**John Donnelly,**

A Model of Continuous Plane Geometry that is Nowhere Geodesic,

Forum Geometricorum, 18 (2018) 255-273.

Abstract. We construct a model **M_1** of plane geometry that satisfies
all of Hilbert's axioms for the euclidean plane (with the exception of Sided-Angle-Side), yet in which the
geodesic line segment connecting any two points *A* and *B* is never the
shortest path from *A* to *B*.
Moreover, the model **M_1** is
continuous in the sense that it satisfies both the Ruler Postulate and
Protractor Postulate from Birkhoff's set of axioms
for the euclidean plane.

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Geom., 18 (2018) Table of Contents