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There are **21** NRICH Mathematical resources connected to **Locus/loci**, you may find related items under Transformations and constructions.

Problem
Primary curriculum
Secondary curriculum
### Making Spirals

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

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Up and Across

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.

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Speeding Up, Slowing Down

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

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### How Far Does it Move?

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

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Rollin' Rollin' Rollin'

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?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Rolling Around

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?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Triangles and Petals

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

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Is There a Theorem?

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?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Construct the Solar System

Make an accurate diagram of the solar system and explore the concept of a grand conjunction.

Age 14 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Mach Attack

Have you got the Mach knack? Discover the mathematics behind exceeding the sound barrier.

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Where Am I?

From the information you are asked to work out where the picture was taken. Is there too much information? How accurate can your answer be?

Age 11 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Like a Circle in a Spiral

A cheap and simple toy with lots of mathematics. Can you interpret the images that are produced? Can you predict the pattern that will be produced using different wheels?

Age 7 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Symmetric Trace

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

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Five Circuits, Seven Spins

A circular plate rolls inside a rectangular tray making five circuits and rotating about its centre seven times. Find the dimensions of the tray.

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Rolling Triangle

The triangle ABC is equilateral. The arc AB has centre C, the arc BC has centre A and the arc CA has centre B. Explain how and why this shape can roll along between two parallel tracks.

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### The Old Goats

A rectangular field has two posts with a ring on top of each post. There are two quarrelsome goats and plenty of ropes which you can tie to their collars. How can you secure them so they can't fight each other but can reach every corner of the field?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Roaming Rhombus

We have four rods of equal lengths hinged at their endpoints to form a rhombus ABCD. Keeping AB fixed we allow CD to take all possible positions in the plane. What is the locus (or path) of the point D?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Set Square

A triangle PQR, right angled at P, slides on a horizontal floor with Q and R in contact with perpendicular walls. What is the locus of P?

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Just Rolling Round

P is a point on the circumference of a circle radius r which rolls, without slipping, inside a circle of radius 2r. What is the locus of P?

Age 14 to 16

Challenge Level