a golden rule calculator

[devonwoody]

The Australian boys have been up all night making an Excel calculator for working out the proportions of the golden rule.

There are a number of different versions all the way through the thread.

http://www.woodworkforums.com/showthrea ... post629264

 

[OllyK]

Interesting, but I'm not convinced the cutting list is correct. Not to be out done by the southerners, I've re-created it as a Windows app, feel free to have a play (you will need the .NET framework), any comments welcome, I did ponder on things like considring board thickness and calculating for an internal set bottom etc, but that'll take a bit longer, let me know what you think.

Golden Rule Calculator

 

[Jhalfa]

Isn't the ratio simply (1+ squareroot(5))/2?

Multiply this by the short measurement to get the long measurement

 

[devonwoody]

They are trying to produce the three dimensions.
how about using your technique above to produce the third after getting the two?

 

[OllyK]

Yes it's just a case of multiplying the shortest by 1.62 to get the middle then multiply that again to get the long. I didn't actually check the maths, but I suppose I should seeing as the cutting list seems to be out.

Where it will get interesting is to take board thickness in to account as you will for an interallly set side, need to reduce the length by twice the thickness of the board to get the correct overall side length.

 

[tnimble]

Calculating the dimensions isn't really hard (unless you haven't got a calculator and have terrible arithmetic skill) both for outside and insides. (Though indeed the inside would require a few more steps)

But what about the other ratio systems like the plastic numer or an old Arabic system to which for instance the Alhambra was build. (the diagonal forms the dimension of the first larger peice, starting with a small square for the first smallest piece)

It would be great to has a piece of software to do various of these systems and possibly also show the result in a 2D of 3D drawing.

And beeing software it should not use the 1.618034 which is only true for large dimensions but solve the q =1 + 1/q equation or the p = 1/p + 1/p2 equation for the plastic number system instead of 1.324718 which is also only true for large dimensions

 

[OllyK]

Calculating the dimensions isn't really hard (unless you haven't got a calculator and have terrible arithmetic skill) both for outside and insides. (Though indeed the inside would require a few more steps)

But what about the other ratio systems like the plastic numer or an old Arabic system to which for instance the Alhambra was build. (the diagonal forms the dimension of the first larger peice, starting with a small square for the first smallest piece)

It would be great to has a piece of software to do various of these systems and possibly also show the result in a 2D of 3D drawing.

And beeing software it should not use the 1.618034 which is only true for large dimensions but solve the q =1 + 1/q equation or the p = 1/p + 1/p2 equation for the plastic number system instead of 1.324718 which is also only true for large dimensions

For the golden ratio, I do calculate the figure as a decimal from the values entered so it will have a fair degree of accuracy:

+/-79,228,162,514,264,337,593,543,950,335 for zero-scaled numbers, that is, numbers with no decimal places. For numbers with 28 decimal places, the range is +/-7.9228162514264337593543950335. The smallest possible non-zero number is 0.0000000000000000000000000001 (+/-1E-28).

I'm happy to look at extending functionality to provide a suite of tools if so desired, obviously the golden ratio bit only took half an hour or so to knock together, other stuff could take rather longer.

 

[tnimble]

For the golden ratio, I do calculate the figure as a decimal from the values entered so it will have a fair degree of accuracy:

+/-79,228,162,514,264,337,593,543,950,335 for zero-scaled numbers, that is, numbers with no decimal places. For numbers with 28 decimal places, the range is +/-7.9228162514264337593543950335. The smallest possible non-zero number is 0.0000000000000000000000000001 (+/-1E-28).

When for instance you're designing one of the drawers for a writing desk which is 2" height and you want the next larger dimension for its width. When multiplying you would get 3.236068 roughly 3.2". This is however incorrect. When solving the Fibonacci set you would find 3" for the width of the drawer.

Since a 3" by 2" drawer would be a bit small (even for a writing desk) you would probably want the second or third dimension. By multiplying that would be 5.2" or 8.5" in width. Solving the set would give 5" and 8" width

Edit:
To clarify a bit more. When designing a building of 233" in width by multiplication you would get 377.001922" for the height. When solving the set you'll get exactly 377" which is pretty much the same height.

I'm happy to look at extending functionality to provide a suite of tools if so desired, obviously the golden ratio bit only took half an hour or so to knock together, other stuff could take rather longer.

Most probably indeed

 

[OllyK]

When for instance you're designing one of the drawers for a writing desk which is 2" height and you want the next larger dimension for its width. When multiplying you would get 3.236068 roughly 3.2". This is however incorrect. When solving the Fibonacci set you would find 3" for the width of the drawer.

Since a 3" by 2" drawer would be a bit small (even for a writing desk) you would probably want the second or third dimension. By multiplying that would be 5.2" or 8.5" in width. Solving the set would give 5" and 8" width

Edit:
To clarify a bit more. When designing a building of 233" in width by multiplication you would get 377.001922" for the height. When solving the set you'll get exactly 377" which is pretty much the same height.

OK, need to do some reading first, but it would seem that it's a case of developing an appropriate rounding mechanism / compare to a set of figures in the case above.

 

[tnimble]

OK, need to do some reading first, but it would seem that it's a case of developing an appropriate rounding mechanism / compare to a set of figures in the case above.

Normaly when using the golden ratio or the plastic number one first graphically draws the set starting from 1. Whith this drawn set at hand one can start designing the piece choosing the smallest measurement.

With the computer at hand (or when one is fund of wrinting many sheets full with numbers) the easiest way to calculate the set is to calculate the sum of the previous results in a iterate loop. (useful only for small numbers as the number of iterations adds up quickly for numbers above a couple of thousand):
1, 1, 1+1=2, 1+2=3, 2+3=5, 3+5=8, 5+8=13, 8+13=21, etc

When a user is to enter a random number for which the next number in the set is given one has also sum the two previous results. Which ofcouse are not known. The easiest way would be to work up calculating the result for 1, 2, 3 etc until you get to the number entered by the user.

Calculating a golden ratio for small number is like finding a prime number.

Also the user cannot enter any number. When for instance the user enters 7.5" there is no result.

In fact the above is not true at all. Any set being a Fibonacci, Perrin, Padovan, or any other set can be scaled. Like as you could build a table to scale. When in the above case asuming a scale factor of 7.5 the resulting answers would be 1 * 7.5, 1 * 7.5, 2 * 7.5, 3 * 7.5, 5 * 7.5, etc

Finding the scale factor to the set is like finding the greatest common divisor or a beter example would be converting decimals to fractions like 0.75 = 3/4.

Within one piece of furnatre the same scale factor has to be used.

So when designing a piece around a first measurement of 6":

6 does not meet q =1 + 1/q so the set has to be scaled.
The smallest possible scale factor would be 2. This would make tis measurement the 4th number in the set. The set being:
1*2, 1*2, 2*2, 3*2, 5*2, 8*2, etc
The next larger dimension for 6" would thus be 10" (not 9.7)

The above can also be done for calculating a plastic number. Which is a Padovan set which is iterataively calculated by the sum of the two previous results skipping one result. i.e.: 1, 1, 1, 1+1=2, 1+1=2, 1+2=3, 2+2=4, 2+3=5, 3+4=7, 4+5=9, 5+7=12, etc

 

[bugbear]

A hopefully relevant discussion from another place, especially the input from Don McConnell.

http://nika.frontier.iarc.uaf.edu/~cswi ... =1#message

BugBear

 

[tnimble]

A hopefully relevant discussion from another place, especially the input from Don McConnell.

http://nika.frontier.iarc.uaf.edu/~cswi ... =1#message

BugBear

Just read the thread and related materials.

After a number of readings (and some attempts at designs), I
started to get cynical about the subject. I started questioning why
one element would be designed to be a proportion of a certain part of
the column, but another element would be the same proportion of a
larger part of the column. For instance, Mack derives the height of a
table from the full height of an Ionic order. Yet when he derives the
dimensions of the leg, he does one derivation by using only the column,
and the next by the height of the column and entablature. No
explanation is given for changing the basis and I haven't figured it
out yet.

This could be exactly what I mean. Often when one studies (or tries to design a piece) one tries to find a component in the design that is 1.6180339887498948482 times smaller or larger. But one cannot fnd a second, thrids component.

That one cannot find such a component is correct. After finding one should look for a component that is 1.615, 1.625, 1.6, 1.667 smaller or larger.

See the ratios in the chart with all the lines and the measurements used for the final table design in this thread

Or try to draw a nautilus shell using 1.6180339887498948482. You would (depending on how you'll end up trying to correct the errors) with a disformed shell or a shell with lots of holes of various sizes.