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#### Resources tagged with Geodesics similar to Pythagoras on a Sphere:

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##### Other tags that relate to Pythagoras on a Sphere
Angles between lines & planes. Vector products. Sine. Geodesics. chemistry. Vectors. Cosine. Spheres. Non Euclidean Geometry. Scalar products.

### 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.

### 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.

### 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.

### 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. . . .

### 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.

### Flight Path

##### Stage: 5 Challenge Level:

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