the Origin is
, where 
is the Riemann Zeta Function.
An invisible figure is a Polygon all of whose corners are invisible. There are invisible sets of every finiteshape. The lower left-hand corner of the invisible squares with smallest 
coordinate of Areas 2 and 3are (14, 20) and (104, 6200).
References
Apostol, T. §3.8 in Introduction to Analytic Number Theory. New York: Springer-Verlag, 1976. Baake, M.; Grimm, U.; and Warrington, D. H. ``Some Remarks on the Visible Points of a Lattice.'' J. Phys. A: Math. General 27, 2669-2674, 1994. Beeler, M.; Gosper, R. W.; and Schroeppel, R. HAKMEM. Cambridge, MA: MIT Artificial Intelligence Laboratory, Memo AIM-239, Feb. 1972. Herzog, F. and Stewart, B. M. ``Patterns of Visible and Nonvisible Lattice Points.'' Amer. Math. Monthly 78, 487-496, 1971. Mosseri, R. ``Visible Points in a Lattice.'' J. Phys. A: Math. Gen. 25, L25-L29, 1992. Schroeder, M. R. ``A Simple Function and Its Fourier Transform.'' Math. Intell. 4, 158-161, 1982. Schroeder, M. R. Number Theory in Science and Communication, 2nd ed. New York: Springer-Verlag, 1990
- Vibration Problem
- Vickery Auction
- Viergruppe
- Vieta's Substitution
- Vigesimal
- Vigintillion
- Villarceau Circles
- Vinculum
- Vinogradov's Theorem
- Virtual Group
- Visibility
- Visible Point
- Visible Point Vector Identity
- Vitali's Convergence Theorem
- Viviani's Curve
- Viviani's Theorem
- Vojta's Conjecture
- Volterra Integral Equation of the First Kind
- Volterra Integral Equation of the Second Kind
- Volume
- Volume Element
- Volume Integral
- von Aubel's Theorem
- von Dyck's Theorem
- von Mangoldt Function