## Decitauths

For the discussion of math. Duh.

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Pfhorrest
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### Decitauths

An interesting thought just occurred to me:

There are tau radians in a circle. Tau is about six. 1/tau (call it a "tauth") of a radian is thus about 1/36 of a circle. So a tenth of a tauth, or a decitauth if you will, turns out to be just shy of 1.1 degrees.

I don't know how exactly in particular, but it seems like that could be useful somehow, a more mathematically-grounded unit of angular measure that's very close in scale to the common conventional unit.
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doogly
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### Re: Decitauths

Tau is dumb.
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Pfhorrest
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### Re: Decitauths

Whatever, it's the number of radians in a circle and that's all I care about for this purpose, not the name.

Divide by that same amount again.

Divide that into tenths.

You've got something remarkably close to 1 degree. Isn't that interesting?
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cyanyoshi
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### Re: Decitauths

Yes, since tau is 6 (relative error ~5%), it stands to reason that 360/tau^2 is 10 (relative error ~10%). I have no idea why one would care to divide the beautiful radian by tau to make something uglier (and then divide that by 10), but hey.

Pfhorrest
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### Re: Decitauths

Because people are already measuring angle in some arbitrary conveniently-factorable number of slices of a circle (degrees) because it's convenient on human scales I guess, and this is very close to that yet more connected to the less-arbitrary way of measuring angle?

It's just an interesting approximate intersection of conventional units and math, like how you can convert miles to kilometers (approximately) using the Fibonacci sequence.
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Flumble
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### Re: Decitauths

doogly wrote:Tau is dumb.

no u

Pfhorrest wrote:conveniently-factorable

Hmm, how is τ conveniently factored?

I'd rather suggest working with the "turn", i.e. τ rad or 360°. It's easily factored, since dividing the circle into n pieces gives you angles of 1/n turn. And it's less arbitrary than degrees or decitauths because it's simply 1 per full turn.
"But", I hear you say, "how do you sum angles?" You'll have to teach (mostly) kids how to make two fractions have a common denominator and then add them together. You can also teach them to always convert to a default denominator with lots of factors, like 360, before summing the angles. This way you don't have to find the least/convenient common multiple of the denominators. Maybe even measure the angles in these fractions and make the denominator implicit.
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Carlington
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### Re: Decitauths

Tau is 360 degrees. Tau/360 (tau/36/10) is 1 degree. Nearly tau/360 is nearly a degree.
I don't want to come off as being overly blunt or harsh but...yes? 6 is a reasonable approximation to tau if you don't need too much accuracy, and 1/60 radians is a reasonable approximation for a degree in the same way.
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gmalivuk
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### Re: Decitauths

Fractions with pi in the denominator (or tau if you're an asshole) feel a lot grosser to work with than when it's in the numerator.
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Pfhorrest
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### Re: Decitauths

Flumble wrote:
Pfhorrest wrote:conveniently-factorable

Hmm, how is τ conveniently factored?

I meant that 360 is conventiently factorable.
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Eebster the Great
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### Re: Decitauths

gmalivuk wrote:Fractions with pi in the denominator (or tau if you're an asshole) feel a lot grosser to work with than when it's in the numerator.

This continues to look strange in the expression for the error function, even though I understand what it's doing there.

doogly
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### Re: Decitauths

Pfhorrest wrote:
Flumble wrote:
Pfhorrest wrote:conveniently-factorable

Hmm, how is τ conveniently factored?

I meant that 360 is conventiently factorable.

That is why the Babylonians picked it. They made sense, not like those Frenchies with their metric system.
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Eebster the Great
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### Re: Decitauths

This strikes me as less interesting than eπ - π = 20.

jewish_scientist
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### Re: Decitauths

Pfhorrest wrote:I meant that 360 is conventiently factorable.

360 is actually an anti-prime (a.k.a. highly composite numbers). A number is an anti-prime if no smaller number has the same about or more factors. Almost all of the conversion factors in the Imperial system are anti-primes because they are so easy to divide, makes trade easier. Don't believe me;

You are selling rope at \$10 per foot. Someone comes in asking for \$6 worth of rope. How much do you give them?
Standard practice is to always cut rope exactly where a mark on the measuring stick is. Is anyone being short-changed in this transaction.

gmalivuk
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### Re: Decitauths

10 isn't anti prime so what's your point?
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doogly
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### Re: Decitauths

babylon > france
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Xanthir
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### Re: Decitauths

jewish_scientist was explicitly talking about the imperial system, in which 10 is not a used conversion ratio.

That said, I don't know what the \$10 vs \$6 example is about, because 6/10 isn't a ratio you can express with inches and feet. Maybe trying to illustrate that 10 is a *bad* base to use? I dunno.
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Eebster the Great
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### Re: Decitauths

I think the idea was that 12 is demonstrably superior to 10 because it has more factors. Of course, "decitauths" rely on the calculation (2π)2*10 = τ2*10 ≈ 62*10 = 360, so it's sort of the worst of both worlds.