Search by Topic

Resources tagged with Geodesics similar to Pythagoras on a Sphere:

Filter by: Content type:
Stage:
Challenge level:

There are 8 results

Broad Topics > 3D Geometry, Shape and Space > Geodesics

Pythagoras on a Sphere

Stage: 5 Challenge Level:

Prove Pythagoras' Theorem for right-angled spherical triangles.

Weekly Challenge 47: Weird Universes

Stage: 5 Challenge Level:

Consider these weird universes and ways in which the stick man can shoot the robot in the back.

Over the Pole

Stage: 5 Challenge Level:

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.

How Many Geometries Are There?

Stage: 5

An account of how axioms underpin geometry and how by changing one axiom we get an entirely different geometry.

When the Angles of a Triangle Don't Add up to 180 Degrees

Stage: 4 and 5

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. . . .

Flight Path

Stage: 5 Challenge Level:

Use simple trigonometry to calculate the distance along the flight path from London to Sydney.

Spherical Triangles on Very Big Spheres

Stage: 5 Challenge Level:

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.

Geometry and Gravity 1

Stage: 3, 4 and 5

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.