Abstract This survey highlights some foundational history and some interesting recent discoveries in elementary geometry that deserve to be better known, such as the hierarchies of axiom systems, ...

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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 ...

The course presents a rigorous treatment of the foundations of Euclidean and non-Euclidean geometries. The discovery of non-Euclidean geometry in the first half of the 19th century shattered the ...

Virtual reality can take you to some far-out places — mountaintops, distant cities and even fantastical game worlds. A team of artists and mathematicians is now adding to that list: universes where ...