Locus/loci

There are 21 NRICH Mathematical resources connected to Locus/loci
Making Spirals
problem
Favourite

Making spirals

Age
7 to 11
Challenge level
filled star filled star filled star

Can you make a spiral for yourself? Explore some different ways to create your own spiral pattern and explore differences between different spirals.

Triangles and petals
problem
Favourite

Triangles and petals

Age
14 to 16
Challenge level
filled star filled star empty star
An equilateral triangle rotates around regular polygons and produces an outline like a flower. What are the perimeters of the different flowers?
Rolling Around
problem
Favourite

Rolling around

Age
11 to 14
Challenge level
filled star filled star empty star
A circle rolls around the outside edge of a square so that its circumference always touches the edge of the square. Can you describe the locus of the centre of the circle?
An Unusual Shape
problem
Favourite

An unusual shape

Age
11 to 14
Challenge level
filled star filled star empty star
Can you maximise the area available to a grazing goat?
Rollin' Rollin' Rollin'
problem
Favourite

Rollin' rollin' rollin'

Age
11 to 14
Challenge level
filled star filled star filled star
Two circles of equal radius touch at P. One circle is fixed whilst the other moves, rolling without slipping, all the way round. How many times does the moving coin revolve before returning to P?
How far does it move?
problem
Favourite

How far does it move?

Age
11 to 14
Challenge level
filled star empty star empty star

Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the dot affects the distance it travels at each stage.

Speeding up, slowing down
problem
Favourite

Speeding up, slowing down

Age
11 to 14
Challenge level
filled star filled star empty star

Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the dot affects its speed at each stage.

Up and across
problem
Favourite

Up and across

Age
11 to 14
Challenge level
filled star filled star filled star

Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the dot affects its vertical and horizontal movement at each stage.

Is there a theorem?
problem
Favourite

Is there a theorem?

Age
11 to 14
Challenge level
filled star filled star empty star
Draw a square. A second square of the same size slides around the first always maintaining contact and keeping the same orientation. How far does the dot travel?
Five circuits, seven spins
problem

Five circuits, seven spins

Age
16 to 18
Challenge level
filled star filled star empty star
A circular plate rolls inside a rectangular tray making five circuits and rotating about its centre seven times. Find the dimensions of the tray.