# Resources tagged with: Locus/loci

### There are 16 results

Broad Topics >

Transformations and constructions > Locus/loci

##### Age 14 to 16 Challenge Level:

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 11 to 14 Challenge Level:

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:

Can you maximise the area available to a grazing goat?

##### Age 11 to 14 Challenge Level:

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. . . .

##### 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?

##### 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?

##### Age 7 to 16 Challenge Level:

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 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?

##### 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?

##### Age 14 to 16 Challenge Level:

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. . . .

##### Age 14 to 16 Challenge Level:

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

##### 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.

##### Age 11 to 14 Challenge Level:

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:

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 16 Challenge Level:

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 14 to 18 Challenge Level:

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