Hidden meaning in a cutting board

[gypsie]

Re: Hidden meaning in a cutting board

I love Bilbao, it's unbelievable to walk around.
In form it is astonishing. In function less so.

Lucas numbers are like the flip side of Fibonacci. They average to the golden rule, like a mirror with the golden rule in between.

[Jim Bow]

Re: Hidden meaning in a cutting board

I learned something new today. Thanks.

Four thousand holes in Blackburn, Lancashire?

[JayInOz]

Re: Hidden meaning in a cutting board

I made this as a wedding present for my cousin who is an architect,

[ATTACH=CONFIG]137951[/ATTACH]

Some people stopped by my shop after work yesterday to drink beers and hang out. To my surprise, out of six people, only one got what I was illustrating. Thought it might be fun to post it here and see it.

You win. I have absolutely no bloody idea what that thing is supposed to be.

[Canoeyawl]

Re: Hidden meaning in a cutting board

For most woodworking projects you can round to 5/8ths, plus or minus

[Nicholas Carey]

Re: Hidden meaning in a cutting board

You win. I have absolutely no bloody idea what that thing is supposed to be.

It is a logarithmic spiral, based on the Fibonacci sequence. One begins with two arbitrary, non-negative integers, conventionally 1 and 1. Each successive value in the sequence is the sum of the preceding two values: so, 1, 1, 2, 3, 5, 8, 13, 21, 34, . . .

the interesting thing about it is that as you proceed along the Fibonacci sequence, any adjacent pair of values more and more closely approximates the value of the irrational number Φ (phi, the Golden Mean) — ( 1+ sqrt(5) ) / 2. Approximately 1.618...

Phi is an interesting number because it is the only number whose reciprocal is itself less 1. That is

1 / Φ = Φ - 1

It is even more interesting in that it is the basis of all natural harmonies. Tree branches are radially arranged according to Φ. Musical scales are tied to Φ. The shape of the shell of the chambered nautilus is arranged according to Φ

Φ is literally everywhere.

Rectangular shapes we find harmonious — sheets of paper, common proportions for image sizes are Φ-based. Think 3x5 index cards, 4x6, 8x10 or 11x14 pictures. All are approximations of Φ. It seems to be hardwired into the world and into our psyches.

There are books written about it. Academic papers, too.

https://www.penguinrandomhouse.com/books/102878/the-golden-ratio-by-mario-livio/

https://kara.reviews/the-golden-ratio/

[P.I. Stazzer-Newt]

Re: Hidden meaning in a cutting board

One for anyone with O Level physics.

Screenshot from 2023-06-04 09-04-37.jpg

It rather elegantly splits engineers from mathematicians.

[Breakaway]

Hidden meaning in a cutting board

Cool!

Curious: are any of the dimensions of either the finished piece, or its laminations, according to Fibonacci?

Kevin


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[Jfitzger]

Re: Hidden meaning in a cutting board

Cool!

Curious: are any of the dimensions of either the finished piece, or its laminations, according to Fibonacci?

Kevin

Yes to both. I planed the maple to 1" and the final outside dimensions are 8x13. The mathematically perfect dividing line between sections runs in the middle of the inlays.

[David G]

Re: Hidden meaning in a cutting board

Yes, the human brain is a fascinating critter.

Pi-based stuff really IS a pleasing shape to humans.

I also find Cake a pleasing shape.

[P.I. Stazzer-Newt]

Re: Hidden meaning in a cutting board

Yes, the human brain is a fascinating critter.

Pi-based stuff really IS a pleasing shape to humans.

I also find Cake a pleasing shape.

Donning once more my pedant hat...
Phi, not Pi
N.B. neither are rational.

[David G]

Re: Hidden meaning in a cutting board

Donning once more my pedant hat...
Phi, not Pi

While I sympathize... it has been shown that 'pedant shaped' is not NEARLY as pleasing <G>

But seriously... thanks for the spellcheck!

[Gerarddm]

Re: Hidden meaning in a cutting board

C-l-e-a-n, and I don't just mean mathematically. Kudos.

[Breakaway]

Yes to both. I planed the maple to 1" and the final outside dimensions are 8x13. The mathematically perfect dividing line between sections runs in the middle of the inlays.

Nice!


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[David G]

Re: Hidden meaning in a cutting board

The golden rule. It's automatic for some people. Then you get the Frank Gehrys of the world, who go out of their way to break it, and try to prove it wrong.... And look at the results.....
It's not that pretty at all.

I'll just borrow PISN's hat for a moment and remind everyone that phi... that number that is slowly revealed by a fib... is known as the 'golden ratio'. 1.618 etc. And yes, for practical purposes, I often simply layouts by using 5/8, or 0.625, - rather than the precise golden ratio. Seems to make no difference in terms of a pleasing shape.

[P.I. Stazzer-Newt]

Re: Hidden meaning in a cutting board

phi-formula-image-300x52.png