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#### tvincent

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Hi everyone; Gained a little more knowledge reading the FAQ. Now I would like to post my drawing along with the calculations. I made this to find an accurate center point of a 3-point base mounting diagram. I have recently generated this to accommodate a Large Router base mounting method for a table Router using a 9" x 12" x 3/8" insert.

Attached below you will find my drawing ... hopefully if I do everything correctly it will appear. If anybody has any questions, please post them and I will try to answer all of them. I classified the drawing as Engineering Notes to share, not as a tutorial.

Thomas

#### 4DThinker

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Using a compass set to the radius of the router plate, two arcs drawn from two points on the edge anywhere close to 120 degree apart will intersect at the center of the plate.
4D

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#### The Hobbyist

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It takes a lazy man to find the easiest way to do anything.

Joe

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My brain hurts.

Joe

#### 4DThinker

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I usually don't bother with the 2 arc method as any circle I draw in my CNC software has that center point as a snap to active spot. Gave an assignment to my college furniture design students to design and make a stool with 3 legs (or less). With a few minutes I heard a student ask for help on how to draw an equilateral triangle. The 2-arc method worked there as well.
Of course if you don't have a compass then a stick of wood with two holes near the ends can serve that purpose. Of course you needed a way to make the holes for a pencil and a nail or thumb tack. Want a good challenge then tell me the maximum size of an equilateral triangle you can cut from a perfect square of 10" on each side? What would its area be? Lets use a laser cutter that magically leaves no kerf loss.

#### The Hobbyist

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I am just a high school graduate with a 3.0 GPA because I didn't "apply myself" according to Catholic School Sister Scary Tarantula. Sitting at my recliner without a computer anywhere near me, but a pocket calculator on my phone, I could give you an answer. We would start with the base of 5 inches wide, which would equal three in a three, four, five triangle, so if five equals three then 1.66666 equals one therefore 1.66666 x 4 = 6.664 would be the maximum height And the diagonal of those two would equal the five, or 8.33. That would make an area of 6.664 x 5 or just a hair under 33.32 square inches. Since the triangle is 2/3 of the height of the box, yet only occupies 1/3 of the box area, the mirrored triangles would equal the second 1/3, and the rectangle above the tip would equal the third 1/3 + the remaining .04% 100 - (33.32 x 3). How did I do?

Joe

#### 4DThinker

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Not bad, but not quite right. A triangle with 10 inch sides in a 10 inch square isn't the biggest triangle you can cut from that square.

#### The Hobbyist

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Not bad, but not quite right. A triangle with 10 inch sides in a 10 inch square isn't the biggest triangle you can cut from that square.

Wait a minute. you said equilateral triangle... NOW I am checking on my computer ...

Okay! You got me!

Joe

#### The Hobbyist

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My 'puter says 10.353" equilateral. Good late night challenge for a guy who doesn't even know what day it is! I really need to get onto a regular sleep schedule!

Joe

#### The Hobbyist

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Is this what you were hoping I would find? I can draw it, but I have no CLUE how to calculate it.

Joe

#### John Smith_

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It takes a lazy man to find the easiest way to do anything.
Joe
I'm not necessarily lazy, but, my math skils are horrible. When it comes to making router base plates, I work out the fastening holes first. Then, once the screw holes are drilled and countersunk, I put the plate on the router and slowly (very slowly) raise an engraving bit upwards (with the router running) to mark the center. Then, take the plate to the drill press and make the desired size hole. And I agree, all those numbers and figureings make my head hurt too.

#### 4DThinker

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Is this what you were hoping I would find? I can draw it, but I have no CLUE how to calculate it.

Joe

View attachment 404468
That's the obvious way. There is another way to make an equilateral triangle from a square and both will have the same area. Some cuts are required.
4D

#### The Hobbyist

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That's the obvious way. There is another way to make an equilateral triangle from a square and both will have the same area. Some cuts are required.
4D

Well ... show me! I am always open to learning something new!

Joe

#### 4DThinker

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I learned it originally from a book call "Mathematical Puzzles and Diversions". Had one student make a set of 4 small tables that could be re-arranged into a square or a triangle using this trick.

#### calabrese55

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OUCH my head is EXPLODING................ I am with The Hobbist except I got through high school with bribery and a few compromising pictures. One or two pictures are worth a few good grades and the negatives are great for future extortion I mean reference
calabrese55

#### 4DThinker

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I did a simpler re-config of a 49" x 25" butcherblock countertop to make it into the largest square possible after the kerf of the cuts was accounted for.
Comes in handy to know a few drafting and geometry tricks if you teach furniture design to college kids. Some associate math also helps.
Used the square as the top for the bench I made for my new Taig CNC mini mill.

4D

#### jw2170

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I follow John on his method.....

4DThinker
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