What should I put on my "Calc Clock"?

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pernero
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What should I put on my "Calc Clock"?

Postby pernero » Sat Jul 18, 2009 9:57 pm UTC

I'm making a clock that has mathematical constants, problems and notations insteal of the 1 to 12 scale.

I need stuff like pi/2, pi, 3pi/3, 2pi, e, limx->0 7x/x and such.

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dakota
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Re: What should I put on my "Calc Clock"?

Postby dakota » Sat Jul 18, 2009 11:08 pm UTC

It's unclear to me whether you are interested more in 12 mathematical constants or 12 ways to obfuscate the integers 1-12 with expressions heavy on notation.

I think the first is more aesthetically pleasing, since for the most part people read analog clocks by their hands anyway.

Therefore I would suggest: 0, the Euler-Mascheroni constant, ln(2), 1, sqrt(2), the golden ratio, pi^2/6, sqrt(pi), 2, e, 2pi, i.

It's a mostly arbitrary list, but each constant has an interesting story to tell. =)
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Re: What should I put on my "Calc Clock"?

Postby t0rajir0u » Sun Jul 19, 2009 1:49 am UTC

My vote is for 163.

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Re: What should I put on my "Calc Clock"?

Postby Ieatsoap6 » Sun Jul 19, 2009 5:28 pm UTC

An infinite series of the geometric sort could easily be manipulated to yield a desired integer if the obfuscation is your goal.

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Re: What should I put on my "Calc Clock"?

Postby HenryS » Mon Jul 20, 2009 3:23 am UTC

I think it would be good to have some number (not necessarily 12) of important constants arranged around the circle at the correct positions mod 12. So pi would appear a little below the right hand middle point of the circle, and 163 would appear in the 7 o clock position.

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Re: What should I put on my "Calc Clock"?

Postby snowyowl » Mon Jul 20, 2009 7:25 am UTC

I heard the formula [imath]e^{\pi i}+1=0[/imath] includes the five most important numbers in the mathematical universe, so they should all go in. I would add [imath]sqrt{2}[/imath], for its contribution to the discovery of irrational numbers, 163, because of [imath]e^{\pi \sqrt{163}}[/imath], perhaps 2 and/or -1, and (I nearly forgot) the golden ratio.
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Re: What should I put on my "Calc Clock"?

Postby Ubiquitous » Mon Jul 20, 2009 8:28 am UTC

My favorite number is Graham's Number, so I'll always vote for that to go on anything. Space might be an issue, though...
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Re: What should I put on my "Calc Clock"?

Postby skeptical scientist » Mon Jul 20, 2009 3:42 pm UTC

dakota wrote:Therefore I would suggest: 0, the Euler-Mascheroni constant, ln(2), 1, sqrt(2), the golden ratio, pi^2/6, sqrt(pi), 2, e, 2pi, i.

It's a mostly arbitrary list, but each constant has an interesting story to tell. =)

Nice list, but where do you put i?
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Re: What should I put on my "Calc Clock"?

Postby Qaanol » Mon Jul 20, 2009 5:04 pm UTC

HenryS wrote:I think it would be good to have some number (not necessarily 12) of important constants arranged around the circle at the correct positions mod 12. So pi would appear a little below the right hand middle point of the circle, and 163 would appear in the 7 o clock position.

This.

I propose:

[imath]\gamma \approx 0.5772[/imath] near the top and a little bit to the right
[imath]\phi \approx 1.6180[/imath] near the top-right and a little bit clockwise
[imath]e \approx 2.7183[/imath] near the right and a little bit up
[imath]\pi \approx 3.1416[/imath] near the right and a little bit down
[imath]\delta \approx 4.6692[/imath] (a Feigenbaum constant)
[imath]ln(256) \approx 5.5451[/imath]
[imath]tan(\sqrt 2) \approx 6.3341[/imath]
[imath]\int_1^2{3x^2 dx} = 7[/imath]
[imath]\pi e \approx 8.5397[/imath] (could also be [imath]R \approx 8.3145 \frac{J}{mol \, K}[/imath])
[imath]33 \frac{1}{3} \equiv 9\frac{1}{3} \pmod{12}[/imath]
[imath]\sum_{n = 1}^4 n = 10[/imath]
[imath]e^{i \pi} = -1 \equiv 11 \pmod{12}[/imath]
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Macbi
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Re: What should I put on my "Calc Clock"?

Postby Macbi » Mon Jul 20, 2009 7:37 pm UTC

And obviously it starts at the far right and goes anti-clockwise.
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Re: What should I put on my "Calc Clock"?

Postby dakota » Tue Jul 21, 2009 1:49 am UTC

skeptical scientist wrote:
dakota wrote:Therefore I would suggest: 0, the Euler-Mascheroni constant, ln(2), 1, sqrt(2), the golden ratio, pi^2/6, sqrt(pi), 2, e, 2pi, i.

It's a mostly arbitrary list, but each constant has an interesting story to tell. =)

Nice list, but where do you put i?


True! As you no doubt noticed, they are in order, with the incomparable exception of [imath]i[/imath] of course =)

Since most everything about this exercise is arbitrary, except for the 12 and even that to an extent, I think aesthetics are the important consideration. Therefore I'd say to put it where it looks best.
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t0rajir0u
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Re: What should I put on my "Calc Clock"?

Postby t0rajir0u » Tue Jul 21, 2009 4:02 am UTC

skeptical scientist wrote:Nice list, but where do you put i?

Isn't it obvious? Behind the clock.

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Re: What should I put on my "Calc Clock"?

Postby Harg » Tue Jul 21, 2009 7:27 am UTC

I suggest making a sundial and putting i on top of the pointy thing.


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