Metric system dumbs us down.

[dlymn]

Originally Posted by StuM

If you take "metric" to be a synonym for "International System of Units (SI)" ( https://en.wikipedia.org/wiki/Metric_system )
then "technically" is superfluous. The Watt is by definition a metric unit.

As purists, we should all be wondering how many horsepower our solar panels put out...[/QUOTE]

According to a few electric propulsion advocates around here, the answer is "at least three times as many as a nominally equivalent diesel engine". [/QUOTE]

and the American dollar is part of a decimal system. Perhaps America could go back to pounds shillings and pence, halfpenny and farthing and still keep on minting the farthing

[Benz]

Originally Posted by StuM

Reminds me of the recipe for rabbit stew which begins with "first catch your rabbit"

How do you determine the perpendicular with just a ruler?

My ruler is metric, it doesn't have 1/8ths marked

And any line between the 0° and 45° lines will automatically cross a 22.5° line at its mid-point. You don't have to "make sure" of anything. In fact that 22.5° line is totally superfluous at this stage.

That doesn't actually work. You are effectively dividing 45° into 1/8ths, so it's not 5°, it's 5.625°.

Draw any line between the two lines at 45° which measures an exact multiple of eight, mark of 1/8ths of the lengths of that line and draw lines from the centre through those marks will give you the same thing. But as I said, you won't get exactly 5° between any of the lines.

If you do that, your chords will not meet the 45° etc line, you will have to keep"fudging it" to allow for that extra 0.625° in each chord.

Ah! now I see why you made that 22.5° line. You can fudge you markings 8 times instead of just 4.

So you are not "dividing a circle into degrees", you are "dividing it into divisions of approximately 5° degrees and fudging the gaps every 45° to make it roughly fit".

I must admit, when you said a "ruler", I was thinking of "a straight edge" as used in geometry (i.e. without having to accurately read numbers on a scale).

Whenever I try to interleave answers among the quotes, disaster ensues, so I'll answer all below.
You can measure a perpendicular with a ruler if the base is cut square. Do they cut metric rulers any which way? I wouldn't be surprised. But any decent inch ruler will have the ends squared to the long sides.
Which brings me up to suggesting that you should ask Santa for a proper ruler. Also, if I had meant merely a straightedge, I would have said so.
When preparing a ghetto compass rose by the method I described, a variation of six hundred and twenty-five one millionths every five degrees won't really make much odds: the width of the pencil mark puts more error in than that! Just remember to always mark to the left of the ruler if you're concerned.

But no one has yet explained when, if ever, rads are used. It seems there are four rads per circle, but a rad is not a quarter circle, so there's two small remainders, or one medium-sized remainder if you add the two. In what alternate fairy universe is this useful? How many rads does a watch's second hand sweep per second? point-something? ugh. It's positively brutish.

[StuM]

You can measure a perpendicular with a ruler if the base is cut square. Do they cut metric rulers any which way?

Originally Posted by Benz

a variation of six hundred and twenty-five one millionths every five degrees won't really make much odds:

That's 625 one thousands.

If you step distances off around 180 degrees as proposed, you will overstep the 45° <-> 225° line by over 5 degrees and overstep the 0° <-> 180° line by over 11 degrees.

[StuM]

Originally Posted by Benz

But no one has yet explained when, if ever, rads are used.

They are used all the time in mathematics and physics.

This will explain why: https://en.wikipedia.org/wiki/Radian

Even Microsoft Excel assumes than angles are in Radians because the calculations are much simpler and quicker.
"The SIN function syntax has the following arguments (argument: A value that provides information to an action, an event, a method, a property, a function, or a procedure.):
Number Required. The angle in radians for which you want the sine.
Remark
If your argument is in degrees, multiply it by PI()/180 or use the RADIANS function to convert it to radians."

[Jason Flare]

Guys guys!

3 4 5 6 8 10 The right triangle thing.

[dlymn]

perpendicular with a ruler. Hang it through the hole or hold it with thumb and forefinger. It hangs fairly vertical and in many cases that's also perpendicular. OK maybe not on a boat.

[Jason Flare]

Originally Posted by StuM

They are used all the time in mathematics and physics.

This will explain why: https://en.wikipedia.org/wiki/Radian
[/I]

Interesting reading, actually.

I built a house once with multiple angles and rooflines and an engineer came by as I was framing it and said, "You must really know your trigonometry."

I said, "I know nothing about trigonometry. I know what it's supposed to look like when it's done. The directions are around here somewhere."

[StuM]

Originally Posted by Jason Flare

Guys guys!

3 4 5 6 8 10 The right triangle thing.

But then you need a piece of knotted string as well as the ruler

[TeddyDiver]

Originally Posted by Benz

Whenever I try to interleave answers among the quotes, disaster ensues, so I'll answer all below.
You can measure a perpendicular with a ruler if the base is cut square. Do they cut metric rulers any which way? I wouldn't be surprised. But any decent inch ruler will have the ends squared to the long sides.
Which brings me up to suggesting that you should ask Santa for a proper ruler. Also, if I had meant merely a straightedge, I would have said so.
When preparing a ghetto compass rose by the method I described, a variation of six hundred and twenty-five one millionths every five degrees won't really make much odds: the width of the pencil mark puts more error in than that! Just remember to always mark to the left of the ruler if you're concerned.

But no one has yet explained when, if ever, rads are used. It seems there are four rads per circle, but a rad is not a quarter circle, so there's two small remainders, or one medium-sized remainder if you add the two. In what alternate fairy universe is this useful? How many rads does a watch's second hand sweep per second? point-something? ugh. It's positively brutish.

StuM is right. A ruler no matter how square the ends are is not a right angle. Besides if you want to devide angles the right method is to use a compass.

BR Teddy

[StuM]

Originally Posted by dlymn

perpendicular with a ruler. Hang it through the hole or hold it with thumb and forefinger. It hangs fairly vertical and in many cases that's also perpendicular. OK maybe not on a boat.

Vertical if only perpendicular if the first line is horizontal and you are working on a vertical sheet of paper.

So how do you ensure that the first line is horizontal and that the paper is vertical? This is getting more and more bizarre

[Benz]

Originally Posted by StuM

That's 625 one thousands.

If you step distances off around 180 degrees as proposed, you will overstep the 45° <-> 225° line by over 5 degrees and overstep the 0° <-> 180° line by over 11 degrees.

Especially of you use that ruler in picture! What kind of dumbbell buys a ruler with round ends? But if you're unsure about the perpendicularity of your lines, you can measure from either end of the horizontal to the tip of the vertical to get it right.

If you're concerned about the extra [B]thousandths[B], you can have a check every 22 1/2 degrees, provided you didn't erase that line! But the point of my question has been missed. Can one draw rads by using simple tools and math that does not require a calculator? A ghetto compass rose drawn as a stopgap until a plotting sheet can be found need not be more accurate than a pencil line can draw. But perhaps that's where the beauty of Imperial shines: where hair-splitting accuracy is not needed, fudging a little still gets you home. The human factor, in celestial navigation, rules out pinpointing one's position to anything finer than a few hundred yards. But the navigator understands that and adjusts his expectations accordingly. The nautical mile is not exactly 6000 feet, but for all practical purposes--not theoretical--assuming it is 6000 feet will suit the purposes of the navigator.

[Benz]

Originally Posted by StuM

They are used all the time in mathematics and physics.

This will explain why: https://en.wikipedia.org/wiki/Radian

Even Microsoft Excel assumes than angles are in Radians because the calculations are much simpler and quicker.
"The SIN function syntax has the following arguments (argument: A value that provides information to an action, an event, a method, a property, a function, or a procedure.):
Number Required. The angle in radians for which you want the sine.
Remark
If your argument is in degrees, multiply it by PI()/180 or use the RADIANS function to convert it to radians."

Again, radians may be fine for theoretical mathematics and physics, but even the article admits that for practical geometry they are not commonly used. Sailors and builders deal with practical geometry, and until something better than a 360 degree circle comes along for my purposes, the theoreticalists can have their radians. Which still don't divide a circle evenly in whole numbers.

[Benz]

Originally Posted by TeddyDiver

StuM is right. A ruler no matter how square the ends are is not a right angle. Besides if you want to devide angles the right method is to use a compass.

BR Teddy

Actually, if you buy a ruler whose end is not a right angle, get your money back. Any decent ruler maker squares their ends, since this is useful in building. You can see whether a ruler was made carefully by ensuring that all the markings on it are in inches. Once they start printing centimeters on 'em, it's anybody's guess whether it will be straight, or flat, or even, because to the metrician, rulers are just another theory. If you don't have to subdivide by the square root of pi to derive an imaginary answer that is the cosine of fatuous credulity, they're not interested.

Ben
zartmancruising dot com

[Benz]

Originally Posted by StuM

Vertical if only perpendicular if the first line is horizontal and you are working on a vertical sheet of paper.

So how do you ensure that the first line is horizontal and that the paper is vertical? This is getting more and more bizarre

I never advocated this, by the way. You kind of need to keep your paper flat.

[StuM]

Originally Posted by Benz

. Can one draw rads by using simple tools and math that does not require a calculator?

Don't need math at all. All you need is a a piece of string the same length as the circle's radius. Wrap it round the circumference of circle and each length is one radian.