pseudosphere

mathematics

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July 15, 2026

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A pseudosphere is a surface with constant negative curvature. It is generated by revolving a curve called a tractrix around its axis. This concept is part of non-Euclidean geometry, which differs from Euclidean geometry.123

In contrast to Euclidean geometry where the sum of a triangle's interior angles is 180 degrees, hyperbolic geometry (which features surfaces like the pseudosphere) has triangles where the sum of interior angles is less than 180 degrees. While the pseudosphere is a model for hyperbolic geometry, it's not a complete one because its "straight lines" can intersect themselves.3

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non-Euclidean geometry
Hyperbolic geometry
… described a surface, called the pseudosphere, that has constant negative curvature. However, the pseudosphere is not a complete model for hyperbolic geometry, because intrinsically straight lines on the pseudosphere may intersect themselves and cannot be continued past the bounding circle (neither of which is true in hyperbolic geometry). In 1901…
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… described a surface, called the pseudosphere, that has constant negative curvature. However, the pseudosphere is not a complete model for hyperbolic geometry, because intrinsically straight lines on the pseudosphere may intersect themselves and cannot be continued past the bounding circle (neither of which is true in hyperbolic geometry). In 1901…
Read More