# Furniture Design



## David (Jan 26, 2007)

*Fibonacci gauge*

*1 • 1 • 2 • 3 • 5 • 8 • 13 • 21 • 34 - The Fibonacci Sequence*

http://blip.tv/scripts/flash/blipplayer.swf?autoStart=false&file=http://blip.tv/file/get/USNERDOC-FibonacciGauge966.flv%3Fsource%3D3

I have been fascinated with The Fibonacci Sequence and The Golden Rectangle for some time. I finally got around to building a Fibonacci Gauge that was featured in WOOD Magazine.










The guage maintains a consatnt proportion of 1:1.618 between the points. It is used to help determine visually appealing proportional dimensions. I am looking forward to using the guage in future projects.

Follow the text below for some interesting history, a fun video from WOOD Magazine demonstrating the Fibonacci Gauge, and some online resources.

This was a fun afternoon project which provided some much needed therapy and piece of mind!










*MY FIBONACCI GAUGE*
Constructed from thin cherry cut-offs from a prior project and finsihed with 2 coats of Tung Oil and 4 coats of lacquer. I found the solid brass binding posts in a little hardware store in Sisters, Oregon.




























*WHO WAS FIBONACCI?*










Leonardo of Pisa, known as Fibonacci [pronounced fib-on-arch-ee], was the "greatest European mathematician of the middle ages". His full name was Leonardo of Pisa, or Leonardo Pisano in Italian since he was born about 1175 AD in Pisa (Italy), the city with the famous Leaning Tower of Pisa.. Pisa was an important commercial town in its day with links to many Mediterranean ports. Leonardo grew up with a North African education under the Moors. Later, he traveled extensively around the Mediterranean coast meeting with many merchants. He learned of their systems of doing arithmetic realizing the many advantages of the "Hindu-Arabic" system over all the others. He was one of the first people to introduce the Hindu-Arabic number system into Europe, the positional system we use today, which is based on ten digits, a decimal point and a symbol for zero.

*THE FIBONACCI SEQUENCE AND ITS RELATIONSHIP TO THE GOLDEN PROPORTION*










The Golden Section, also called The Golden Ratio, The Golden Mean and The Divine Proportion was discovered by the Greek mathematician Pythagoras. Later, an Athenian architect using the Golden Section in building design came up with Phi, the number 1.618. Fibonacci made the next leap when he published a book in 1202 called "Liber Abaci". He introduced a math problem where a pair of rabbits were placed in a field with the provision that they could not escape or die. At the age of 1 month the female gives birth to 2 new rabbits (1 male, 1 female). The female rabbit does this each month for 1 year. How many rabbits would there be at the end of the year? The answer to this question contains a series of numbers (1, 1, 2, 3, 5, 8, 13, 21, 34, 55…..). This series of numbers is called the Fibonacci Series. If you look at the ratio that occurs after the number 3, you will see the number 1:618, which is the Golden Ratio.

Fibonacci devised a series of proportional relations [ 1 : 1 , 1 : 2 , 2 : 3 , 3 : 5 , 5 : 8 , 8 : 13 . . . ]. If you look closely, you will see the Fibonacci Sequence. This set of ratios, arrived at by adding the 2 previous numbers together to give the next number the new series, is been used in many aspects of life from architecture, finance, biology and engineering. Nestled in the Fibonacci series are the ratios 5:8 and 8:13 which are the classic "golden section" proportions.

*WHAT DOES THIS HAVE TO DO WITH WOODWORKING?*

The Golden Section or Fibonacci Numbers can be used to derive pleasing dimensions for any piece of furniture. For example, you have been commissioned to build a table for a client. You decide to use the Golden Rule to help determine construction dimensions that will be pleasing to the eye. The client requires the top to be 20 inches deep. To make the top into a Golden Rectangle, multiply 20 by 1.618 - the result is 32.36 inches. Rounding this to 32.5 yields a Golden rectangle measuring 20 inches x 32.5 inches. Interestingly, if you draw a square within your Golden Rectangle, the remaining rectangle will also be a Golden Rectangle. This principle can be used to scale all the other elements of the table. Ultimately, common sense and your eye should rule over the Golden Section. The Golden Section is a tool that you bring to the bench much like a finely tuned plane, razor sharp chisel or that special dovetail saw.

*Construction of a Golden Rectangle*
1. Construct a unit square.
2. Draw a line from the midpoint of one side to an opposite corner.
3. Use that line as the radius to draw an arc that defines the long dimension of the rectangle.










*Some Interesting Online Fibonacci Resources*

*Fibonacci Gauge and How to Use It Woodworking Plan*
Featured in the November 2006 issue

*YouTube - WOOD Magazine Fibonacci Gauge Demo*

*The Golden Mean Gauge*

*The Golden Number Grid*

*Fibonacci Numbers and The Golden Section in Art, Architecture and Music*


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## WayneC (Mar 8, 2007)

David said:


> *Fibonacci gauge*
> 
> *1 • 1 • 2 • 3 • 5 • 8 • 13 • 21 • 34 - The Fibonacci Sequence*
> 
> ...


Very informative post David. Thanks for taking the time to pull all this together. Glad to see you got some free time.


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## oscorner (Aug 7, 2006)

David said:


> *Fibonacci gauge*
> 
> *1 • 1 • 2 • 3 • 5 • 8 • 13 • 21 • 34 - The Fibonacci Sequence*
> 
> ...


That was a great article in WOOD.


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## LeeJ (Jul 4, 2007)

David said:


> *Fibonacci gauge*
> 
> *1 • 1 • 2 • 3 • 5 • 8 • 13 • 21 • 34 - The Fibonacci Sequence*
> 
> ...


David;

You did a big service to all woodworkers, by coming up with this, and publishind yor article.

Fibonacci series of numbers are consulted prior to us building anything.

Chippendale's feelings on proportions were a man can't be a cabinet maker without a complete understanding of proportions. Sheridan and Hepplewhite had similar convictions about it.

Many things in nature are directly related to the Fibonacci numbers, in addition to the example with the rabbits.

Your own arm is based on those same proportions: Part A: hand , Part B: hand and forearm (to elbow)
Part C: entire arm, from fingers to armpit

A is to B, what AB is to C.

Amazing stuff.

Lee


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## PanamaJack (Mar 28, 2007)

David said:


> *Fibonacci gauge*
> 
> *1 • 1 • 2 • 3 • 5 • 8 • 13 • 21 • 34 - The Fibonacci Sequence*
> 
> ...


Cool Tool David! Thanks!


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## knothead (Aug 4, 2007)

David said:


> *Fibonacci gauge*
> 
> *1 • 1 • 2 • 3 • 5 • 8 • 13 • 21 • 34 - The Fibonacci Sequence*
> 
> ...


The Guy in the video is Jeff Mertz from WOOD Magazine - which happens to be right here where I live - he came to our woodworkers association meeting last fall and gave that very presentation - he is a wonderfull guy to know and was very informative Alot of the woodworking magazines that are out there originate right here so I have the luxury of attending the Woodsmith Seminars and the Shopnotes presentations ect ect.

So Much to learn…................


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## scottb (Jul 21, 2006)

David said:


> *Fibonacci gauge*
> 
> *1 • 1 • 2 • 3 • 5 • 8 • 13 • 21 • 34 - The Fibonacci Sequence*
> 
> ...


It can be very hard to convey that information in a way that doesn't quickly go over peoples heads. I understand the geometry of it, as well as how they discovered this ratio almost everywhere in nature… great set of resources and information you pulled together for us. Despite a fundamental understanding of the numbers, I can still get lost in the math of figuring out dimensions… this was very consice. Nice.


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## Caliper (Mar 12, 2007)

David said:


> *Fibonacci gauge*
> 
> *1 • 1 • 2 • 3 • 5 • 8 • 13 • 21 • 34 - The Fibonacci Sequence*
> 
> ...


Thanks for this post, David.


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## Tangle (Jul 21, 2007)

David said:


> *Fibonacci gauge*
> 
> *1 • 1 • 2 • 3 • 5 • 8 • 13 • 21 • 34 - The Fibonacci Sequence*
> 
> ...


Good work David. The more we learn about design it seems the more there is to learn. I started studying art in high school at the age of fifteen and it seems i still learn more every day. I was lucky to be taught the Golden Mean by an art teacher before the days of "do your own thing".


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## dennis (Aug 3, 2006)

David said:


> *Fibonacci gauge*
> 
> *1 • 1 • 2 • 3 • 5 • 8 • 13 • 21 • 34 - The Fibonacci Sequence*
> 
> ...


great info…Thanks


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## furnitologist (May 31, 2007)

David said:


> *Fibonacci gauge*
> 
> *1 • 1 • 2 • 3 • 5 • 8 • 13 • 21 • 34 - The Fibonacci Sequence*
> 
> ...


He's Baaaaack!!!!!..................and I'm glad.

Hey David:

Like Scottb above….........I seem to get lost in the mathematics during a total design, never fully use my "pisano"...Leonardo of Pisa, but he's always there and shows up at the start.

Love the history…....thanks, and your wording of bringing it to the bench:

*Ultimately, common sense and your eye should rule over the Golden Section. The Golden Section is a tool that you bring to the bench much like a finely tuned plane, razor sharp chisel or that special dovetail saw.*

Thanks David very, very well done….........Neil


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## Karson (May 9, 2006)

David said:


> *Fibonacci gauge*
> 
> *1 • 1 • 2 • 3 • 5 • 8 • 13 • 21 • 34 - The Fibonacci Sequence*
> 
> ...


Lee:

You can go a little further back on the arm. The end of the finger to the first loint as to the second joint.

And the first - second joint to the end of the finger joint. Then that joint to the wrist.

David thanks for bringing up the wood article and showing it made.


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## bbrooks (Jan 3, 2007)

David said:


> *Fibonacci gauge*
> 
> *1 • 1 • 2 • 3 • 5 • 8 • 13 • 21 • 34 - The Fibonacci Sequence*
> 
> ...


Nice job David. All the information in a single place. A nice history lesson, as well as a great application by creating the gauge.

Have you tried it out yet on any projects? How has it worked out for you?


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## David (Jan 26, 2007)

David said:


> *Fibonacci gauge*
> 
> *1 • 1 • 2 • 3 • 5 • 8 • 13 • 21 • 34 - The Fibonacci Sequence*
> 
> ...


Thanks for all the kind comments.

This has been on my "to do list" for a while so it was very satisfing to complete the Fibonacci Gauge. I am looking forward to using it in the design process for future projects. I have a fascination for the beauty and proportion found in nature and how this concept can be found at so many levels.

I have to give credit to *Neil Lamens* at *Furnitology* for simulating my interset in furniture design. Prior to exploring his website, subsequently other online resources and books on furniture design, I looked at each project as a project and did not fully appreciate the design elements and proportion.


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## roosterscoop (Oct 12, 2006)

David said:


> *Fibonacci gauge*
> 
> *1 • 1 • 2 • 3 • 5 • 8 • 13 • 21 • 34 - The Fibonacci Sequence*
> 
> ...


Thanks David, I had read this article and set it aside, thinking of making it later. Then I tried to find it, problem was I thought I had read it in a Woodsmith magazine. Now I can go back and find the article and build it.


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## Sawdust2 (Mar 18, 2007)

David said:


> *Fibonacci gauge*
> 
> *1 • 1 • 2 • 3 • 5 • 8 • 13 • 21 • 34 - The Fibonacci Sequence*
> 
> ...


My Wednesday nite group decided to make these. We were going to end up making 3 each so I found a source to get all the screw posts for everyone for less than Wood was charging for 4 kits.
WSe had a great time making them. Only 2 were accurate.
YOu have to be very close on the holes to have it work correctly.


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## David (Jan 26, 2007)

David said:


> *Fibonacci gauge*
> 
> *1 • 1 • 2 • 3 • 5 • 8 • 13 • 21 • 34 - The Fibonacci Sequence*
> 
> ...


*Thanks everyone for the comments . . . *

*Xavier* - you are absolutely correct that the holes and alignment need to be accurate for the gauge to work correctly. You can always do the math, however, I really like the idea of the gauge and the feel of the wood in my hands. The whole concept of the divine proportion is very intriguing.

*Chris* - I do sincerely hope that Jeff Mertz from WOOD Magazine will not mind the reference and inclusion of his video. The article really struck a chord with me and this is my way of paying homage.


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## mot (May 8, 2007)

David said:


> *Fibonacci gauge*
> 
> *1 • 1 • 2 • 3 • 5 • 8 • 13 • 21 • 34 - The Fibonacci Sequence*
> 
> ...


David,

Excellent writeup. Thanks for taking the time to provide the info for this. I think I have a place on my wall to hang one. I read that article in Wood with great interest and added it as #258 on my list of things to do.

Cheers!


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## LeeJ (Jul 4, 2007)

David said:


> *Fibonacci gauge*
> 
> *1 • 1 • 2 • 3 • 5 • 8 • 13 • 21 • 34 - The Fibonacci Sequence*
> 
> ...


I failed to mention a mentor of mine, who has recently passed away. His name was Jefferson Clark, and he taught design at Drexel University in Philadelphia, PA, in addition to operating a design company.

It is largely at his doing that I became aware of and a student of proportion. As a general contractor, I was priviledged to work with Jeff for close to twenty years, and I was always amazed at his abilities. He could casually walk through a four story building, and after returning to his office, draw the building in remarkable detail, with surprising accuracy, including where the existing furniture was!

He had a way of teaching in a gentle fashion, which rather than raising the ire in someone, would inspire one to reach for a higher level of knowledge of their craft.

He and I spent many an hour researching proportions found in and around the Philadelphia area. This area is steeped in historic buildings, many still remaining form the 18th century. We visited buildings frequented by President Washington, and actually saw a bullet hole in a plaster wall, from a battle on Germantown Avenue, fired by the American army, lead by General Washinton, in the revolutionary war!

Even in his early seventies, with him carrying an oxygen tank, I would make it a point to take him on these outings, and he would insist I drive my corvette, even though he could barely get in and out of the car. I would have to push him aroung in a wheel chair, yet we had a great time. We would go to the Philadelphia Museum of Art and inspect the 18th century american furniture, for which I have an extreme amount of interest in. Their skills, attention to detail, methods of using the divine proportions to arrive at their designs, and conditions in which they worked, astounds me. I feel my abilities are childish in comparison to theirs.

Anyway, I just wanted to mention my friend Jeff, who was largely responsible for my apreciation and awareness of design. Without his guidence, my work would still be lacking in many ways.

Lee


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## MsDebbieP (Jan 4, 2007)

David said:


> *Fibonacci gauge*
> 
> *1 • 1 • 2 • 3 • 5 • 8 • 13 • 21 • 34 - The Fibonacci Sequence*
> 
> ...


sounds like a wonderful man and someone's footsteps to follow in.


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## David (Jan 26, 2007)

David said:


> *Fibonacci gauge*
> 
> *1 • 1 • 2 • 3 • 5 • 8 • 13 • 21 • 34 - The Fibonacci Sequence*
> 
> ...


Lee -

Very busy summer so a bit late responding! Your friend Jeff sounds like a wonderful man. We have had a number of visits to Viginia and D.C. - my son is fascinated with history, The Revolutionary War and The Civil War. We both enjoyed all the mystery and rich history. I appreciate you sharing this story. Next time we are in the area we will call in advance and try to arrange a short visit.


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## CorporalWilly (Jan 7, 2008)

David said:


> *Fibonacci gauge*
> 
> *1 • 1 • 2 • 3 • 5 • 8 • 13 • 21 • 34 - The Fibonacci Sequence*
> 
> ...


This one has come up on me in my educational career a few times in my retirment years. You have spiked my interest in this intriguing formula sequence and I am forced now as curiosity has killed more cats, to partake in an investigation of it. I've even seen it done in class on the board and it was very interesting back then. There simply is not enough hours in my day. Great expose' on this.


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## David (Jan 26, 2007)

David said:


> *Fibonacci gauge*
> 
> *1 • 1 • 2 • 3 • 5 • 8 • 13 • 21 • 34 - The Fibonacci Sequence*
> 
> ...


Rich -

Thanks for looking! I am fascinated with the Fibonacci Sequence and The Divine Proportion. I use this whenever I can in the shop.

David


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## Grumpy (Nov 9, 2007)

David said:


> *Fibonacci gauge*
> 
> *1 • 1 • 2 • 3 • 5 • 8 • 13 • 21 • 34 - The Fibonacci Sequence*
> 
> ...


David, I just found your blog through Karsons blog http://lumberjocks.com/jocks/Karson/blog/4353. a most interesting appreciation of proportion. Thanks for sharing.


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## Dusty56 (Apr 20, 2008)

David said:


> *Fibonacci gauge*
> 
> *1 • 1 • 2 • 3 • 5 • 8 • 13 • 21 • 34 - The Fibonacci Sequence*
> 
> ...


Again you have brought me more useful knowledge…thank you for all of the helpful links as well : )


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## David (Jan 26, 2007)

David said:


> *Fibonacci gauge*
> 
> *1 • 1 • 2 • 3 • 5 • 8 • 13 • 21 • 34 - The Fibonacci Sequence*
> 
> ...


Grumpy -

Well, I am responding very late to your very kind comments. Thank you!

Dusty56 -

Thank you!

David


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## a1Jim (Aug 9, 2008)

David said:


> *Fibonacci gauge*
> 
> *1 • 1 • 2 • 3 • 5 • 8 • 13 • 21 • 34 - The Fibonacci Sequence*
> 
> ...


I'm late responding also I would like to know what you think of it once you've used it.


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## depictureboy (Jun 5, 2008)

David said:


> *Fibonacci gauge*
> 
> *1 • 1 • 2 • 3 • 5 • 8 • 13 • 21 • 34 - The Fibonacci Sequence*
> 
> ...


Thats the thing I wanted the dude to build out in sketchup…since I do all my designing in sketchup now, It would be nice to have that flexibility. I just couldnt get my explanation good enough for him to understand what I was looking for.


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## lwllms (Jun 1, 2009)

David said:


> *Fibonacci gauge*
> 
> *1 • 1 • 2 • 3 • 5 • 8 • 13 • 21 • 34 - The Fibonacci Sequence*
> 
> ...


It's interesting but also a lot of fantasy. Let's see, "Leonardo of Pisa, known as Fibonacci,...was one of the first people to introduce the Hindu-Arabic number system into Europe…" Yet "The Golden Mean and The Divine Proportion was discovered by the Greek mathematician Pythagoras. Later, an Athenian architect using the Golden Section in building design came up with Phi, the number 1.618." Ahhh, Greece is part of Europe and Pythagoras lived about 500 BC and Fibonacci lived more than 1500 years later. So the Greeks worked out the Golden Ratio in something like Roman Numerals? I'd like to see those calculations! BTW, it wasn't an Athenian architect who assigned the Golden Ratio to the Greek letter phi or Φ, it was American mathematician, Mark Barr, around 1909. It was Mark Barr's single contribution to math, lets not take that from him. In fact if you actually search, you'll find the concept of using the Golden Ratio or the Fibonacci numbers for architectural or furniture design is a wholly 20th Century idea.

I have searched. I've read the translations of Vitruvius and Palladio. I can't find any mention of the Golden Ratio there. I've studied the Classic Orders and can only find whole number ratios, not a single 1:618 to be found. When I research proportion and design I find things like the sector, the forerunner of the slide rule. It's an amazing tool that goes back to the 1600's and was called "the proportional rule" in Europe.

More power to you if you want to try to construct things around mystique and a difficult to use single ratio. It's your choice. I prefer real history and design tools that evolved over centuries. It's pretty cool stuff. Here's a sector we've been studying and working with in our shop-it's about a hundred years older than the idea of using the golden ratio for furniture design:


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## wannadoitall (Sep 30, 2010)

David said:


> *Fibonacci gauge*
> 
> *1 • 1 • 2 • 3 • 5 • 8 • 13 • 21 • 34 - The Fibonacci Sequence*
> 
> ...


David -

Great video and article contribution! I really enjoyed it, and look forward to looking more into it soon, as I have always been interested in Divine Proportion. Interesting concept, and you presented in such an easy way to grasp-

Thank you! (and I now have another thing on my to-do list - that gauge!)


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## bigike (May 25, 2009)

David said:


> *Fibonacci gauge*
> 
> *1 • 1 • 2 • 3 • 5 • 8 • 13 • 21 • 34 - The Fibonacci Sequence*
> 
> ...


For some reason I can't get into this but I do want to make one.


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## jack1 (May 17, 2007)

David said:


> *Fibonacci gauge*
> 
> *1 • 1 • 2 • 3 • 5 • 8 • 13 • 21 • 34 - The Fibonacci Sequence*
> 
> ...


Just ran into this on this month's newsletter. I like your explanation and jig. I teach a few math courses at a tech school (Heald) and with your permission, would like to use it when we touch on this.
Thanks again for your work.

Jack


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## Shoni (Jul 20, 2014)

David said:


> *Fibonacci gauge*
> 
> *1 • 1 • 2 • 3 • 5 • 8 • 13 • 21 • 34 - The Fibonacci Sequence*
> 
> ...


Very nice article and informative too. Thanks for sharing with us. Your designs are very awesome.

Thanks


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## WayneC (Mar 8, 2007)

David said:


> *Fibonacci gauge*
> 
> *1 • 1 • 2 • 3 • 5 • 8 • 13 • 21 • 34 - The Fibonacci Sequence*
> 
> ...


This topic came up again 12 years or so later. Hope you're doing well.


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## jack1 (May 17, 2007)

David said:


> *Fibonacci gauge*
> 
> *1 • 1 • 2 • 3 • 5 • 8 • 13 • 21 • 34 - The Fibonacci Sequence*
> 
> ...


An easy way to think about the Fibonacci sequence is the think about a bag of chips turned upside down. 
The small stuff is on top and the chips get bigger as you approach the bottom.


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