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GeezerVison is showing mathworld.wolfram.com — Möbius Net -- from Wolfram MathWorld 
Möbius Net
The perspective image of an infinite checkerboard. It can be constructed starting from any triangle 
The adjacent tile
1. The new vertices
2. The diagonal
3. The line
Similarly, the corner-neighbor
1. Point
2. Point
3. Line 
Iterating the above procedures will yield the complete picture. This construction shows how naturally projective geometry arises
from perspective design, since 
The Möbius net is the result of a projective transformation of the two-dimensional lattice. Unlike in affine geometry, the length proportions along the two perpendicular
directions are not preserved, whereas the cross ratio, which is invariant by central
projection, is. The "horizontal" sides of the projected tiles have different
lengths, but are related by the central projections from
This entry contributed by Margherita Barile Explore with Wolfram|Alpha
ReferencesFauvel, J.; Flood, R.; and Wilson, R. J. (Eds.). Möbius and his Band: Mathematics and Astronomy in Nineteenth-Century Germany. Oxford, England: Oxford University Press, p. 91, 1993.Referenced on Wolfram|AlphaMöbius NetCite this as:Weisstein, Eric W., with contributions by Margherita Barile. "Möbius Net." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/MoebiusNet.html Subject classifications | ||||||||
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,
and 
form the near corner of the floor, and 
is the horizon (left figure). If 
is the corner tile, the lines 
and 
must be parallel to 
and 
respectively. This means that in the drawing they will meet 
and 
at the horizon, i.e., at point 
and point 
respectively (right figure). This property, of course, extends
to the two bunches of perpendicular lines forming the grid.
(left figure) can then be determined by the following conditions:
and 
lie on lines 
and 
respectively.
meets the parallel line 
at the horizon 
.
passes through 
.
of 
(right figure) can be easily constructed requiring
that:
lie on 
.
lie on the common diagonal 
of the two tiles.
pass through 
.
and 
can be interpreted as two coordinate axes in the 
and 
their 
.
(left figure) and 
(right figure), so that
