What should I put on my "Calc Clock"?
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What should I put on my "Calc Clock"?
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.
I need stuff like pi/2, pi, 3pi/3, 2pi, e, limx>0 7x/x and such.
Re: What should I put on my "Calc Clock"?
It's unclear to me whether you are interested more in 12 mathematical constants or 12 ways to obfuscate the integers 112 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 EulerMascheroni 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. =)
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 EulerMascheroni 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"?
An infinite series of the geometric sort could easily be manipulated to yield a desired integer if the obfuscation is your goal.
Re: What should I put on my "Calc Clock"?
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.
Re: What should I put on my "Calc Clock"?
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"?
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"?
dakota wrote:Therefore I would suggest: 0, the EulerMascheroni 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"?
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 topright 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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Re: What should I put on my "Calc Clock"?
And obviously it starts at the far right and goes anticlockwise.
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Re: What should I put on my "Calc Clock"?
skeptical scientist wrote:dakota wrote:Therefore I would suggest: 0, the EulerMascheroni 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.
Winston: What if the Party says that it is not to be trusted?
O'Brien: Well, doublethink, um... *turns knob*
O'Brien: Well, doublethink, um... *turns knob*
Re: What should I put on my "Calc Clock"?
skeptical scientist wrote:Nice list, but where do you put i?
Isn't it obvious? Behind the clock.
Re: What should I put on my "Calc Clock"?
I suggest making a sundial and putting i on top of the pointy thing.
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