Two places are diametrically opposite each other on the same line
of latitude. Compare the distances between them travelling along
the line of latitude and travelling over the nearest pole.
An account of how axioms underpin geometry and how by changing one axiom we get an entirely different geometry.
Prove Pythagoras' Theorem for right-angled spherical triangles.
This article outlines the underlying axioms of spherical geometry giving a simple proof that the sum of the angles of a triangle on the surface of a unit sphere is equal to pi plus the area of the. . . .
Shows that Pythagoras for Spherical Triangles reduces to
Pythagoras's Theorem in the plane when the triangles are small
relative to the radius of the sphere.
Consider these weird universes and ways in which the stick man can shoot the robot in the back.
Use simple trigonometry to calculate the distance along the flight
path from London to Sydney.
This article (the first of two) contains ideas for investigations.
Space-time, the curvature of space and topology are introduced with
some fascinating problems to explore.