Welcome to the final issue of Parabola for 2007. The focus of this issue is on practical applications of mathematics.
The cartoon reproduced below first appeared in The New Yorker. It so caught the fancy of the Mathematical Association of America that they acquired the rights to it
One of the most difficult problems to be faced by developed countries throughout the world over the next fifty years is the ageing population problem. This problem is essentially a result of the "baby boom generation" (people born in the period 1946 to 1962)
The Earth’s climate is the result of myriad interactions between the Earth’s atmosphere and its surface, which is composed of oceans, land masses and ice-caps.
The success of Google is predominantly due to its page rank algorithm. All web crawlers can index each page for the terms contained in each page.
Q1251 Show that the product of 4 consecutive integers is always one less than a perfect square.
Q1241 Show that Simpson's Elementary Rule
$$\int^b_a f (x) dx \approx \left(\frac{b-a}{6}\right)\left( f(a) + 4f\left(\frac{a+b}{2}\right) + f(b)\right) $$
is an exact equality for the quadratic function
$$f(x) = Ax^2 + Bx + C.$$