Triangle Bright Spot in Flatland Night

I was thinking about the figures in Flatland. What actually determines a shape? Is it a line? A line is by itself, is infinitely thin. A shape is not defined by a line, it has an edge, a divider between inside and outside. I don’t think the residents of Flatland would confuse a bright spot […]

Roundhouse in Flatland

Imagine the scene below squished into two dimensions. That is the world of Flatland. The manhole cover becomes a platform with the ability to swivel. Lines (or rectangles) can advance onto its surface and be rotated. If, as shown below, a rectangle is only partly on board, it can be broken apart. It’s a good […]

Collections of Geometric Shapes in Flatland

Here are a number of different shaped creatures that may be found in Flatland. The rectangle on the left, may have had encounters with intrusive lines, as evidenced by the discolored scars on its body. The other blue rectangle may have just had a corner lopped off by a dangerous, sharp triangle. One can see […]

Flatland Shadow on Old White Line Universe

Unlike yesterday’s post, it is possible to determine two separate universes from the third dimension, as seen in the photo below. The curb-level universe casts a shadow on the plane below, which is the realm of the old white line. If this wizened native of the nether flatland has ever encountered shadows from other worlds […]

Parallel Yellow Lines in Parallel Flatland Universes

This vertical view of Flatland belies the fact that these two sets of yellow lines are in separate Flatland universes. In the three-dimensional world these lines are on two different steps of a staircase. The yellow lines on the left are on a step higher than the ones on the right. Are there parallel universes […]

Parallel Parking in Flatland

One can see that Flatland, as viewed from the third dimension is rife with texture. What is texture in Flatland? I imagine it manifests as inexplicable holes in two dimensional space and its figures. The rectangular figure below must have been surprised when it fractured while parallel parking. It suddenly spawned several other irregularly shaped […]

Old White Line at Fulcrum and Slanty Curb Viewed From the Top

I’ve been using my street photography recently to spy on the goings on in Flatland. ‘Flatland‘ is a book written by the mathematician Edwin Abbott, about geometric creatures who live in a two-dimensional world. Parking lots are great places to see lines, circles and (dangerous) pointy triangles. The  dotted rubber mat indicates that there is […]