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#### Resources tagged with Spheres similar to Weekly Challenge 47: Weird Universes:

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##### Other tags that relate to Weekly Challenge 47: Weird Universes
Torus. Topology. Geodesics. Visualising. Networks/Graph Theory. Investigations. Non Euclidean Geometry. Spheres. 2D representations of 3D shapes. chemistry.

### There are 13 results

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

### Pack Man

##### Stage: 5 Challenge Level:

A look at different crystal lattice structures, and how they relate to structural properties

### 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. . . .

### Curvature of Surfaces

##### Stage: 5

How do we measure curvature? Find out about curvature on soccer and rugby balls and on surfaces of negative curvature like banana skins.

### Pythagoras on a Sphere

##### Stage: 5 Challenge Level:

Prove Pythagoras' Theorem for right-angled spherical triangles.

### The Dodecahedron Explained

##### Stage: 5

What is the shortest distance through the middle of a dodecahedron between the centres of two opposite faces?

### 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.

### Ball Packing

##### Stage: 4 Challenge Level:

If a ball is rolled into the corner of a room how far is its centre from the corner?

### Mouhefanggai

##### Stage: 4

Imagine two identical cylindrical pipes meeting at right angles and think about the shape of the space which belongs to both pipes. Early Chinese mathematicians call this shape the mouhefanggai.

### Mesh

##### Stage: 5 Challenge Level:

A spherical balloon lies inside a wire frame. How much do you need to deflate it to remove it from the frame if it remains a sphere?

### Air Routes

##### Stage: 5 Challenge Level:

Find the distance of the shortest air route at an altitude of 6000 metres between London and Cape Town given the latitudes and longitudes. A simple application of scalar products of vectors.

### 2D-3D

##### Stage: 5 Challenge Level:

Two circles of equal size intersect and the centre of each circle is on the circumference of the other. What is the area of the intersection? Now imagine that the diagram represents two spheres of. . . .

### Three Balls

##### Stage: 4 Challenge Level:

A circle has centre O and angle POR = angle QOR. Construct tangents at P and Q meeting at T. Draw a circle with diameter OT. Do P and Q lie inside, or on, or outside this circle?