The maths behind cutting these bevels?

[Adam W.]

No, geometry is an area of mathematics that concerns the properties of shapes and space. Geometry can be used to create art but it is mathematics.

I'll let you believe what you want, many others view it a different way.

Craftsmen were creating hyperboilc and Gaussian 3D forms with compasses and string many centuries before mathematicians discovered them.

 

[mudman]

I'll let you believe what you want, many others view it a different way.

Craftsmen were creating hyperboilc and Gaussian 3D forms with compasses and string many centuries before mathematicians discovered them formulated the theorems that described the mathematics used in creating these forms that allowed the techniques used, to be formalized into a set of underlying principles.

Fixed that for you.

You are making the mistake of believing that mathematics only deals with numbers and abstract formulae. It doesn't. It can also be as simple as understanding that a certain shape will fit into a certain shape hole, or that folding a circular piece of paper in half will give you a semicircle with the same radius as the first circle. Seems obvious but both involve mathematical principles.
Everything involves mathematics, you may not be performing difficult or complex calculations or solving abstract formulae, but the act of scribing singing with a piece of string is still a process that utilizes mathematical principles.

 

[J-G]

I'll let you believe what you want, many others view it a different way.

Craftsmen were creating hyperboilc and Gaussian 3D forms with compasses and string many centuries before mathematicians discovered them.

Mathematics simply 'explains' how to create the shapes that are found naturally. ie. mathematicians didn't 'discover' hyperbolic or gaussian forms they just made it possible to re-create them repeatedly.

In a similar way there are cooks who never use scales to weigh ingredients - they consider their work to be an 'art' - personally I weigh everything and achieve the same result time after time. Maths (in all its guises) is simply a very useful tool.

 

[Adam W.]

Maths is just one tool which can be to used to describe 3D shapes and forms. It doesn't mean, however, that a tool which can be used to describe 3D shapes or forms is maths.

I can create regular 3D solids, both positive and negatives, in wood or stone without the use of mathematics, repeatedly, by drawing and scratching a line.

It's not maths and I'm not a mathematician.

 

[mudman]

Maths is just one tool which can be to used to describe 3D shapes and forms. It doesn't mean, however, that a tool which can be used to describe 3D shapes or forms is maths.

I can create regular 3D solids, both positive and negatives, in wood or stone without the use of mathematics, repeatedly, by drawing and scratching a line.

It's not maths and I'm not a mathematician.

So you just chip away randomly at a piece of stone or wood until the shape you want magically appears?

 

[J-G]

I can create regular 3D solids, both positive and negatives, in wood or stone without the use of mathematics

I'm having difficulty trying to imagine a 'Negative' 3D solid !

 

[Adam W.]

So you just chip away randomly at a piece of stone or wood until the shape you want magically appears?

That's right, I just chip away and at any old random rock or tree it appears out of nowhere, as if by magik. No maths involved.

I'm having difficulty trying to imagine a 'Negative' 3D solid !

Alright, so my English is not quite up to scratch. How about a Gaussian pseudosphere with a constant negative curvature and a hole to fit it in then ?

Edit: I can make that repeatedly with practical geometry and without maths, easy peasy.

 

[Woody2Shoes]

One example of what I think Adam is driving at is the old way of cutting roof timbers, based on a simple ratio of 'Rise' to 'Run'.

If you'd said to one of the ol-timers, 'I want my roof pitched at 43.2 degrees' they'd have looked at you like you'd just beamed down from another planet, but if you'd simply said 'I want to pitch the roof at eleven inches per foot', no probs. One solution involves trigonometry, one just involves measuring (OK, maybe also knowing what a right angle is!).

 

[Woody2Shoes]

So, to sum up:

Possible methods include:

1) Using a router and/or router table to bevel the edge all the way round (ends first, Jacob?!).
2) Using a handsaw to cut the bevels all the way round and a sanding block to tidy up.
3) Using a handplane, as Jacob has ably demonstrated (ends or sides first, take your pick - in this case there's precious little difference).
4) Using a table saw (scary with small-ish workpieces without special work-holding).
5) Using a band saw (similar considerations as 4, but marginally less scary).
6) Using a CNC machine.
7) Lasers

For someone new to woodworking, 2, 3 and maybe 5 would be my favoured options.

In any case using rotating machinery is potentially (pant-wettingly) dangerous and needs to be under supervision until someone can show that they know enough to use a machine safely.

In all cases, drawing - on paper, followed by accurate marking up on the workpiece from the drawing - is the most 'maths-free' way of doing things.

I hope the OP has not lost the will to keep reading....

 

[baldkev]

I hope the OP has not lost the will to keep reading....

Probably lost the will to live

 

[Adam W.]

One example of what I think Adam is driving at is the old way of cutting roof timbers, based on a simple ratio of 'Rise' to 'Run'.

If you'd said to one of the ol-timers, 'I want my roof pitched at 43.2 degrees' they'd have looked at you like you'd just beamed down from another planet, but if you'd simply said 'I want to pitch the roof at eleven inches per foot', no probs. One solution involves trigonometry, one just involves measuring (OK, maybe also knowing what a right angle is!).

Sort of.

What I'm trying to get at is, that you don't need to resort to maths to be able to do complex carpentry or joinery.

 

[Jacob]

...... the act of scribing singing with a piece of string is still a process that utilizes mathematical principles.

Wrong again. It utilises a piece of string.
You don't need to know anything about the principles.

 

[mudman]

Sort of.

What I'm trying to get at is, that you don't need to resort to maths to be able to do complex carpentry or joinery.

I don't think you get what I'm saying. You are right, you may not resort to complex definitions, formulae, principles but what you are doing is mathematics. If you create a cube out of wood or stone, you know that opposing faces have to have the same dimensions and be parallel to each other and thus the internal angles will be 90 degrees. You may not use anything more complex than a piece of string and a set square to lay it out, but you are making use of basic mathematical principles.
Mathematics underlies everything we do and indeed are you don't need to be solving 4th order quadratic equations to be "doing math".

 

[mudman]

Wrong again. It utilises a piece of string.
You don't need to know anything about the principles.

If you use a piece of string and nail to scribe a circle, you utilise the piece of string and the principle that a circle can be defined as the line traced by a point that is always the same distance from another point in two dimensions. That is a mathematical principal, you may not know it but you are using maths to draw your circle.
To draw a circle in that way, you need to understand that principle, you might not realise it but you are using mathematics.

 

[johna.clements]

There are graphical methods of calculating the loads in trusses.



Is this maths.

 

[Adam W.]

I don't think you get what I'm saying. You are right, you may not resort to complex definitions, formulae, principles but what you are doing is mathematics. If you create a cube out of wood or stone, you know that opposing faces have to have the same dimensions and be parallel to each other and thus the internal angles will be 90 degrees. You may not use anything more complex than a piece of string and a set square to lay it out, but you are making use of basic mathematical principles.
Mathematics underlies everything we do and indeed are you don't need to be solving 4th order quadratic equations to be "doing math".

I do understand what you're saying, but I view geometry as a branch of drawing, hence my view of it as art, not maths.

 

[johna.clements]

I do understand what you're saying, but I view as a branch of drawing, hence my view of it as art, not maths.

Geometry is a branch of maths.

 

[Adam W.]

Geometry is a branch of maths.

Perhaps maths is a branch of geometry.

 

[johna.clements]

Perhaps maths is a branch of geometry.

No.

From Britannica.


Among the principal branches of mathematics are algebra, analysis, arithmetic, combinatorics, Euclidean and non-Euclidean geometries, game theory, number theory, numerical analysis, optimization, probability, set theory, statistics, topology, and trigonometry.

 

[Adam W.]

That's just the opinion of encyclopedia Britannica, it doesn't mean that it is true. Geometry has been around for thousands of years, that's a fact not an opinion.