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First Friday Math Quiz

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Woodman

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Here it is! September 2022 First Friday Math Quiz.  I'm a little early as come Thursday I'll be away from the laptop, likely until next week.

 

I have a slat 5/8" wide and 24" long.  I want to cut the 24" into a number of pieces and glue these pieces together to make one square piece, maximizing the available 24".

 

Disregarding blade width, as there is more than 24" there, what length will I cut my pieces to maximize the available wood?

 

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37 minutes ago, lew said:

5/8” slat was cut into 5/8” lengths

I know what you are doing. Steering me into staining half another shade, and gluing all 36 into a checkerboard pattern. 
 

Tell ya what. I’ll do that with other stock. Something 1.25” or so wide, with a straight tight grain. Instead of stain, I’ll turn the B pieces 90°. 

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5 hours ago, Gerald said:

So how can you get the formula without thickness??

Lew's solution called for 35 cuts to make 36 pieces 5/8" x 5/8".  Whew! :Hot:

 

After wrestling with notepaper for many minutes, I was no closer to an answer than a horse to pizza. Bending Lew's Sketchup, I see six pieces 3.75" [.625 x 6] long will form a square. And use ≤ 24" of linear plank .625" wide.

 

I'll have nice single slats, saved often from near the pith. They are sometimes the most amazing, the tightest growth. 30-40 RPI or higher. The thickness varies. The width varies. Rather than continue to use them as perimeter, I'm wanting to make base while the sun shines.

 

This is an impossible formula.  Bet M.I.T. prof bite lip off coffee cup when posed question.

 

Here's a start:  The sides are of equal length,  A and B.  Width of slat = W   Length of slat = X

A = B

W = .625

X ≤ 24

 

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8 hours ago, Gerald said:

how can you get the formula without thickness??

Sorry, Gerald, I forgot to answer your question :blink:

 

This is a two-dimension plane, creating as large a square as possible from a board of X length and W width.

 

So I could have a piece of stock 5/16" square and 52" long. What equal lengths do I cut my 52" to create as large a square as possible, after gluing the pieces together.

 

When dissecting an old beam, I end up with a lot of odd-shaped strips, slats, boards. Some of the most amazing grain, just not a whole lot of it. Keeping apples with apples, I want to begin making "single origin tray base blanks" with these single slats. At least cut up a dozen for future projects.

 

I've got two big projects in the 'works', half a dozen small projects cut and ready for fitting / gluing / finishing, one really big project in infancy (a portable cabana with door, made to assemble in a clever manner, pinned with 8-12 ebony violin pegs), and now want to cut up a few of these scrap strips for later assembly into squares.  The squares are for undetermined future projects.

 

Waste not, want not. I spent seven days and 20 hours taking the beam apart (three hours acquiring and moving the beam). From that latest beam I still have two choice 5 x 5 x 20 now awaiting a 12" sliding miter saw, and one 2.5 x 2.5 x 58 or so for a sun shutter [Panel No. 4]. The rest became my 10.8 pound camp shower enclosure frame, an 18 gallon Rubbermaid full of winter burning pleasure, and a lot of small milled wood for small handcrafted projects.

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Maybe I'm thinking of this a different way, but I don't think the pieces need to be cut into squares, strips would work?  But this confirms Lew's and Woodman's result, without Sketchup.

 

As such, by induction,

 

number of strips      width   height

     1                         5/8      24     (not very square)

     2                         1 1/4   12             "

     3                         1 7/8    8

     4                         2 1/2    6

     5                         3 1/8    4.8

     6                         3 3/4    4       <--- we have a winner, 6 strips @ 3 3/4 make a square

     7                         4 3/8    3.4

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0.625*24=15 sq inches of material before cutting.

 

square root of 15 = 3.873, just under 3-7/8"

so ideally, you'd have a square of just under 3-7/8"

 

3.875/0.625=6.2 pieces...so that's 5 measured cuts, each taking up 1/8" of kerf, so a gross use of 3.875+.125=4.00

 

so 6 pieces cut to 3-7/8", each 0.625 wide, 6*0.625=3.75"....so i'd do a square of 3-3/4" and have a pile of sawdust as scrap.

 

what do i win?

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16 hours ago, Woodman said:

what length will I cut my pieces to maximize the available wood?

 

1 hour ago, kmealy said:

I don't think the pieces need to be cut into squares, strips would work?

--> Exactly. Strips is how it is cut. I did the spreadsheet thing a few times, even substituting a prime audiobook last night for pad and pen.

 

DAB, methinks you figured it out. As with all great ideas, the solution is 9-year-old simple. Most elegant.

 

I'm throwing kerf out of the equation. May or may not round up slat length, but will allow for final trimming, get the ends nice and flush after glue-up.

 

1 hour ago, DAB said:

what do i win?

 

I'll experiment with the Method-DAB next week and report back (headed offline for a few days). Kudos is the preferred reward. But . . . A small block of longleaf pine also comes to mind [Small USPS Flat Rate Box]. Or a Medium USPS Flat Rate Box filled with whatever is on the shelf? Reclaimed longleaf pine, possibly reclaimed eastern white pine, something like that. Craft-worthy 'scrap'. 

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2 hours ago, DAB said:

0.625*24=15 sq inches of material before cutting.

 

square root of 15 = 3.873, just under 3-7/8"

so ideally, you'd have a square of just under 3-7/8"

 

what do i win?

correcting a math error:

 

(for some reason, couldn't edit it)

 

24" / 3.875" = 6.19 pieces

 

6 pieces * 0.625" wide = 3.75"

 

so cut each piece to 3.75" long, stack 6 pieces (each 0.625 wide) together to get a square of 6 * 0.625 = 3.75 wide by 3.75 long.  a square using the most wood.

 

 

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2 minutes ago, DAB said:

correcting a math error:

 

(for some reason, couldn't edit it)

 

24" / 3.875" = 6.19 pieces

 

6 pieces * 0.625" wide = 3.75"

 

so cut each piece to 3.75" long, stack 6 pieces (each 0.625 wide) together to get a square of 6 * 0.625 = 3.75 wide by 3.75 long.  a square using the most wood.

 

 

  uhhh-

 

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