Construction and Loci - Short Problems

This is part of our collection of Short Problems.

You may also be interested in our longer problems on Construction and Loci.

Either Side

KS 3 Short Challenge Level:

Weekly Problem 7 - 2012
A disc with a pencil inside it is rolled around the outside and inside of a wire equilateral triangle. What shape is drawn by the pencil?

White Round the Pink Square

KS 3 Short Challenge Level:

Weekly Problem 36 - 2013
The white square slides once around the pink square. Through what distance does the point P on the white square move?

Defined Distances

KS 3 Short Challenge Level:

Weekly Problem 51 - 2009
Mark writes four points on a line at different lengths. What is the distance between the two points furthest apart?

Pencil Turning

KS 3 & 4 Short Challenge Level:

Weekly Problem 37 - 2011
Rotating a pencil twice about two different points gives surprising results...

3-sided

KS 3 & 4 Short Challenge Level:

Weekly Problem 9 - 2015
How many triangles can Jack draw with two sides of lengths $6$cm and $8$cm and an area of $7$cm$^2$?

Folded A4

KS 3 & 4 Short Challenge Level:

Weekly Problem 45 - 2011
What shapes can be made by folding an A4 sheet of paper only once?

Snail's Pace

KS 3 & 4 Short Challenge Level:

Weekly Problem 29 - 2014
snail is at one corner of a cube. What proportion of the surface of the cube could the snail reach in one hour?

Triangular Wheel

KS 3 & 4 Short Challenge Level:

Weekly Problem 36 - 2014
An equilateral triangle is rolled along a line. What is the length of the path traced out by one of its vertices?