## Decitauths

**Moderators:** gmalivuk, Moderators General, Prelates

### 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.

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.

Forrest Cameranesi, Geek of All Trades

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- doogly
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### Re: Decitauths

Tau is dumb.

LE4dGOLEM: What's a Doug?

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Noc: A larval Doogly. They grow the tail and stinger upon reaching adulthood.

Keep waggling your butt brows Brothers.

Or; Is that your eye butthairs?

### 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 a circle into radians.

Divide by that same amount again.

Divide that into tenths.

You've got something remarkably close to 1 degree. Isn't that interesting?

Divide a circle into radians.

Divide by that same amount again.

Divide that into tenths.

You've got something remarkably close to 1 degree. Isn't that interesting?

Forrest Cameranesi, Geek of All Trades

"I am Sam. Sam I am. I do not like trolls, flames, or spam."

The Codex Quaerendae (my philosophy) - The Chronicles of Quelouva (my fiction)

"I am Sam. Sam I am. I do not like trolls, flames, or spam."

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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.

### 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.

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.

Forrest Cameranesi, Geek of All Trades

"I am Sam. Sam I am. I do not like trolls, flames, or spam."

The Codex Quaerendae (my philosophy) - The Chronicles of Quelouva (my fiction)

"I am Sam. Sam I am. I do not like trolls, flames, or spam."

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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.

Dammit, I've reinvented degrees, haven't I?

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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.

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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Eebster the Great: What specifically is moving faster than light in these examples?

doogly: Hands waving furiously.

Eebster the Great: What specifically is moving faster than light in these examples?

doogly: Hands waving furiously.

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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.

### 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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### 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.

LE4dGOLEM: What's a Doug?

Noc: A larval Doogly. They grow the tail and stinger upon reaching adulthood.

Keep waggling your butt brows Brothers.

Or; Is that your eye butthairs?

Noc: A larval Doogly. They grow the tail and stinger upon reaching adulthood.

Keep waggling your butt brows Brothers.

Or; Is that your eye butthairs?

- Eebster the Great
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### Re: Decitauths

This strikes me as less interesting than e

^{π}- π = 20.-
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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.

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- gmalivuk
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### Re: Decitauths

10 isn't anti prime so what's your point?

- doogly
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### Re: Decitauths

babylon > france

LE4dGOLEM: What's a Doug?

Noc: A larval Doogly. They grow the tail and stinger upon reaching adulthood.

Keep waggling your butt brows Brothers.

Or; Is that your eye butthairs?

Noc: A larval Doogly. They grow the tail and stinger upon reaching adulthood.

Keep waggling your butt brows Brothers.

Or; Is that your eye butthairs?

- 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.

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.

(defun fibs (n &optional (a 1) (b 1)) (take n (unfold '+ a b)))

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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 = τ^{2}*10 ≈ 6^{2}*10 = 360, so it's sort of the worst of both worlds.### Who is online

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