This is doing my head in ...
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Imagine this: you have a piece of square stock wood: 4x4 say. You want to cut it so that the square profile becomes an octagon. So you tilt your table saw to 45o and move your fence across so that a single pass will cut off a triangular corner. You can then pass each side against the fence and voila! (Or possibly violin.) The question is "how far should the fence be from the cutting edge of the blade?". I did this this morning: I measured the stock, subtracted a bit under 4 cm, set my fence and cut a test piece. It was spot on, each of the eight edges was the same length (with marginal variation because the stock wasn't exactly square but close enough) and I moved on. Except I've been sitting here trying to work out the geometry, and just how I got my number from the original side length. And I have no idea how the heck I did it, because I didn't use geometry, I didn't use a calculator, and it's the first time I've done this. I just went "oh, it's 9.3cm, so I want 3.8cm edges, that's 6.5cm from the blade edge". And I was right. But it's doing my head in trying to work out how I knew what the numbers were ... and why I was right first time ...
"I have no idea what I did, but I'm taking full credit for it." - ThisOldTony "Common sense is so rare these days, it should be classified as a super power" - Random T-shirt AntiTwitter: @DalekDave is now a follower!
"I have no idea what I did, but I'm taking full credit for it." - ThisOldTony
"Common sense is so rare these days, it should be classified as a super power" - Random T-shirt -
Imagine this: you have a piece of square stock wood: 4x4 say. You want to cut it so that the square profile becomes an octagon. So you tilt your table saw to 45o and move your fence across so that a single pass will cut off a triangular corner. You can then pass each side against the fence and voila! (Or possibly violin.) The question is "how far should the fence be from the cutting edge of the blade?". I did this this morning: I measured the stock, subtracted a bit under 4 cm, set my fence and cut a test piece. It was spot on, each of the eight edges was the same length (with marginal variation because the stock wasn't exactly square but close enough) and I moved on. Except I've been sitting here trying to work out the geometry, and just how I got my number from the original side length. And I have no idea how the heck I did it, because I didn't use geometry, I didn't use a calculator, and it's the first time I've done this. I just went "oh, it's 9.3cm, so I want 3.8cm edges, that's 6.5cm from the blade edge". And I was right. But it's doing my head in trying to work out how I knew what the numbers were ... and why I was right first time ...
"I have no idea what I did, but I'm taking full credit for it." - ThisOldTony "Common sense is so rare these days, it should be classified as a super power" - Random T-shirt AntiTwitter: @DalekDave is now a follower!
Cos you're inspirational and clever :-D
Life should not be a journey to the grave with the intention of arriving safely in a pretty and well-preserved body, but rather to skid in broadside in a cloud of smoke, thoroughly used up, totally worn out, and loudly proclaiming “Wow! What a Ride!" - Hunter S Thompson - RIP
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Cos you're inspirational and clever :-D
Life should not be a journey to the grave with the intention of arriving safely in a pretty and well-preserved body, but rather to skid in broadside in a cloud of smoke, thoroughly used up, totally worn out, and loudly proclaiming “Wow! What a Ride!" - Hunter S Thompson - RIP
Says a man who has never met me ... :laugh: My brain is screaming "0.707" at me, which is half root two, so it's probably bloody obvious Pythagoras, but I'm damned if I can see it. Or do square roots in my head. :sigh: I suspect this is going to keep me awake tonight.
"I have no idea what I did, but I'm taking full credit for it." - ThisOldTony "Common sense is so rare these days, it should be classified as a super power" - Random T-shirt AntiTwitter: @DalekDave is now a follower!
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Says a man who has never met me ... :laugh: My brain is screaming "0.707" at me, which is half root two, so it's probably bloody obvious Pythagoras, but I'm damned if I can see it. Or do square roots in my head. :sigh: I suspect this is going to keep me awake tonight.
"I have no idea what I did, but I'm taking full credit for it." - ThisOldTony "Common sense is so rare these days, it should be classified as a super power" - Random T-shirt AntiTwitter: @DalekDave is now a follower!
I had a professor many moons ago, when he couldn't readily explain a particular step of a mathematical proof, would say with a smirk, "it's IOTTMCO!" (Intuitively Obvious To The Most Casual Observer), and he'd move on.
"the debugger doesn't tell me anything because this code compiles just fine" - random QA comment "Facebook is where you tell lies to your friends. Twitter is where you tell the truth to strangers." - chriselst "I don't drink any more... then again, I don't drink any less." - Mike Mullikins uncle
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Imagine this: you have a piece of square stock wood: 4x4 say. You want to cut it so that the square profile becomes an octagon. So you tilt your table saw to 45o and move your fence across so that a single pass will cut off a triangular corner. You can then pass each side against the fence and voila! (Or possibly violin.) The question is "how far should the fence be from the cutting edge of the blade?". I did this this morning: I measured the stock, subtracted a bit under 4 cm, set my fence and cut a test piece. It was spot on, each of the eight edges was the same length (with marginal variation because the stock wasn't exactly square but close enough) and I moved on. Except I've been sitting here trying to work out the geometry, and just how I got my number from the original side length. And I have no idea how the heck I did it, because I didn't use geometry, I didn't use a calculator, and it's the first time I've done this. I just went "oh, it's 9.3cm, so I want 3.8cm edges, that's 6.5cm from the blade edge". And I was right. But it's doing my head in trying to work out how I knew what the numbers were ... and why I was right first time ...
"I have no idea what I did, but I'm taking full credit for it." - ThisOldTony "Common sense is so rare these days, it should be classified as a super power" - Random T-shirt AntiTwitter: @DalekDave is now a follower!
Draw as square. Now draw a 45 degree diagonal across a corner. The lengths of the triangle sides are 1, 1, sqrt(2). That hypotenuse has to be the same length as the edge of the square timber that does not get sawn off. So, in terms of the corner you saw off, the length of a given side is 2+sqrt(2) units. That means for a 4" square timber, your diagonal cuts need to be made approximately 1.17" from the edge. This gives a side of your octagon of about 1.65 inches. e.g 1.17 + 1.65 + 1.17 = 3.99
Keep Calm and Carry On
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Imagine this: you have a piece of square stock wood: 4x4 say. You want to cut it so that the square profile becomes an octagon. So you tilt your table saw to 45o and move your fence across so that a single pass will cut off a triangular corner. You can then pass each side against the fence and voila! (Or possibly violin.) The question is "how far should the fence be from the cutting edge of the blade?". I did this this morning: I measured the stock, subtracted a bit under 4 cm, set my fence and cut a test piece. It was spot on, each of the eight edges was the same length (with marginal variation because the stock wasn't exactly square but close enough) and I moved on. Except I've been sitting here trying to work out the geometry, and just how I got my number from the original side length. And I have no idea how the heck I did it, because I didn't use geometry, I didn't use a calculator, and it's the first time I've done this. I just went "oh, it's 9.3cm, so I want 3.8cm edges, that's 6.5cm from the blade edge". And I was right. But it's doing my head in trying to work out how I knew what the numbers were ... and why I was right first time ...
"I have no idea what I did, but I'm taking full credit for it." - ThisOldTony "Common sense is so rare these days, it should be classified as a super power" - Random T-shirt AntiTwitter: @DalekDave is now a follower!
This how I visualised it, draw your 4cm square, then draw another 4cm square directly over the top of the first but at 45 degrees rotation. From here you can see that the dimension you need is the diagonal of the 4cm square minus 4cm side all divided by 2, which is (sqrt(32)-4)/2 =. 828cm
