How to pronounce “line segment” in English

It's completely one-dimensional and not a fractal at all.Hausdorff assigned this line segment a value of 1.0.But now imagine adding a few bends and more bends to those bends.

You wrote down some axioms, and then you proved some theorems.You take a little line segment.

You wrote down some axioms, and then you proved some theorems.Initially straight line segment.

You wrote down some axioms, and then you proved some theorems.You can take a little line segment at the equator.

You wrote down some axioms, and then you proved some theorems.You shoot off initial straight parallel lines away from that line segment at right angles.

You wrote down some axioms, and then you proved some theorems.And imagine doing it for every possible orientation of the initial line segment?

You wrote down some axioms, and then you proved some theorems.Reimann says, the general formula for the length of a really tiny line segment in a general geometry, we'll

You wrote down some axioms, and then you proved some theorems.You tell me where you are, what your initial line segment is, how you shoot out these initially parallel lines.

If you keep doing this, the line becomes more and more fractal-like.Eventually, if you keep applying the right kind of contortions, that one-dimensional line segment fills up an entire region of the 2D plane.Hausdorff assigned these space-filling fractal curves a value of 2.0, corresponding to their dimensionality.