# Sunday Afternoon Maths XXVII

**Posted on 2014-09-07**

## Sine

A sine curve can be created with five people by giving the following instructions to the five people:

A. Stand on the spot.

B. Walk around A in a circle, holding this string to keep you the same distance away.

C. Stay in line with B, staying on this line.

D. Walk in a straight line perpendicular to C's line.

E. Stay in line with C and D. E will trace the path of a sine curve as shown here:

What instructions could you give to five people to trace a cos(ine) curve?

What instructions could you give to five people to trace a tan(gent) curve?

## Triangles between squares

Prove that there are never more than two triangle numbers between two consecutive square numbers.

If you enjoyed these puzzles, check out Advent calendar 2019,

puzzles about triangle numbers, or a random puzzle.

puzzles about triangle numbers, or a random puzzle.