The shortest distance between two points is a straight line. This is one of the basic principles of Euclidean geometry. But we live on a spherical Earth, so we cannot travel the straight line path ...

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One hypothesis about the shape of the universe is that the universe is in the space of Euclidean geometry and flat. In Euclidean geometry, it is assumed that straight lines extend everywhere, planes ...

Most trigonometry students look at triangles on a flat surface. However, people from ancient astronomers to modern navigators calculated the arc lengths and angles of triangles on a sphere. They used ...

This paper gives the exact evaluation of the shape density on the shape space Σ (S2,3) for a labelled random spherical triangle whose vertices are i.i.d.-uniform in a 'cap' of S2 bounded by a 'small' ...

THE author of this book, who is one of the naval instructors on H.M.S. Britannia, has brought together the most important rules which are used in the solution of spherical triangles, and, after ...

Is it possible to fill space “cubically” with shapes that act like spheres? A proof at the intersection of geometry and theoretical computer science says yes. In the fourth century, the Greek ...

Villagers belonging to an Amazonian group called the Mundurucú intuitively grasp abstract geometric principles despite having no formal math education, say psychologist Véronique Izard of Université ...