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Broad Topics >

Functions and Graphs > Loci

##### Age 16 to 18 Challenge Level:

Consider the mechanics of pole vaulting

##### 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 16 to 18 Challenge Level:

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 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:

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 16 to 18 Challenge Level:

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 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. . . .