Symmetry

problem

Angular Reflection

Age

11 to 14

Challenge level

Weekly Problem 28 - 2013
Two lines meet at a point. Another line through this point is reflected in both of these lines. What is the angle between the image lines?
problem

Notes on a Triangle

Age

11 to 14

Challenge level

Can you describe what happens in this film?
problem

Troublesome Dice

Age

11 to 14

Challenge level

When dice land edge-up, we usually roll again. But what if we didn't...?
problem

Drawing Celtic Knots

Age

11 to 14

Challenge level

Here is a chance to create some Celtic knots and explore the mathematics behind them.
problem

Classifying Solids Using Angle Deficiency

Age

11 to 16

Challenge level

Toni Beardon has chosen this article introducing a rich area for practical exploration and discovery in 3D geometry
problem

Trominoes

Age

11 to 16

Challenge level

Can all but one square of an 8 by 8 Chessboard be covered by Trominoes?
problem

A Roll of Patterned Paper

Age

14 to 16

Challenge level

A design is repeated endlessly along a line - rather like a stream of paper coming off a roll. Make a strip that matches itself after rotation, or after reflection
problem

Overlap

Age

14 to 16

Challenge level

A red square and a blue square overlap. Is the area of the overlap always the same?
problem

Two Triangles in a Square

Age

14 to 16

Challenge level

Given that ABCD is a square, M is the mid point of AD and CP is perpendicular to MB with P on MB, prove DP = DC.
problem

One Reflection Implies Another

Age

14 to 16

Challenge level

When a strip has vertical symmetry there always seems to be a second place where a mirror line could go. Perhaps you can find a design that has only one mirror line across it. Or, if you thought that was impossible, could you explain why ?