Volume 20
, Issue 1

1984

In 1733 the French biologist G.L.L. Buffon (1707-1788) proposed an interesting experiment for obtaining estimates of the constant $\pi$.

It is a remarkable fact that quite ordinary families can suddenly throw up quite extraordinary mathematical genius.

In 1742 Goldbach suggested in a letter to Euler that every even integer greater than 4 is the sum of two odd primes.

A cube, as shown below, can be made up from 6 square pyramids.

In the 1983 HSC 4 unit (Unique) paper there were some interesting problems on functions and thier graphs.

Q.588 We are given a set of 201 different numbers with the property that the sum of any 100 of them is less than the sum of the remaining 101. Prove that all of the numbers are positive.

Q.563 In the figure, $X$ and $Y$ are the centres of the circular arcs $AB$ and $AC$ respectively, and $A$ is the centre of the circular arc $BC$.