Rectangle PQRS has X and Y on the edges. Triangles PQY, YRX and XSP have equal areas. Prove X and Y divide the sides of PQRS in the golden ratio.
Straight lines are drawn from each corner of a square to the mid points of the opposite sides. Express the area of the octagon that is formed at the centre as a fraction of the area of the square.
Find the ratio of the outer shaded area to the inner area for a six pointed star and an eight pointed star.
The topic of music can make a good connection between science and mathematics
The nature of sound and the working of the ear are rich areas of applied mathematics.
The ratio emphasis follows from harmonics or overtones and rests on ideas like lowest common multiple.
One teacher has offered the following comment : This Stage 4 work makes practice in multiplying and dividing fractions purposeful. And in school invites collaboration between the music and mathematics departments.