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The train track is a closed loop that visits every square exactly once, only moves horizontally or vertically from one square to the next, visits every station in numerical order (with ONE following NINE), and never makes a turn when passing through a station.
Many people conclude that the corner triangles can be arranged to cover the inner square exactly, without any gap or overlap.
Our concern is with the visual route to the following: The parts of a square beyond its inner square (formed by joining midpoints of adjacent sides of the original square) can be arranged to fit the inner square exactly, without overlap or gap, without change of size or shape.
This is because visual experience (of sight or imagination) has limited acuity and so does not enable us to discriminate between a situation in which the outer triangles fit the inner square exactly and a situation in which they fit inexactly but well enough for the mismatch to escape visual detection.
We left out the center square and presented only the lower and upper squares with the offset of the lower square exactly timed to the onset of the top square (Fig. 1 D ).
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(By contrast, as noted earlier, while the proposition, "if a Keplerian ellipse exactly, then inverse-square exactly," is true, the proposition, "if a Keplerian ellipse quam proxime, then inverse-square quam proxime," is not true when the eccentricity of the ellipse is not large, as explained in Smith, 2002).
My own experience with Larry Summers squares exactly with Sheryl Sandberg's.
Two Latin squares are said to be orthogonal if, when superposed, any symbol of the first square occurs exactly once with each symbol of the second square.
It was adopted because the moon's surface area, if expressed in square lunars, exactly equals the moon's volume in cubic lunars.
But they said that if the project is measured by zoning rules, which do not count mechanical and basement space, it was and is 2.1 million square feet, exactly as required by planning guidelines.
According to the theory of random walks on lattices and the FPT distributions, we propose an LMC simulation algorithm and prove that such LMC simulation can reproduce both the mean and the mean square displacement exactly in the long-time limit.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com