Ratio and proportion

What angle is needed for a ball to do a circuit of the billiard table and then pass through its original position?

We use statistics to give ourselves an informed view on a subject of interest. This problem explores how to scale countries on a map to represent characteristics other than land area.

Show that it is rare for a ratio of ratios to be rational.

Move the point P to see how P' moves. Then use your insights to calculate a missing length.

The scale on a piano does something clever : the ratio (interval) between any adjacent points on the scale is equal. If you play any note, twelve points higher will be exactly an octave on.

Two right-angled triangles are connected together as part of a structure. An object is dropped from the top of the green triangle where does it pass the base of the blue triangle?

Weekly Problem 37 - 2007
This regular hexagon has been divided into four trapezia and one hexagon.... what is the ratio of the lengths of sides p, q and r?

Which exact dilution ratios can you make using only 2 dilutions?

Use the grids to draw pictures to different scales.