Mark, Can you please explain in a little more detail exacttly what you want to know as I am confused by your post.

Hi Mark,

Put a bit of paper over the end of the grider (with a hole for the spindle). Push a pencil through each of the mounting holes and spin it round. It will be much easier to measure the spacing of the holes from the paper copy, or you can use it as a template..

Also, it is easier to meaure between the edges of the holes than their centres, just make sure you use the same point (e.g. far right edge) of the two holes!

Joey

Mark,

If, as I suspect, you can only measure the centre distance of the three holes you may find the following trig formulae helpful.

Diameter is obviously 2 x r

Bob D

And if you substitute a = b = c in Bob's first formula (assuming the holes are equally spaced around the circle), the PCD diameter is 2a/sqrt(3) = 1.1547a

Michael G,

Begging the earlier question has caused me to think a little deeper about my interpretation of the Geometry.

I saw Mark with a piece of metal with three holes in it. and he wants to find a centre point and figure out a unique diameter passing through the three holes.

Unless he has some form of cordinate measuring machine to generate a datum point and x,y, coordinates for each hole he cannot readily derive the position of the three holes or work out the diameter using the coordinate formulae.

Without really thinking about it previously I now realise that I was brought up on Euclidian Geometry that has much less dependency on cordinates being defined and leans to solving problems based on the old Geometry theorums.

This method may have limitations in solving advanced mathmatics problems that are more readily handled with coordinate geometry principles. However, at the workshop level it is more likely that the simpler methods will suffice

I hope Mark can get his Tool Grinder problem sorted with the aid of just a pair of dividers, a steel rule, paper and pencil.

My schooling was at a Grammar School but more like 62 years ago and yes, I loved that form of Maths but I also was lucky enough to be involved in coordinate geometry through my working life so hopefully I see both sides

I still think its a pity that there is so little emphasis on the Mathmatics in current education programmes

Bob D

If you can mark the hole centre positions on a piece of paper held against the metal, the PCD centre is simply the intersection of the perpendicular bisectors of the lines connecting the centres.

The lines connecting the hole centres are chords of the PCD circle. The bisectors of these lines must pass through the PCD centre. This is trivial geometry.

The diagram shows that it works even for non-equilateral triangles.

Gary

A rather bizarre aspect of poor maths ability is that so many celebrities and TV presenters seem to be proud and somewhat amused by their lack of mathematical comprehension. Lack of numeracy (and also literacy) is an ongoing complaint by prospective employers due to so many students being failed by the teaching profession. (?)

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1. Teaching Maths In 1970
A logger sells a lorry load of timber for £1000.
His cost of production is 4/5 of the selling price.
What is his profit?

2. Teaching Maths In 1980
A logger sells a lorry load of timber for £1000.
His cost of production is 4/5 of the selling price, or £800.
What is his profit?

3. Teaching Maths In 1990
A logger sells a lorry load of timber for £1000.
His cost of production is £800.
Did he make a profit?

4. Teaching Maths In 2000
A logger sells a lorry load of timber for £1000.
His cost of production is £800 and his profit is £200.
Your assignment: Underline the number 200.

5. Teaching Maths In 2008
A logger cuts down a beautiful forest because he is totally selfish and inconsiderate and cares nothing for the habitat of animals or the preservation of our woodlands.
He does this so he can make a profit of £200. What do you think of this way of making a living?
Topic for class participation after answering the question: How did the birds and sheep feel as the logger cut down their homes? (There are no wrong answers.
If you are upset about the plight of the animals in question counselling will be available)

6. Teaching Maths 2018
Ø£ المسجل تبيع حموله شاحنة من الخشب من دولار. صاحب تكلÙ?Ø© الانتاج من> الثمن. ما هو الربح له؟

Michael

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Edited By michael m on 15/04/2013 19:15:47

Edited By JasonB on 15/04/2013 20:52:02

Well done Gary!

Rob – that use of trivial is the mathematical meaning of the word as in "of no difficulty or interest", in other words in no need of further explanation.

Michael

In all years the answer is £0 – if he has a half decent accountant, what about the running costs of that lorry for a start? He needs to go on a small business training course.

I take it that in 2018 the logger is swearing because either he can't find any trees or buy any petrol.

Neil

Nice one Neil, though my own interpretation of 2018 was that by that year mathematics teaching had degenerated from drivel to total garbage. We'll see.

Michael