Euclidean geometry is the branch of mathematics describing shapes and the spatial relationships between objects in two-dimensional (2D) and three-dimensional (3D) settings. The rules of Euclidean ...

THIS work will be found really valuable by all students of geometry, especially by those who know little or nothing of the non-Euclidean theories. First of all we have a discussion of the ...

We’ve all learned “parallel lines never intersect” in high school geometry. But what your teachers failed to explain is that “parallel lines never intersect” is only true in Euclidean ...

For high school students, math skills and understandings are organized not by grade level but by concept. In geometry, students work primarily with plane, or Euclidean geometry (with and without ...

There's a simple way to learn geometry over the summer ... he’s practicing Euclidean geometric proofs and he’s only in first grade. Of course, he doesn’t understand what he’s doing ...

This article was originally published with the title “ Non-Euclidean Geometry before Euclid ” in Scientific American Magazine Vol. 221 No. 5 (November 1969), p. 87 doi:10.1038 ...

THE philosopher Kant declared that Euclidean geometry was inherent in the human mind and expressed the truth about space. We now recognize that non-Euclidean geometry is equally valid as an ...