Here is the difference!

 

The squaw of the hippopotamus is only equal to the squaw of the other two hides if its a right triangle! On can continually bisect the length of the side either with a tape or use the tape as a compass. from a straight line (180 degrees) to less than one degree is 8 times.

 

Certainly true, REO. Kelly actually was sort of on that path but tried to split into many segments in a single step instead of recursively solving the problem with pure bisection (cutting in half). I would generally rather calculate directly rather than trying to maintain accuracy across measuring and marking 8 different lines. Still, there are good times for each technique and it's just as well to know them all.

 

http://www.shopnotes.com/files/issues/114/framing-square.pdf

 

I lay them out using my CAD program, which is sort of cheating on the math but the accuracy is extremely good.

 

A²+B²=C²

http://www.mathsisfun.com/algebra/trig-solving-triangles.html

 

Pi r squared
!https://s

- waho6o9

Pi r squared
- waho6o9

Nope…pie are round. Cake are square.

- hotbyte

My thoughts exactly }G{

 

This is cake, and highly accurate, with a rudimentary divider or compass (or beam with holes), and straight edge (not a ruler, no measurement marks required). Zero math involved beyond basic counting…

But I'm not tellin how… ;^)

 

Rly?

I can do it with a cinder block and three chewed pieces of hubba bubba bubble gum.

 

The original post must not have been clear:

1) The only tool available to find a specific angle was a ruler, since all protractors available were too small and allowed room for significant error, when the lines were projected even a couple feet out;

2) Like others, I don't have a calculator or smartphone (when I retired, I retired) with which to calculate trig or other advanced math processes;

3) Even if I had a calculator, or calculator function by which I could find the lengths of legs of an angle, I, like most others here and other woodworking forums, don't have the math background, so wouldn't know what to do with those functions; and,

. . . .

 

To create an angle using a complex formula using only a calculator and a ruler (or equiv) would, I presume, require I draw a line, measure a calculated distance along that line, then measure over to another line, which, also, would have to be a specific length, and running back to the initial line starting point of the first line.

No?

 

I can name that tune in three notes…......

Rly?

I can do it with a cinder block and three chewed pieces of hubba bubba bubble gum.

- Buckethead

 

Buckethead, thanks. Many forget they no more know the terms of other sciences we may work in than we do theirs. Without that, all the references to it mean nothing.

 

Good one. Thanks Rick.

http://www.shopnotes.com/files/issues/114/framing-square.pdf

- Rick M.

 

These will probably help!!!!!

http://www.wixey.com/digitalprotractor/index.html

 

Does this make any more sense? As noted earlier, running both digital and analog protractors on the results laid out on a large sheet indicates this does work. That said, I believe I understand the points sought to be made, but I believe points made here [and, perhaps, not well described earlier] are valid.


- Not surprisingly, since this is a woodworking forum, this was about solving a problem in woodworking. That should have been a qualifying statement up front. That [now] said, in woodwork, 1/128" (.008") or less tolerances are better than pretty damn good.

- Using an L-square, draw lines following both legs. You can extend the lines a little or a lot, the lines will remain a ninety degree angle. The more accurate the intersection point and the lines, the more accurate the end results.

- Measure out the same distance on both legs, near the end of the angle you require, then draw a line between the two points. Dividing this line by ninety will give a mark for EACH degree of that ninety degree angle. The spaces between each WILL be exactly the same, regardless how far the lines were projected (see note below).

Because lines can be sloppier than they appear, it's best to move as near the open end of the angle as possible for the forty-five degree line. The gap between each line (degree mark) will remain, exactly, the same as the others on that line (for these purposes, it would be impossible to have "15.9" degree reading where the twenty degree mark should be), even if the line is moved farther from or closer to the initial intersection.

- For convenience, and depending on the size of the angle being drawn, increments of 1/16", 1/8", 1/4", 1/2", 5mm, 10mm and so on can be used, but using a specific fraction or mm measurement to represent each degree requires measuring up from the intersection of the two legs a specific distance for a given increment.

- The importance of the foregoing approach is in that the line is ran at an angle, USING THE TOOLS AVAILABLE (e.g., an L square and a ruler, tape or yardstick).

_

The squaw of the hippopotamus is only equal to the squaw of the other two hides if its a right triangle! On can continually bisect the length of the side either with a tape or use the tape as a compass. from a straight line (180 degrees) to less than one degree is 8 times.

- REO

Certainly true, REO. Kelly actually was sort of on that path but tried to split into many segments in a single step instead of recursively solving the problem with pure bisection (cutting in half). I would generally rather calculate directly rather than trying to maintain accuracy across measuring and marking 8 different lines. Still, there are good times for each technique and it s just as well to know them all.

- altendky

 

Does this make any more sense? As noted earlier, running both digital and analog protractors on the results laid out on a large sheet indicates this does work. That said, I believe I understand the points sought to be made, but I believe points made here [and, perhaps, not well described earlier] are valid.

- Kelly

I'm sorry, but your method does not work! (no matter how much you want it to)
I did it your way on the computer and printed you the results. (did you not look at the pictures?)

"The gap between each line (degree mark) will remain, exactly, the same as the others on that line (for these purposes, it would be impossible to have "15.9" degree reading where the twenty degree mark should be), even if the line is moved farther from or closer to the initial intersection."

Using your method trying to find a 20 degree angle ends up with a 15.9 degree angle. (4.1 degrees off)
I can't demonstrate it any better. It's done on the computer, no sloppy lines.

If someone cares to correct me, please do.
(Trust me, there's a line of people would love to prove me wrong)

The segments have to be laid on on the radius line of the circumference circle.
Your method is only correct for a 45 degree angle!

I'm not trying to beat you up, but it just doesn't work.

 

Kelly, either you're leaving out some steps, explaining it unclearly, or your method is simply incorrect.

Mostly in large-scale woodwork (and in small scale for that matter), you don't need to worry about angles, but rise and run, a simple ratio.

It's easy as pie to check the accuracy of you 20 degrees, by the way. Use your method and then measure and mark a point 27+1/2 out and 10 up. If your 20 degrees is accurate, your line from the point of origin will coincide exactly with the line drawn from the same point of origin through the point there. 20 degrees coincides with a 1:2.75 rise:run.

 

bobro, this all started from setting up to cut angles (two 10 degree cuts) for a musical instrument. Rise and run?

 

Thanks, Roger, but they look much like one of my two (a twelve inch and my Bosch).

These will probably help!!!!!

http://www.wixey.com/digitalprotractor/index.html

- RogerM

 

SOH CAH TOA is still the way to go.

 

bobro, this all started from setting up to cut angles (two 10 degree cuts) for a musical instrument. Rise and run?

- Kelly

Read carefully: I said "rise and run, a simple ratio".

It's the ratio that's important, not whether or not you're using stairwell or roofer terminology. The same problems arise with fretting string instruments, where logarithmic (like for equal temperament) measurements and ratios don't coincide but it's divisions of string length, simple measurments in ratios that give very accurate approximations to logarithmic measurements as well, that are usually used to place frets around the world, regardless of whether it's equal temperament or not.

If you need a 10 degree angle and your protractor's too small, just measure out 56.7 cm and up 10 cm and scribe through that. Very accurate- your method is not (unless you're not explaining it to us).

 

I just went out in the shop to prove everyone wrong.

It didn't go well.

Sorry for being frustrating, but when done, I'll "own" the relative processes.

 

You're a honest man Kelly.

 

Think of it this way, You draw your line and divide it into 90 segments. Then when you split the angle in half to get 45 you have 2 right angles on each side of your 45 degree line. Now when you mark a different angle line you no longer have the right angles. Your Division line becomes skewed and that is what throws of the angle so that you can't use the same division segments. (if that makes sense)

Don't feel bad. It took me a long time to figure out why this didn't work.
I figured on a 24" wide pc measure over 24" (off of 90) and it would give me a perfect 45
Well then why not cut that in half (12" and 12") to get a 22 1/2? Didn't work.
I think it's kind of the same thing, the legs on the two sides aren't 90 deg as the angle changes off the middle.

(You look pretty stupid trying to line up to countertops, on the job, and end up with a big gap in the middle
Just sayin)

It's all good,