The maths behind cutting these bevels?

[Adam W.]

Yes Euclid and Pythagoras defined parts of mathematics geometry in the branch called geometry geometric proof. More is being defined as time progresses. I would not be surprised in new branches are added in the future.

This is the same way dinosaurs where defined but did exist before then. We will discover more groups of extinct species as we continue to dig around on this planet. But what we have not yet discovered does exist, we just haven't seen it yet.

There, FTFY.

 

[Yojevol]

not necessary

possibly quicker if you've got space on your workpiece to do it

 

[Adam W.]

Maths is everywhere.

You just did that to wind @Yojevol up, didn't you?

​

 

[johna.clements]

Can be done with dividers if you do the step out process along the line first but make sure the error is +, then make this line your second line, to which you have the dividers already set very precisely to 1/3.
So it's trial and error by a different route.

But there is no need to do it by trial and error if you draw a second line. Why would you want to do it by trial and error if you don't have too. All you need is a straight edge and a square and an object to mark units.

 

[Jacob]

But there is no need to do it by trial and error if you draw a second line. Why would you want to do it by trial and error if you don't have too. All you need is a straight edge and a square and an object to mark units.

How would you divide the 2nd line equally?

 

[johna.clements]

There, FTFY.

Cambridge Dictionary

geometry
noun [ U ]


the area of mathematics relating to the study of space and the relationships between points, lines, curves, and surfaces:

https://dictionary.cambridge.org/dictionary/english/geometry

You can define words to have non accepted meanings if you wish.


Should I define wood as cheese from now on, chisels are cheese knives, saws are cheese wires and the wood store is the fridge. Do you think that changing the meaning of words is helpful.

 

[johna.clements]

How would you divide the 2nd line equally?

You have an object of convenient fixed length. A compass would work but you could use other things.

 

[Adam W.]

Cambridge Dictionary

geometry
noun [ U ]


the area of mathematics relating to the study of space and the relationships between points, lines, curves, and surfaces:

https://dictionary.cambridge.org/dictionary/english/geometry

You can define words to have non accepted meanings if you wish.


Should I define wood as cheese from now on, chisels are cheese knives, saws are cheese wires and the wood store is the fridge. Do you think that changing the meaning of words is helpful.

If you wish.

 

[Jacob]

You have an object of convenient fixed length. A compass would work but you could use other things.

Your first line is already an object of convenient fixed length. You have the same problem trying to divide the 2nd line.
So what you use for 2nd line is your 1st line plus divider error, which you have already conveniently set the divider to divide exactly into 3 parts.

 

[Phill05]

What's the article that this comes from, as the link only directs to the institution?

Adam, Sorry wrong link, I came across this researching roman flooring and it spelt out what you and Jacob have been saying practical first maths later.

Download the PDF or join and read online

https://www.researchgate.net/public...matical_Machines_A_Laboratory_for_Mathematics

 

[Jacob]

You have an object of convenient fixed length. A compass would work

How?

but you could use other things.

 

[johna.clements]

How?

We were taught this in maths back in the 70s.

 

[Jacob]

We were taught this in maths back in the 70s.

Yes so was I (in the 50s!). But here we are dividing with dividers only, without recourse to scales.

 

[johna.clements]

Yes so was I (in the 50s!). But here we are dividing with dividers only, without recourse to scales.

No need for scales just straight edge, square and something of fixed length to mark with.

 

[Adam W.]

You can use geometry to divide a line into any number of equal parts that you wish.......Avoiding the use of cumbersome maths and the use of squares and measurements.

 

[johna.clements]

You can use geometry to divide a line into any number of equal parts that you wish.......Avoiding the use of cumbersome maths and the use of squares and measurements.

The maths I showed in the video above was quite simple. No measurements were required all you need is a gauge to mark consistent distances.

 

[Jacob]

No need for scales just straight edge, square and something of fixed length to mark with.

Oh OK so you make a scale with compass strokes or a handy object, and then use it on your drawing.
I think my way is easier i.e. dividing the error by eye or using your line plus error as your 2nd line.

 

[niall Y]

This thread has shown, above all, that people approach making things in wildly different ways. The original post I found a bit puzzling, as it was enquiring about the mathematics involved in cutting 'these bevels ' which I though was a bit of a detour from the task in hand, which was to reproduce something that was 'to hand'. This I would have done with the use of a table saw, a rule, and sliding bevel.

Mathematics is a way of looking at things, and understanding the world. And as such, is in everything. But we do not all need to be mathematicians to carry out basic woodworking tasks. Woodwork is working with wood, it is not, as I used to tell my customers, - wood engineering. Wood does not behave as metal does, therefore an engineering approach is not necessarily needed.

I worked with a friend and colleague, years ago, making and fitting lots of doors to cabinets. He was a very capable and tidy cabinet maker, but I was surprised to find on his bench a small notebook crammed with lines and lines of beautifully written , but tiny numbers, that covered page after page like some secret code. We were both carrying out, the self same task, but our approaches to it were completely different.

My approach is a lot more intuitive and pragmatic. If want to work out how much to vary the height of drawers in a chest, I will do it so that it looks right - no complicated formulas, or golden mean, anywhere to be seen

 

[Adam W.]

The maths I showed in the video above was quite simple. No measurements were required all you need is a gauge to mark consistent distances.

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

 

[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.