Pi squared on six (1 Viewer)

[buchanan]

 

[buchanan]

I've attached a solution to the 2002 HSC question 8a (i)-(iii) with this extension.

 

[Yip]

For interest, here are 14 different proofs for zeta(2): http://www.secamlocal.ex.ac.uk/people/staff/rjchapma/etc/zeta2.pdf
Proof 11 is quite a nice proof imo.

 

[buchanan]

In 2002, Bill Pender said it's too hard for High School students in the following document:
http://members.optusnet.com.au/limkw/SGS_harder3U_2002.zip (on page 8)

Clearly that is wrong. That same year the exam committee put it in the HSC! Furthermore, the examiner's report for 2002 indicated many High School students could do it.

The HSC question is essentially Proof 9 in Chapman's pdf (see Yip's post). The most famous proof is the Fourier Series method (Chapman's Proof 5) which is also the easiest way to do it. Since Fourier Analysis isn't taught in High School, this is what Pender had in mind when he said it's too hard for High School.

It's a classic case of where a more abstract proof is much easier than a more elementary one. This seems contradictory. But it takes a whole page using the HSC method, whereas the Fourier Series method only takes a few lines.