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Resources tagged with Geodesics similar to Spherical Triangles on Very Big Spheres:

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

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Spherical Triangles on Very Big Spheres

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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.

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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.

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Flight Path

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

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

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Weekly Challenge 47: Weird Universes

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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

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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. . . .

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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.

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Pythagoras on a Sphere

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Prove Pythagoras' Theorem for right-angled spherical triangles.

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Over the Pole

Stage: 5 Challenge Level: Challenge Level:1

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.