wrote:
On 23 Jul, 08:39, Andy Wade wrote:

Hence if you can prove
the bisection of the angle and side above and accept Pythagoras (which
can be proved in several ways)

I think that is one of the few mathematical proofs I ever mastered! ;-)

This was second form stuff when I was at school. It's a bit worrying to
read things like

My 1988 GCSE Maths didn't stretch to the relationships of Pythagoras
and trig. Why does sqrt(3)/2 = cos(30deg)?
(Discuss.)

I did GCE O level maths in '83 or '84, and don't recall trig getting
much beyond basic right angle triangle stuff, with a possible
requirement to be able to use the sine or cosine rules. I was not
sufficiently a fan of maths (at the time) to take it at A level.

I do remember having quite a nasty shock when doing maths at university
to find there was a whole world about trig identities and equivalents
that I knew absolutely nothing about! (Much of the difficulty stemming
from the fact that there were several maths groups one could be in, and
I happened to get the one where 95% of the students who had done A level
maths, and the very obtuse Welshman teaching, thought he could race
through it all as a "quick bit of revision"). After a few weeks of that
I decided to switch groups and found that the alternative was a running
at a much more sensible pace (the first group had almost finished course
in the first four weeks!)

Perhaps only worrying in that its now 20 years ago and (despite being
an accountant) I left maths far behind me so it may simply be my
forgetfulness.

It surprising really how even after having spent almost all of my
working life in quite technical roles, just how little maths one is
called upon to use.

Though I'm fairly sure that Pythagoras and trig were taught as
sequential steps - first learn Pythagoras such that the dimensions of
any right angled triangle can be worked out. Then learn trig in order
that angles or lengths can be derived based on given information.

So whilst we all knew SOHCAHTOA etc, and we all knew Asqr = Bsqr +

Hmm - yes remember that one ;-)

(I think I preferred one of my maths teachers mnemonics of "Two Old
Aunts Sat On High Chairs and Howled)

Perhaps what I should have written was "my 1998 Maths GCSE didn't
stretch to being explicit about formulae which merged Pyth and trig,
and instead kept them separate (but highly related of course) to make
a two step process rather than a single step"

That (I discovered later in life) was one of the problems I often had
with maths at that level - it was never really built from first
principles and hence never really satisfied my desire to know *why*
something worked.

A good example would be something like matrix operations. At O level
there was never any worthwhile application given for why you might want
to carry out these manipulations - which made them seem all rather
pointless. Its only later when you realise you can convolve data sets,
solve simultaneous equations, and do all sorts of fancy graphics with
them (to name but a few applications) that you realise they do actually
have a purpose.




--
Cheers,

John.

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