The maths behind cutting these bevels?

[Inspector]

uziwood786 it is a good thing you didn't ask how to do it with a dinosaur bone or there would be the added aspect of creationism verses evolutionism to the mix and would the dinosaurs have used math, geometry or rule of claw to figure it out.

I being a new world barbarian would have used the table saw by attaching a sacrificial wood fence to the existing fence, tilted the blade to 35º from vertical, and brought the spinning blade up into the sacrificial fence until the tips were buried. Pass some scrap along the fence to cut the bevel. The eventual top will be down on the table surface. THERE WILL BE TRIANGULAR SLIVER/OFFCUT THAT WILL PROBABLY SHOOT OUT TOWARDS YOU. MAKE SURE YOU STAND ASIDE. Put a sheet of plywood or OSB behind you to stop the offcuts from poking holes into stuff you don't want holes in. You can refine the bevel by dropping the blade and repositioning the fence and then bring the blade back up until buried again. Once happy you take your stock, pre-cut to length and width and bevel both long sides, then without touching the fence use the mitre gauge to hold the piece against the fence to cut the ends. All the bevels will be the same. Set up fingerboards for narrow stock and feed with push sticks. Now if you really wanted to raise an eyebrow or three you would use a dado stack rather than a single blade. The wider cut would eat up the wood that would have become offcuts and removed the waste kickback hazard.

Pete

 

[baldkev]

Im tired just reading it all

 

[Sgian Dubh]

Im tired just reading it all

I thought it was just starting to get interesting, ha, ha. Slainte.

 

[J-G]

I haven't responded for a while - not because I've given up my side of the discussion but because I've been busy designing a small box to contain a 'floral' broach which my Grandson is making as my sister's 80th birthday present. I'll probably spend most of tomorrow on this same project and will not even consider which of the many exotic timbers I have at my disposal until I'm satisfied that I know exactly what size each component will be and how they will fit together. This will include the bespoke 'secret button' spring catch that will be made on the same milling machine on which the box components will be made.

Most of the arguments in this thread regarding the history of mathematics brings to mind the brainless ramblings on another forum - concering mathematics - where there are a few zelots insisting that Pi has been incorrectly evaluated for centuries, whatever arguments are put forward by learnéd professors the zelots simply repeat their ****-eyed assertions over and over simply going around in circles.

I have no doubt that it is possible to layout many geometric shapes in all manner of materials without ever having to resort to a pre-marked measuring stick of whatever ilk.

My assertion is that if you wish to produce multiple identical copies of that shape at some disparate time then you have to resort to at least recording the dimensions which will of necessity involve some calculations that involve at the very least arithmetic and much more likely mathematics.

Incidentally, my grandson will be making the silver broach, based around an Amerthyst, by hand without physically measuring any of the petals. He will, naturally, use maths to calculate the precise length of the silver needed to create the collet into which he will mount the gem-stone.

 

[Adam W.]

Sounds lovely, I hope it turns out beautifully.

 

[Scruples]

If you wish.

Addendum: That's a bit like saying Pythagoras invented geometry.

No numbers required, just drawing

View attachment 148106

I was just stating the facts,

 

[Scruples]

Yes but all maths is only useful if numbers are ultimately applied. Mathematical concepts are developed from past observations of the real world in order to predict what will (or 'might' in statistical maths) happen in the future. Such concepts provide a framework but need numbers to turn them into reality.
My blood was made to boil recently by that young lady on the box, Prof(even) Hannah Fry asserting that EVERYTHING depends on maths. No, it's the other way round, maths depends on everything, or at least, everything we understand.
Brian

I know what you mean, but what they really mean is that there is a mathematical model to fit everything so, by extension, mathematics is used not only explain matter but to predict it's existence.

 

[Yojevol]

I know what you mean, but what they really mean is that there is a mathematical model to fit everything so, by extension, mathematics is used not only explain matter but to predict it's existence.

I think the problem is that we engineers (in the broadest sense) use mathematical processes to achieve predictability and precision whereas mathematicians have developed ways of assessing non-precise systems which involve the notions of risk, chance and even chaos. Look at the branches of maths as noted earlier in this discussion. It's such a wide term these days that it is almost meaningless. To some people, eg, Prof HF it has become a god.
In the finality the big M cannot cover everything because we are still searching for the Theory of Everything.
Must get on, I'm off to Cosford today
Brian

 

[Adam W.]

I was just stating the facts,

Actually, what you were stating is that you have been conditioned to believe that geometry is mathematics.

 

[Jacob]

.........

My assertion is that if you wish to produce multiple identical copies of that shape at some disparate time then you have to resort to at least recording the dimensions which will of necessity involve some calculations that involve at the very least arithmetic and much more likely mathematics.

No you just use the original and copy it. No problem. If you haven't got the original to hand you just have a stab at it.
Or you get into the habit of always using the same thing as your base measurement: Your foot would be handy. Divide it (with dividers) into 12 and you have your own personal inch, accompanying you wherever you go. Hence introducing you to maths, or "sums" as we used to call it.

 

[Scruples]

Actually, what you were stating is that you have been conditioned to believe that geometry is mathematics.

Like history, here are many versions of the truth. It depends on who you listen to and what you're prepared to believe. Facts are only facts until proved otherwise, which is what science and mathematics is all about.

 

[Jameshow]

uziwood786 it is a good thing you didn't ask how to do it with a dinosaur bone or there would be the added aspect of creationism verses evolutionism to the mix and would the dinosaurs have used math, geometry or rule of claw to figure it out.

I being a new world barbarian would have used the table saw by attaching a sacrificial wood fence to the existing fence, tilted the blade to 35º from vertical, and brought the spinning blade up into the sacrificial fence until the tips were buried. Pass some scrap along the fence to cut the bevel. The eventual top will be down on the table surface. THERE WILL BE TRIANGULAR SLIVER/OFFCUT THAT WILL PROBABLY SHOOT OUT TOWARDS YOU. MAKE SURE YOU STAND ASIDE. Put a sheet of plywood or OSB behind you to stop the offcuts from poking holes into stuff you don't want holes in. You can refine the bevel by dropping the blade and repositioning the fence and then bring the blade back up until buried again. Once happy you take your stock, pre-cut to length and width and bevel both long sides, then without touching the fence use the mitre gauge to hold the piece against the fence to cut the ends. All the bevels will be the same. Set up fingerboards for narrow stock and feed with push sticks. Now if you really wanted to raise an eyebrow or three you would use a dado stack rather than a single blade. The wider cut would eat up the wood that would have become offcuts and removed the waste kickback hazard.

Pete

With all this maths flying around it's amazing we all evolved!

 

[Adam W.]

Like history, here are many versions of the truth. It depends on who you listen to and what you're prepared to believe. Facts are only facts until proved otherwise, which is what science and mathematics is all about.

OK, prove to me that geometry is mathematics.

 

[Adam W.]

..............That may take you some time and while you're at it, can you prove the existence of god as well.

 

[Tom K]

OK, prove to me that geometry is mathematics.

That’s easy, describe an arc with a radius of 50mm. There is the proof ! Of course it doesn’t work if no number is applied? I have the answer to the existence of god too, it goes I say if there is a god why would he create me in his image and also a parasitic worm to make me blind? And the answer seems to be we couldn’t just have evolved or you have to have faith

 

[Jacob]

That’s easy, describe an arc with a radius of 50mm. There is the proof ! Of course it doesn’t work if no number is applied?

I just described an arc. It measured exactly 112mm. The arc came before the measurement, which wasn't necessary at all!
Arc with no measurement, no problem.
Measurement with no arc, meaningless.

 

[Tom K]

I just described an arc. It measured exactly 112mm. The arc came before the measurement, which wasn't necessary at all!
Arc with no measurement, no problem.
Measurement with no arc, meaningless.

That’s fair enough OK how long is a piece of string I want to describe an arc with it? Your measurement with no arc might fill a gap you could store it with your offcuts!

 

[Jacob]

That’s fair enough OK how long is a piece of string I want to describe an arc with it?

You choose?

 

[Tom K]

You choose?

It’s a trick question I bet the answer is I want to keep it!

 

[johna.clements]

Just do it with a pair of dividers with parallel lines drawn from each end of the line, it's much more accurate.

Post a video to explain. Hopefully it will explain as well as the thumb nail of the video I posted.

Why can't you explain your method.