Reference squares , Cylindrical squares and absolute methods .

Very useful summary

Thanks for posting

MichaelG.

Hi Michael W,

thanks for the thorough explanation, much appreciated.

Rergards

Thor

Wow, that's really interesting. The picture helps too. Thanks Michael.

Now I get the method I can also see how to make a 60 degree 'square' with three buttons and a 30 degree one with four, arranged in a diamond, then removing one button.

This could be the raw material of a useful artilc]e for one of the mags?

Neil

Of course [at the limit] the difficulty comes in Michael's first instruction; "Make some identical rollers".

I am certain that Michael is perfectly aware of this; and in no way does it detract from the elegant method ... but [if striving for perfection] it is worth recognising.

MichaelG.

Thanks Michael (W) very interesting! Initially, I had a problem making sense of number 4 but eventually it clicked, brain not as agile as it once was.

I think though I will stick with what I call " Workshop Grade Cylindrical Squares"

I am sure most will know, but for those that do not. Builders have in the past used three bars screwed together with distances between the screws probably being 3, 4 and 5 feet. I used the method when setting out walls in a new garden.

For the mathematically minded 5, 12 and 13 also produces a perfect square, but of course much less practical.

Harold

Edited By Harold Hall 1 on 21/02/2013 10:15:53

Errr, I think that a number that is a perfect square is an integer that is a square of an integer, not related to right angle triangles.

A right angle triangle where all the sides are integers is a Pythagorean triangle, and the integers that represent the three sides form a Pythagorean triple. Euclid's formula can be used to generate Pythagorean triples, given two postive non-equal integers.

Regards,

Andrew

That makes it all very clear now!!!

Len. P.

Edited By The Merry Miller on 21/02/2013 11:25:43

Or :- the square on the hypotenuse equals the sum of the squares on the other two sides.

Doesn't making item (4) assume your cross slide is accuately at 90 to the bed which is won't be. The making of a cylindrical square in a trued up lathe specificly avoids that assumption as only the outermost rim touches the surface plate.

'Good enough for me'. I use a spacer from a horizontal arbor. Seems to have been made quite good and square to avoid introducing bend into the aerbor when clamped up.

.

The real beauty of 3 4 5 is that [to Builders' tolerances] you can set out a right angle with nothing more than a piece of string. ... No need for any measuring instruments at all.

Take a suitable length of string [maybe the full length of your proposed building]

Fold it in half, then quarters; marking each fold.

You now have something four units long, which can be used to "measure" strings of 3 and 5.

.... Further investigation along the same lines will give you the Golden Ratio.

Divine Proportion = Expediency ? : Let's Discuss

MichaelG.

The squirrel on the hippopotamus is equal to the squirrels on the other two lions.

Joey

Well, it was all getting a bit too highbrow.

I must remember the string method Michael (G) next time I lay out a brand new garden on a hillside, but that is unlikely. Too old now to even contemplate it on the flat.

Sorry to say you final comment leaves me standing, will have to leave it at that.

Joseph. Your translation of Pythagoras's Theorem is new to me, like it. Actually, my wife was only saying this morning that we had not seen the squirrels in our garden for a couple of months, I can now tell here were they have gone.

Harold

For those who have reservations about their machine ability, may I suggest alternative sources of accurately machined bar such as the use of rollers from a roller bearing or silver steel or precision ground mild steel. All above may be obtained fairly cheaply if one is prepared to shop around for obsolete or odd-sized stock or even bar ends.

Punch line of old joke.. " the squaw on the hippopotomus is equall to the sons of the squaws on the other two hides".. guess it was some sort of tug of (sq)war......

"kinky naughty canibals must ask zombies for supper"

Try coins. Old halfpennies were 1 inch diameter

I don't know the tolerance on the diameter of the old 1/2d, Paul, but on the modern £1 coin it's 0.1mm either side of 22.5mm, so one brand new, unworn £1 might be 0.2mm or 0.008" bigger than the next. That's way outside the precision that Michael was describing in his original post.

£1, £2 and "silver" UK coins wouldn't do anyway, because of their milled edges, which only leaves coppers. I suspect that tolerances on those may be wider, because vending machines, parking meters etc don't take them any more.

Andy

Now I know why they invented CNC!

Cheers Michael.