$2\wedge 3\wedge 4$ could be $(2^3)^4$ or $2^{(3^4)}$. Does it make any difference? For both definitions, which is bigger: $r\wedge r\wedge r\wedge r\dots$ where the powers of $r$ go on for ever, or $(r^r)^r$, where $r$ is $\sqrt{2}$?

By inscribing a circle in a square and then a square in a circle
find an approximation to pi. By using a hexagon, can you improve on
the approximation?

Small Steps

Age 16 to 18 Challenge Level:

The point $P=(x,y)$ has image $P'=(ax+by, cx+dy)$. Draw diagrams
and consider the effect of the transformation on the line $OP$
joining $P$ to the origin.