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Broad Topics >

Functions and Graphs > Loci

##### 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:

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:

Can you maximise the area available to a grazing goat?

##### 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:

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:

A triangle ABC resting on a horizontal line is "rolled" along the
line. Describe the paths of each of the vertices and the
relationships between them and the original triangle.

##### 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 14 to 16 Challenge Level:

A blue coin rolls round two yellow coins which touch. The coins are
the same size. How many revolutions does the blue coin make when it
rolls all the way round the yellow coins? Investigate for a. . . .

##### 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:

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