Metric circles have 512 degrees. The senate is voting on a law that bans government use of metric circles in favor of American circles which have 360 degrees.

Some renegade teen males are measuring their 'endowment' using metric rulers; film at 11:00...

Where the $*#k did you get 512 from? A circle still has 360 degrees the last I heard.

In the SI (metric) system, angles are in RADIANS. And there are 2 PI (6.283) radians in a circle.

It was a joke stemming from someone's mistaken belief, stated the other day, that a meter was just short of six feet in length.

A metric meter or an SAE meter ? What is today's date ?

Nice one Dave, although everyone knows metric circles contain 100 degrees. It's obvious ;-)

Actually, there are metric ways to measure circles. They're called "gradians" or "grads" for short, and a right angle is equal to 100 of them. A full circle is 400 grads.

Who uses them? Maybe the French, for some specific applications. Why? French!

https://en.wikipedia.org/wiki/Gradian

And now you know!

In the 1970's and 80's, some pocket calculators could be set to do angular/trigonometric calculations in grads. Maybe they still can. I was a chemist, not an engineer, so I never bothered with it. If I even knew or cared what a grad was, I'd forgotten until just now.
The idea of 360 degrees in a circle comes from ancient Egyptian and Babylonian astronomical observations. It's the 365.2422-day year, rounded down.
The radian is the natural unit of angular measure in calculus, but I didn't think it had anything specific to do with the Metric System. According to Wiki, it was first worked out--although not with that name--by an associate of Isaac Newton in 1714. https://en.wikipedia.org/wiki/Radian

I wrote the above before seeing the following posts by bradley and BoJ. Fascinating stuff there, guys. I knew the Babylonians were sharp, but didn't realize how sharp. Of course, they didn't have television and they had to occupy themselves somehow.

My understanding is that the use of 60/360 was based not on the number of days in a year but rather on the fact that those numbers are uniquely easy to use in calculations. Consider, for instance, how easy it is to divide 60 and get answers in whole numbers.

Such divisors for the number 60 include 1,2,3,4,5,6,10,12,15,20,30, and 60. That fact makes 60/360 really good for those who must do math problems without modern calculators.

I was hoping it was a joke...... I remember having an argument with someone that demanded I get them a "metric crescent wrench."

Back to more mundane worries.....like Covid-19.

360 degrees comes from ancient Babylonian mathematics, which used base 60 arithmetic. That’s why there are 60 minutes in an hour, etc. It’s interesting how they treated circles. Because of the way they thought about numbers, as exact things rather than approximations, they accepted inaccuracy in the circle calculations. They could have made corrections by sacrificing elegance. It’s like the number system was more important than physical reality.

Yes, Babylonians gave us the representation we traditionally use for measuring the earth (degrees, minutes, seconds) and time (hours, minutes seconds, plus 12 hours for day and 12 hours for night).

I don't think they used 3 for pi because they were philosophically opposed to fractional values. I think they just didn't have a very good handle on the value of pi. They used 3 for a long time, and used 3 and 1/8th later on. The value 3.125, is probably close enough to right for construction purposes if you are working with hand made clay bricks.

The Egyptians had better values for pi than the Babylonians, but the Babylonians had a value for the square root of 2 that totally kicked butt. The cuneiform tablet YBC7289 (YBC == Yale Babylonian Collection), dating to about 1700 BCE, had a value for sqrt(2) that in base 60 was 1 + 24/60 + 51/60^2 + 10/60^3.

If you get out your trusty calculator and convert that to decimal, and compare it to your calculator's sqrt(2), the Babylonian value is only off by 1 in the sixth decimal place. We don't know exactly how they calculated the value, but that is in fact the exact value you would get from a continued fraction expansion of sqrt(2) in base 60, truncated to 3 base 60 digits.

Holy Diagonal, Batman! For people working 17 centuries BCE, that is pretty impressive. The Babylonians also did extensive tables of integers, their squares and cubes, and their reciprocals.

They did squares and cubes because they worked with quadratic (NB, macaRomney) and cubic equations, and they had tables of reciprocals because even 4,000 years ago, they had figured out that long division was a pain in the butt, but multiplication, while tedious, was not that hard. So, instead of dividing a number by 12, they multiplied it by 1/12th. You get the same answer, except for the truncation error from fractions that can't be exactly represented base 60. It's the same problem we have in decimal with reciprocals like ⅓ = 0.333333... so we just quit writing threes at some point and chop off the infinite tail of threes.

The nice thing about base 60 is that a rather large percentage of reciprocals can be represented exactly in base 60. For example, a third = 20/60, compared to the above mentioned 0.3333... in decimal.

Babylonians also treated fractions essentially the same way we do now, except for the fact that they used base 60, and they used a positional notation, instead of coming up with a new letter for larger powers of 10 (or 60, whatever) like most other cultures did (e.g. Roman numerals X=10, C=100, M=1,000, etc). They didn't have a zero or "decimal point", so the reader had to figure that out by context. They did usually provide contextual hints so it was possible to figure that out.

Egyptians had a completely different way of dealing with fractions. Too complex to go into here. It worked, but both addition and multiplication of their fractions was a nightmare, and they stuck with their system for 2,000 years, up into the Roman Empire. Never underestimate the power of a bad idea. Compare to the US still using Imperial measure. :)

ETA: https://johncarlosbaez.wordpress.com/2011/12/02/babylon-and-the-square-root-of-2/

ETA2: the above blog post has about 20 or 30 pages worth of comments, which, deeply uncharacteristic of the average "comments" section, are EXCELLENT!! I recommend taking a look if you are interested in Babylonian math/cultural development, or ways to calculate sqrt(2).



Edited 2 time(s). Last edit at 04/01/2020 05:02PM by Brother Of Jerry.

MCGA = Make Circles Great Again

Convert it to base 10 so it runs 10 times as fast since that pesky binary is a Democrat hoax.

Pffft.

Computers have been running base 16 for decades.

I have it on good authority that Bill Gates owns the patent on Base 16.

You laugh. There have been more than a few people who have tried to patent/trademark various fundamental software ideas and get rich charging license fees. I know of two such "business plans" that BYU students hatched. One was an attempt to patent B-trees, the other was a claim that the company was the One True Owner of the UNIX operating system. Both fizzled.

Actually computer hardware all runs base 2. Base 16 is a software construct.

It all runs base 16. Base 2 is a simplification for the feeble. ;)

Digital Equipment Corp tried to do all their documentation base 8, and look what happened to them. They went from the world's second largest computer company, to being ignominiously bought for scrap by Compaq, which itself then went out of business.

They refused to admit that clumping data 3 bits per digit was a mistake. IBM refused for several decades to admit that ASCII was a better character code design than EBCDIC. They figured they were the 800 pound gorilla, and what they said was automatically the standard. They finally admitted defeat when the IBM PC came out. They adopted ASCII, then Unicode. I have no idea what their mainframes use these days.

[And don't even get me started on little-endian versus big-endian!]

BTW, I was tongue-in-cheek about computers running in base-16, though the IBM 360 family floating point format had genuine base 16 exponents. The exponent did not represent powers of two. It represented powers of 16. Changing the exponent by one was the equivalent of shifting the fractional part of the number four bits.

OK. More than you wanted to know. :)

As for base 16 being a software construct, human consciousness is a software construct. That doesn't make it any less real. [Henry Bemis' head will explode in 5, 4, 3, ...]



Edited 1 time(s). Last edit at 04/01/2020 06:21PM by Brother Of Jerry.

Do I need to teach you the concept of a bit ?

@Brother Of Jerry:
"It all runs base 16. Base 2 is a simplification for the feeble. ;)"

==In computer science classes, people are though hexadecimal (base16) bc it is more convenient.
Each character is 4 bit.
For example, a value of F would represent 1111 in binary.
A value of 3F would be 00111111 in binary.

I run twice as fast to 3rd base ;P

You don't score any points for getting to third base.