Locus/loci

There are 21 NRICH Mathematical resources connected to Locus/loci

problem

Favourite

Making spirals

Age

7 to 11

Challenge level

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

problem

Favourite

Up and across

Age

11 to 14

Challenge level

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.

problem

Favourite

Is there a theorem?

Age

11 to 14

Challenge level

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?

problem

Favourite

Triangles and petals

Age

14 to 16

Challenge level

An equilateral triangle rotates around regular polygons and produces an outline like a flower. What are the perimeters of the different flowers?

problem

Favourite

Rolling around

Age

11 to 14

Challenge level

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?

problem

Favourite

An unusual shape

Age

11 to 14

Challenge level

Can you maximise the area available to a grazing goat?

problem

Favourite

Rollin' rollin' rollin'

Age

11 to 14

Challenge level

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?

problem

Favourite

How far does it move?

Age

11 to 14

Challenge level

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.

problem

Favourite

Speeding up, slowing down

Age

11 to 14

Challenge level

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

problem

Symmetric trace

Age

14 to 16

Challenge level

Points off a rolling wheel make traces. What makes those traces have symmetry?

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For younger learners

Locus/loci

Making spirals

Up and across

Is there a theorem?

Triangles and petals

Rolling around

An unusual shape

Rollin' rollin' rollin'

How far does it move?

Speeding up, slowing down

Symmetric trace