Giving measurements on the Forum

[The Grand Wazoo]

I remember reading somewhere when I was a teenager that there is at least one recorded instance of a scientific body rounding pi to 4!

[StanleyB]

I remember reading somewhere when I was a teenager that there is at least one recorded instance of a scientific body rounding pi to 4!

[The Grand Wazoo]

Nay, nay and thrice 3.141592653589793238462643383279502884197169399375 1058209... times nay.
Stanley, you are a bad, bad man!

[MartinT]

One case was with one of the lenses on the Hubble telescope.

I thought it was the main mirror itself, an astonishing error?

[dave2010]

Damn right! I think re-imperialisation is the only way forward. We could go back to buying cars in Guineas and paying 'two and twelve pence halfpenny' for a bag of gob stoppers. Petrol could then go back to being 7/6d per gallon.

I don't think petrol ever did get to 7/6d per gallon - except perhaps under extreme circumstances and maybe a black market. The last pre-decimal price I remember was about 3/6d.

[Barry]

The error in the argument occurs after step 4: with the second and subsequent corners removed, the stepped perimeter ceases to touch the circle at all points. If this process is repeated infinitely, one achieves a non-circular shape having a perimeter larger than the circle (i.e 4), but only touches the circle at the four points shown in step 3.

[Barry]

After due consideration (whilst in the pub and after a few pints of beer), I realise I was incorrect in my dismissal of Stan’s quoted ‘proof’ that π = 4.

I claimed that subsequent removal of the corners of the enclosing square would, if carried on infinitely, create an enclosing perimeter that would only touch the circle in 4 places. I was wrong, on two counts. First it would contact the enclosed circle at eight points and, more importantly, the ‘proof’ actually assumed subsequent corner removal could be rectangular in shape rather than square (and therefore could contact the circle at an indefinite number of points).

Even so, the fallacy of the ‘proof’ is one of confusing, or assuming, that the enclosing perimeter would, in the limit, coincide with the circumference of the enclosed circle. The fallacy is that the enclosing perimeter, being made up of many elemental triangles, confuses the hypotenuse of such triangular elements as being the same as the sum of the other two sides; and that in the limit as the size of the triangle becomes vanishing small, this error becomes negligible.

It does not; the sum of the sides of a right angle triangle is always greater than its hypotenuse, regardless of the size of a triangle. So in the limit the enclosing perimeter so formed will always be greater than the circumference of the enclosed circle.

[The Grand Wazoo]

Indeed. If continued to the conclusion that's suggested, each error in itself is tiny. But as there are an infinite number of them, they add up to the same error as the first one.
No matter how close each outer point is to the circumference, it will never touch it.

The whole thing is a load of loblocks.
As I said, Mr Beresford is a bad, bad man!

[Reffc]

How should we go about defining drift of components? For large variations (ie voicecoils that get heated up) could we refer to the drift as being "continental"?

For small areas of drift with time, should this be referred to as a "slip" and if making the components just out of tolerance, is this then an "oops"?

[Naughty Nigel]

I don't think petrol ever did get to 7/6d per gallon - except perhaps under extreme circumstances and maybe a black market. The last pre-decimal price I remember was about 3/6d.

When my dad got our first car, a Vauxhall Victor, petrol was £1 for four gallons, or in other words, 5/- per gallon! That is 5.5 pence per litre in modern parlance!

Where, when and why did it all go so wrong?

Nigel.