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Archimedes and Numerical Roots

The problem is how did Archimedes calculate the lengths of the sides of the polygons which needed him to be able to calculate square roots?

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Rationals Between...

What fractions can you find between the square roots of 65 and 67?

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Root to Poly

Find the polynomial p(x) with integer coefficients such that one solution of the equation p(x)=0 is $1+\sqrt 2+\sqrt 3$.

Equal Temperament

Age 14 to 16 Challenge Level:

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.