Fao Buenchico.

[10ClarionSt]

I notice in your reply about congestion that you said you have a degree in Mathematics. I was useless at maths but did manage to obtain an "O" level in the subject back in the sixties. However, a friend of mine was absolutely brilliant at maths. Sailed through all his exams at Queens College, London University and obtained a Phd, then went to work for NASA in California. Unfortunately, this was at the same time as they were planning to scrap the moon landings in the 70's, so, as a professor of maths, he went lecturing at Montreal University. He used to write his own theories, one of which was to try and prove the difference between plus nought and minus nought. I believe he wrote a book on that subject! Don't ask me Chris. I haven't got a clue but he really was exceptional in his field. He now lives in Texas but he came over last week and I spent a day with him catching up, as you do. Not maths though!

[albaqwerty]

a catch-up is always good.

Never understood maths, but for my O Level, was lucky enough to have the Head of (oh, whichever) and he suggested that I look on it as a language (he knew I was studying quite a few), wonderful man

[Buenchico]

Maths is/was one of the very few things I've ever been good at. (I'm rubbish at art, sport, relationships and about a zillion other things). However I do admit that when I look back at my degree thesis I'm left wondering what it was all about!

I'd love to prove some wonderful new theorem in the subject but I don't think that I'm anywhere near good enough. There is one classic proof in higher maths textbooks though that had to be rewritten in later editions because I discovered a far more elegant solution for it during my college days. (Many moons ago, I also represented the UK as the 'British young teacher delegate' at an international maths education conference in Adelaide. That was the only real perk I ever got from teaching maths!)

However if I ever start to think of myself as 'bright' I only need to meet up with an Italian friend of mine to bring me down to earth. I'm not in the same league as him!
http://www.phys.virginia.edu/People/personal.asp?UID=sc2k

[wolf63]

Chris, does you Italian friend appreciate the disdain and contempt of a furry family member?

[Buenchico]

Wolf:
My Italian friend is married to my Scottish friend (who I'll see this evening on one of her frequent visits from Trieste), who is even more cat-mad than I am. She's currently only got two cats living in her home (because two have sadly passed on within the past year) but she feeds dozens of street cats, trapping those which haven't been neutered and arranging for it to be done. Her whole life is devoted to cats. She can't even visit a charity shop without leaving clutching loads of attractive dishes to feed all the street cats in. (They only get the finest china - which leads to fellow residents of Trieste constantly nicking them!) Whenever she and her husband visit the UK together it involves loads of incredibly complex arrangements to ensure that someone is still there to look after all the cats.

So I reckon that Sergio (or Boby, as he's known to his friends) knows all about cats ;-)

[goodgoalie]

Chris, maybe you should introduce your Italian friend to AB's 'theprof' - he has four (or maybe five) Oxbridge doctorates!
Talking of maths, that was my poorest subject at school, but a couple of times recently I've watched something on TV about how Scotland was first properly mapped, using triangulation, which really fascinated me. They measured a baseline (10 miles, I think) very accurately using a chain - so they had the distance AB. Then a bloke was sent to point C to make a triangle, and they measured the angles AB/AC and BA/BC, which, using trigonometry, enabled them to ascertain the lengths of AC and BC, thus giving them two more baselines, and they just kept going.....evidently when they got back to where they began, they were only a few inches out.
But what is the trig that gives the lengths AC and BC? Only if you can be bothered!

[Flonska]

GG, I too wasn't that good either but I think remember that for a right angle triangle that Sine, (Opposite/Hypotenuse), Cosine, (Adjacent/Hypotenuse) and Tangent, (Opposite/Adjacent) were used to determine distances?

[goodgoalie]

But the angles wouldn't be right angles as the side lengths would be unequal - so, er, scalene triangles

[Buenchico]

Flonska's answer assumes that a right-angled triangle was involved but, on the scale mentioned by GG, that would be impractical. (If the surveyors tried to set a line at 90 degrees to the base line, even a tiny fraction of a degree out would make a lot of difference at the end of the line several miles away).

So they used the rules of trigonometry which apply to all triangle (not just to right-angled ones). They are the Sine Rule, explained here
http://www.bbc.co.uk/bitesize/standard/maths_ii/trigonometry/sin_cosine_area_triangle/revision/1/
and the Cosine Rule, here:
http://www.bbc.co.uk/bitesize/standard/maths_ii/trigonometry/sin_cosine_area_triangle/revision/2/

[goodgoalie]

Thanks for that, Chris, shall explore in detail.

Really enjoy finding out these sorts of things that have been nagging away at the back of my mind. Recently on AB EDDIE51 explained something else I'd always wondered about: why Americans don't have kettles!

[melv16]

Sine and cosine.... I've just broken out in a cold sweat:-(

[goodgoalie]

Know what you mean, melv. I remember at school having to 'prove the sine rule' (and cosine, tangent), and, because I have a good memory, I just learnt it by heart and could regurgitate it, but I never understood it.

[Flonska]

Thank you Buenchico and GG for putting me in the picture. Maybe, if you had been my teachers at the time I would have done a lot better than just scraping a 5 at "O" level.

I have been fortunate on a couple of occasions to remember and use the formulae for volume of a cylinder and area of a circle - so perhaps all is not totally lost?

[Flonska]

GG. The mnemonic we were taught was:-

The Cat Sat On An Orange and Howled Horribly =
The (Tangent) Cat (Cosine) Sat (Sine)
On (Opposite) An (Adjacent) Orange (Opposite)
And (Adjacent) Howled (Hypotenuse) Horribly (Hypotenuse)

[Buenchico]

^^^ Ruddy 'eck! That looks complicated!

I just taught kids about a fictional volcanic island, called SOHCAHTOA.

[woofgang]

oh Sohcahtoa.......the place of nightmares

[goodgoalie]

Never come across those mnemonics - like the island, though, Chris!

[melv16]

Quadratic equations are also the stuff of nightmares :-/

[Captain2]

Nice post.

I always enjoyed Maths and managed an A level in Pure Maths. Latterly I'll enjoy a Maths puzzle to a) stimulate the brain and b) to see if/what I can still remember.
Our daughter also has a mathematical brain and as a toddler would much prefer wading through advanced (for her age) maths books as a relaxation in preference usually to reading.

[fiction-factory]

For me at school it was Sons Of Harlech Come And Harken To Our Anthem. The kids generally just try to remmeber Buuenchico's volcano (SOHCAHTOA) but somehave their own mnemonics now, some of which I daren't repeat.