Clock Hand Swap Times

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Clock Hand Swap Times

Palmen, KEV (Karl)
Dear Lance and Calendar People

Thinking again about clocks whose hands turn at a constant rate, there are only certain times that would remain valid, if the two hands of the clock were swapped. For example, half past five is not such a time, because if the hands were swapped the hour hand would point directly to an hour almost half way through an hour.

These times do include all the 11 times when both hands point the same way (swapping does not change the time) and also the 13 times when to two hands are arranged symmetrically (because the mirror image of each valid time is also valid).

The first such time after 12 o'clock is very soon after five past twelve.

I leave it to you to work out when all these times occur, in a 12-hour clock and then more generally in a clock where the fast hand goes round an integer N times faster than the slow hand.

Karl

08(04(19
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Re: Clock Hand Swap Times

Ed Kohout
Interestingly, the hands of a clock at 3:33 form a perfect right angle,
or a square.

Masonically,
Ed K



--- "Palmen, KEV (Karl)" <[hidden email]> wrote:

> Dear Lance and Calendar People
>
> Thinking again about clocks whose hands turn at a constant rate,
> there are only certain times that would remain valid, if the two
> hands of the clock were swapped. For example, half past five is not
> such a time, because if the hands were swapped the hour hand would
> point directly to an hour almost half way through an hour.
>
> These times do include all the 11 times when both hands point the
> same way (swapping does not change the time) and also the 13 times
> when to two hands are arranged symmetrically (because the mirror
> image of each valid time is also valid).
>
> The first such time after 12 o'clock is very soon after five past
> twelve.
>
> I leave it to you to work out when all these times occur, in a
> 12-hour clock and then more generally in a clock where the fast hand
> goes round an integer N times faster than the slow hand.
>
> Karl
>
> 08(04(19
>
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Re: Clock Hand Swap Times

VictorEngel
In reply to this post by Palmen, KEV (Karl)
What is so interesting about 3:33? 5:11 is actually a bit closer, as are
00:49, 06:49, and 11:11. I get the following times:

00:16
00:49
01:22
01:55
02:27
03:00
03:33
04:05
04:38
05:11
05:44
06:16
06:49
07:22
07:55
08:27
09:00
09:33
10:05
10:38
11:11
11:44



> -----Original Message-----
> From: East Carolina University Calendar discussion List
> [mailto:[hidden email]]On Behalf Of Ed Kohout
> Sent: Thursday, June 15, 2006 10:30 AM
> To: [hidden email]
> Subject: Re: Clock Hand Swap Times
>
>
> Interestingly, the hands of a clock at 3:33 form a perfect
> right angle,
> or a square.
>
> Masonically,
> Ed K
>
>
>
> --- "Palmen, KEV (Karl)" <[hidden email]> wrote:
>
> > Dear Lance and Calendar People
> >
> > Thinking again about clocks whose hands turn at a constant rate,
> > there are only certain times that would remain valid, if the two
> > hands of the clock were swapped. For example, half past five is not
> > such a time, because if the hands were swapped the hour hand would
> > point directly to an hour almost half way through an hour.
> >
> > These times do include all the 11 times when both hands point the
> > same way (swapping does not change the time) and also the 13 times
> > when to two hands are arranged symmetrically (because the mirror
> > image of each valid time is also valid).
> >
> > The first such time after 12 o'clock is very soon after five past
> > twelve.
> >
> > I leave it to you to work out when all these times occur, in a
> > 12-hour clock and then more generally in a clock where the fast hand
> > goes round an integer N times faster than the slow hand.
> >
> > Karl
> >
> > 08(04(19
> >
>
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Re: Clock Hand Swap Times

Palmen, KEV (Karl)
Dear Victor, Ed and Calendar People

-----Original Message-----
From: East Carolina University Calendar discussion List
[mailto:[hidden email]]On Behalf Of Engel,Victor
Sent: 15 June 2006 17:07
To: [hidden email]
Subject: Re: Clock Hand Swap Times


What is so interesting about 3:33?

KARL SAYS: I make it 7/11 second after 3:32:43.

5:11 is actually a bit closer, as are
00:49, 06:49, and 11:11. I get the following times:

00:16
00:49
01:22
01:55
02:27
03:00
03:33
04:05
04:38
05:11
05:44
06:16
06:49
07:22
07:55
08:27
09:00
09:33
10:05
10:38
11:11
11:44

KARL SAYS: None of these 22 times are exactly clock hand swap times, when both hands can be swapped to a valid time.

Karl

08(04(19


> -----Original Message-----
> From: East Carolina University Calendar discussion List
> [mailto:[hidden email]]On Behalf Of Ed Kohout
> Sent: Thursday, June 15, 2006 10:30 AM
> To: [hidden email]
> Subject: Re: Clock Hand Swap Times
>
>
> Interestingly, the hands of a clock at 3:33 form a perfect
> right angle,
> or a square.
>
> Masonically,
> Ed K
>
>
>
> --- "Palmen, KEV (Karl)" <[hidden email]> wrote:
>
> > Dear Lance and Calendar People
> >
> > Thinking again about clocks whose hands turn at a constant rate,
> > there are only certain times that would remain valid, if the two
> > hands of the clock were swapped. For example, half past five is not
> > such a time, because if the hands were swapped the hour hand would
> > point directly to an hour almost half way through an hour.
> >
> > These times do include all the 11 times when both hands point the
> > same way (swapping does not change the time) and also the 13 times
> > when to two hands are arranged symmetrically (because the mirror
> > image of each valid time is also valid).
> >
> > The first such time after 12 o'clock is very soon after five past
> > twelve.
> >
> > I leave it to you to work out when all these times occur, in a
> > 12-hour clock and then more generally in a clock where the fast hand
> > goes round an integer N times faster than the slow hand.
> >
> > Karl
> >
> > 08(04(19
> >
>
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Re: Clock Hand Swap Times

VictorEngel
In reply to this post by Palmen, KEV (Karl)
Dear Karl, Ed, and Calendar People,


> What is so interesting about 3:33?
>
> KARL SAYS: I make it 7/11 second after 3:32:43.

Right. So it's almost 17 seconds out, which is why I said 5:11 is closer.

Victor
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Right Angle Times RE: Clock Hand Swap Times

Palmen, KEV (Karl)
In reply to this post by VictorEngel
Dear Victor and Calendar People

I work out the exact right angle times in the first 6 hours. The times in the second 6 hours are exactly 6 hours after those in the first 6 hours.

00:16:21 9/11
00:49:05 5/11
01:21:49 1/11
01:54:32 8/11
02:27:16 4/11
03:00:00 0/11
03:32:43 7/11
04:05:27 3/11
04:38:10 10/11
05:10:54 6/11
05:43:38 2/11

Ed may note that although there is such a time near 3:33 there are none near of 1:11 or 2:22, but there is a time within the 30 seconds proceeding each of 5:11, 1:22, 3:33, 5:44 and 1:55:
05:10:54 6/11
01:21:49 1/11
03:32:43 7/11
05:43:38 2/11
01:54:32 8/11

Karl

08(04(20
 

-----Original Message-----
From: East Carolina University Calendar discussion List
[mailto:[hidden email]]On Behalf Of Engel,Victor
Sent: 15 June 2006 17:07
To: [hidden email]
Subject: Re: Clock Hand Swap Times


What is so interesting about 3:33? 5:11 is actually a bit closer, as are
00:49, 06:49, and 11:11. I get the following times:

00:16
00:49
01:22
01:55
02:27
03:00
03:33
04:05
04:38
05:11
05:44
06:16
06:49
07:22
07:55
08:27
09:00
09:33
10:05
10:38
11:11
11:44



> -----Original Message-----
> From: East Carolina University Calendar discussion List
> [mailto:[hidden email]]On Behalf Of Ed Kohout
> Sent: Thursday, June 15, 2006 10:30 AM
> To: [hidden email]
> Subject: Re: Clock Hand Swap Times
>
>
> Interestingly, the hands of a clock at 3:33 form a perfect
> right angle,
> or a square.
>
> Masonically,
> Ed K
>
>
>
> --- "Palmen, KEV (Karl)" <[hidden email]> wrote:
>
> > Dear Lance and Calendar People
> >
> > Thinking again about clocks whose hands turn at a constant rate,
> > there are only certain times that would remain valid, if the two
> > hands of the clock were swapped. For example, half past five is not
> > such a time, because if the hands were swapped the hour hand would
> > point directly to an hour almost half way through an hour.
> >
> > These times do include all the 11 times when both hands point the
> > same way (swapping does not change the time) and also the 13 times
> > when to two hands are arranged symmetrically (because the mirror
> > image of each valid time is also valid).
> >
> > The first such time after 12 o'clock is very soon after five past
> > twelve.
> >
> > I leave it to you to work out when all these times occur, in a
> > 12-hour clock and then more generally in a clock where the fast hand
> > goes round an integer N times faster than the slow hand.
> >
> > Karl
> >
> > 08(04(19
> >
>
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Re: Clock Hand Swap Times

Palmen, KEV (Karl)
In reply to this post by VictorEngel
Dear Victor, Ed and Calendar People

I reckon there are 143 times in 12 hours that are valid if the hands are swapped and that they occur at equal intervals. They include the times where both hands point the same way (once every 13 intervals) and the times that the two hands are place symmetrically. I won't list all 143, just 7 of them and their valid hand swapped times. Times are in hours, minutes, seconds and 1/143 seconds.

12:00:00 000   12:00:00 000
12:05:02 014   01:00:25 025
12:10:04 028   02:00:50 050
12:15:06 042   03:01:15 075
12:20:08 056   04:01:40 100
12:25:10 070   05:02:05 125
12:30:12 084   06:02:31 007

One way of seeing this is to plot the position of the minute hand against the position of the hour hand and then superimpose the same plot with the axes swapped. The resulting graph is then a grid of rhombuses. The swap times correspond to where the lines cross in this grid. There are 12*12=144 of these intersections, but two of them occurring at opposite corners of the plot correspond to the same time 12:00, so there are 143 in all and they can be seen to occur at equal intervals.

Another way of seeing this is to note that the position M of the minutes hand is given in terms of the position H of the hour hand thus:

(M = 12*H) mod C

where C is a whole circle = 360 degrees = 2pi radians.

For a hand swap time also

(H = 12*M) mod C

Hence

(H = 144*H) mod C
(0 = 143*H) mod C

Hence H is any integer multiple of C/143 and so the hand swap times occur at equal intervals from 12:00 143 times over 12 hours.

For a clock where the fast hand goes round N times faster than the slow hand. The hand swap times occur at equal intervals
N^2-1 = (N-1)*(N+1) times in a clock cycle.

For any of these times to have the hands at right angles, N+1 must be divisible by four. Then, every time with the hands at right angles can have its hands swapped.
For N=3 we have:

0:0 0/8 s both up
0:1 1/8 r     1:0 3/8
0:2 2/8 o     2:0 6/8
1:0 3/8 r     0:1 1/8
1:1 4/8 s both down
1:2 5/8 r     2:1 7/8
2:0 6/8 o     0:2 2/8
2:1 7/8 r     1:2 5/8

where
s = hands in same direction
r = hands at right angles
o = hands in opposite direction and horizontal

Karl

08(04(20

 

> --- "Palmen, KEV (Karl)" <[hidden email]> wrote:
>
> > Dear Lance and Calendar People
> >
> > Thinking again about clocks whose hands turn at a constant rate,
> > there are only certain times that would remain valid, if the two
> > hands of the clock were swapped. For example, half past five is not
> > such a time, because if the hands were swapped the hour hand would
> > point directly to an hour almost half way through an hour.
> >
> > These times do include all the 11 times when both hands point the
> > same way (swapping does not change the time) and also the 13 times
> > when to two hands are arranged symmetrically (because the mirror
> > image of each valid time is also valid).
> >
> > The first such time after 12 o'clock is very soon after five past
> > twelve.
> >
> > I leave it to you to work out when all these times occur, in a
> > 12-hour clock and then more generally in a clock where the fast hand
> > goes round an integer N times faster than the slow hand.
> >
> > Karl
> >
> > 08(04(19
> >
>
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Re: Right Angle Times RE: Clock Hand Swap Times

VictorEngel
In reply to this post by Palmen, KEV (Karl)
If repeating numbers is the goal, I would proffer 11:11.

> -----Original Message-----
> From: East Carolina University Calendar discussion List
> [mailto:[hidden email]]On Behalf Of Palmen, KEV (Karl)
> Sent: Friday, June 16, 2006 7:03 AM
> To: [hidden email]
> Subject: Right Angle Times RE: Clock Hand Swap Times
>
>
> Dear Victor and Calendar People
>
> I work out the exact right angle times in the first 6 hours.
> The times in the second 6 hours are exactly 6 hours after
> those in the first 6 hours.
>
> 00:16:21 9/11
> 00:49:05 5/11
> 01:21:49 1/11
> 01:54:32 8/11
> 02:27:16 4/11
> 03:00:00 0/11
> 03:32:43 7/11
> 04:05:27 3/11
> 04:38:10 10/11
> 05:10:54 6/11
> 05:43:38 2/11
>
> Ed may note that although there is such a time near 3:33
> there are none near of 1:11 or 2:22, but there is a time
> within the 30 seconds proceeding each of 5:11, 1:22, 3:33,
> 5:44 and 1:55:
> 05:10:54 6/11
> 01:21:49 1/11
> 03:32:43 7/11
> 05:43:38 2/11
> 01:54:32 8/11
>
> Karl
>
> 08(04(20
>  
>
> -----Original Message-----
> From: East Carolina University Calendar discussion List
> [mailto:[hidden email]]On Behalf Of Engel,Victor
> Sent: 15 June 2006 17:07
> To: [hidden email]
> Subject: Re: Clock Hand Swap Times
>
>
> What is so interesting about 3:33? 5:11 is actually a bit
> closer, as are
> 00:49, 06:49, and 11:11. I get the following times:
>
> 00:16
> 00:49
> 01:22
> 01:55
> 02:27
> 03:00
> 03:33
> 04:05
> 04:38
> 05:11
> 05:44
> 06:16
> 06:49
> 07:22
> 07:55
> 08:27
> 09:00
> 09:33
> 10:05
> 10:38
> 11:11
> 11:44
>
>
>
> > -----Original Message-----
> > From: East Carolina University Calendar discussion List
> > [mailto:[hidden email]]On Behalf Of Ed Kohout
> > Sent: Thursday, June 15, 2006 10:30 AM
> > To: [hidden email]
> > Subject: Re: Clock Hand Swap Times
> >
> >
> > Interestingly, the hands of a clock at 3:33 form a perfect
> > right angle,
> > or a square.
> >
> > Masonically,
> > Ed K
> >
> >
> >
> > --- "Palmen, KEV (Karl)" <[hidden email]> wrote:
> >
> > > Dear Lance and Calendar People
> > >
> > > Thinking again about clocks whose hands turn at a constant rate,
> > > there are only certain times that would remain valid, if the two
> > > hands of the clock were swapped. For example, half past
> five is not
> > > such a time, because if the hands were swapped the hour hand would
> > > point directly to an hour almost half way through an hour.
> > >
> > > These times do include all the 11 times when both hands point the
> > > same way (swapping does not change the time) and also the 13 times
> > > when to two hands are arranged symmetrically (because the mirror
> > > image of each valid time is also valid).
> > >
> > > The first such time after 12 o'clock is very soon after five past
> > > twelve.
> > >
> > > I leave it to you to work out when all these times occur, in a
> > > 12-hour clock and then more generally in a clock where
> the fast hand
> > > goes round an integer N times faster than the slow hand.
> > >
> > > Karl
> > >
> > > 08(04(19
> > >
> >
>
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Re: Clock Hand Swap Times

VictorEngel
In reply to this post by Palmen, KEV (Karl)
Dear Karl,

> 12:05:02 014   01:00:25 025

I must be misunderstanding. If you take 12:05:02 and swap hands in the same
position, wouldn't you get 01:00:02 (approximately)? Wait a minute. I think
you are using only two hands. Correct?

Victor
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Re: Clock Hand Swap Times

Palmen, KEV (Karl)
Dear Victor and Calendar People

-----Original Message-----
From: East Carolina University Calendar discussion List
[mailto:[hidden email]]On Behalf Of Engel,Victor
Sent: 16 June 2006 14:42
To: [hidden email]
Subject: Re: Clock Hand Swap Times


Dear Karl,

> 12:05:02 014   01:00:25 025

I must be misunderstanding. If you take 12:05:02 and swap hands in the same
position, wouldn't you get 01:00:02 (approximately)? Wait a minute. I think
you are using only two hands. Correct?

KARL SAYS: Of course - The hour and minute hand.

Karl


08(04(20
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Re: Right Angle Times RE: Clock Hand Swap Times

Ed Kohout
In reply to this post by Palmen, KEV (Karl)
Dear Karl,

Unsurprising as 33/60 = .55

This is why that giant sundial in the backyard of the White House
stands at 555.55 feet in height.

- Ed K




--- "Palmen, KEV (Karl)" <[hidden email]> wrote:

> Dear Victor and Calendar People
>
> I work out the exact right angle times in the first 6 hours. The
> times in the second 6 hours are exactly 6 hours after those in the
> first 6 hours.
>
> 00:16:21 9/11
> 00:49:05 5/11
> 01:21:49 1/11
> 01:54:32 8/11
> 02:27:16 4/11
> 03:00:00 0/11
> 03:32:43 7/11
> 04:05:27 3/11
> 04:38:10 10/11
> 05:10:54 6/11
> 05:43:38 2/11
>
> Ed may note that although there is such a time near 3:33 there are
> none near of 1:11 or 2:22, but there is a time within the 30 seconds
> proceeding each of 5:11, 1:22, 3:33, 5:44 and 1:55:
> 05:10:54 6/11
> 01:21:49 1/11
> 03:32:43 7/11
> 05:43:38 2/11
> 01:54:32 8/11
>
> Karl
>
> 08(04(20
>  
>
> -----Original Message-----
> From: East Carolina University Calendar discussion List
> [mailto:[hidden email]]On Behalf Of Engel,Victor
> Sent: 15 June 2006 17:07
> To: [hidden email]
> Subject: Re: Clock Hand Swap Times
>
>
> What is so interesting about 3:33? 5:11 is actually a bit closer, as
> are
> 00:49, 06:49, and 11:11. I get the following times:
>
> 00:16
> 00:49
> 01:22
> 01:55
> 02:27
> 03:00
> 03:33
> 04:05
> 04:38
> 05:11
> 05:44
> 06:16
> 06:49
> 07:22
> 07:55
> 08:27
> 09:00
> 09:33
> 10:05
> 10:38
> 11:11
> 11:44
>
>
>
> > -----Original Message-----
> > From: East Carolina University Calendar discussion List
> > [mailto:[hidden email]]On Behalf Of Ed Kohout
> > Sent: Thursday, June 15, 2006 10:30 AM
> > To: [hidden email]
> > Subject: Re: Clock Hand Swap Times
> >
> >
> > Interestingly, the hands of a clock at 3:33 form a perfect
> > right angle,
> > or a square.
> >
> > Masonically,
> > Ed K
> >
> >
> >
> > --- "Palmen, KEV (Karl)" <[hidden email]> wrote:
> >
> > > Dear Lance and Calendar People
> > >
> > > Thinking again about clocks whose hands turn at a constant rate,
> > > there are only certain times that would remain valid, if the two
> > > hands of the clock were swapped. For example, half past five is
> not
> > > such a time, because if the hands were swapped the hour hand
> would
> > > point directly to an hour almost half way through an hour.
> > >
> > > These times do include all the 11 times when both hands point the
> > > same way (swapping does not change the time) and also the 13
> times
> > > when to two hands are arranged symmetrically (because the mirror
> > > image of each valid time is also valid).
> > >
> > > The first such time after 12 o'clock is very soon after five past
> > > twelve.
> > >
> > > I leave it to you to work out when all these times occur, in a
> > > 12-hour clock and then more generally in a clock where the fast
> hand
> > > goes round an integer N times faster than the slow hand.
> > >
> > > Karl
> > >
> > > 08(04(19
> > >
> >
>
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Re: Right Angle Times RE: Clock Hand Swap Times

Palmen, KEV (Karl)
Dear Ed and Calendar People

-----Original Message-----
From: East Carolina University Calendar discussion List
[mailto:[hidden email]]On Behalf Of Ed Kohout
Sent: 16 June 2006 17:11
To: [hidden email]
Subject: Re: Right Angle Times RE: Clock Hand Swap Times


Dear Karl,

Unsurprising as 33/60 = .55

KARL ASKS: Ed hasn't told use what is so special about .55 .

Taken as fractions of an hour we get the times as

 3/11
 9/11
15/11  = 1 4/11 (1:22)
21/11  = 1 10/11 (1:55)
27/11  = 2 5/11
33/11  = 3
39/11  = 3 6/11 (3:33)
45/11  = 4 1/11
51/11  = 4 7/11
57/11  = 5 2/11 (5:11)
63/11  = 5 8/11 (5:44)
and so for the other six hours

So one could say
"Unsurprising as 33/60 is close to 6/11 as they are 0.55 and 0.54545454 recurring respectively."

I said:
"Ed may note that although there is such a time near 3:33 there are none near of 1:11 or 2:22, but there is a time within the 30 seconds proceeding each of 5:11, 1:22, 3:33, 5:44 and 1:55:
05:10:54 6/11
01:21:49 1/11
03:32:43 7/11
05:43:38 2/11
01:54:32 8/11"

These times and their nearest minute approximations are as follows when expressed as a decimal fractions of hours:
Minute           Exact
5:11 5.18333...  5.18181818...
1:22 1.36666...  1.36363636...
3:33 3.55        3.54545454...
5:44 5.73333...  5.72727272...
1:55 1.91666...  1.90909090...


ED CONTINUES:
This is why that giant sundial in the backyard of the White House
stands at 555.55 feet in height.


KARL SAYS: That's taller than the spike in the front yard!
http://www.cr.nps.gov/nr/travel/wash/dc72.htm
which is 555.427 feet in height.

Karl

08(04(22 till noon





--- "Palmen, KEV (Karl)" <[hidden email]> wrote:

> Dear Victor and Calendar People
>
> I work out the exact right angle times in the first 6 hours. The
> times in the second 6 hours are exactly 6 hours after those in the
> first 6 hours.
>
> 00:16:21 9/11
> 00:49:05 5/11
> 01:21:49 1/11
> 01:54:32 8/11
> 02:27:16 4/11
> 03:00:00 0/11
> 03:32:43 7/11
> 04:05:27 3/11
> 04:38:10 10/11
> 05:10:54 6/11
> 05:43:38 2/11
>
> Ed may note that although there is such a time near 3:33 there are
> none near of 1:11 or 2:22, but there is a time within the 30 seconds
> proceeding each of 5:11, 1:22, 3:33, 5:44 and 1:55:
> 05:10:54 6/11
> 01:21:49 1/11
> 03:32:43 7/11
> 05:43:38 2/11
> 01:54:32 8/11
>
> Karl
>
> 08(04(20
>  
>
> -----Original Message-----
> From: East Carolina University Calendar discussion List
> [mailto:[hidden email]]On Behalf Of Engel,Victor
> Sent: 15 June 2006 17:07
> To: [hidden email]
> Subject: Re: Clock Hand Swap Times
>
>
> What is so interesting about 3:33? 5:11 is actually a bit closer, as
> are
> 00:49, 06:49, and 11:11. I get the following times:
>
> 00:16
> 00:49
> 01:22
> 01:55
> 02:27
> 03:00
> 03:33
> 04:05
> 04:38
> 05:11
> 05:44
> 06:16
> 06:49
> 07:22
> 07:55
> 08:27
> 09:00
> 09:33
> 10:05
> 10:38
> 11:11
> 11:44
>
>
>
> > -----Original Message-----
> > From: East Carolina University Calendar discussion List
> > [mailto:[hidden email]]On Behalf Of Ed Kohout
> > Sent: Thursday, June 15, 2006 10:30 AM
> > To: [hidden email]
> > Subject: Re: Clock Hand Swap Times
> >
> >
> > Interestingly, the hands of a clock at 3:33 form a perfect
> > right angle,
> > or a square.
> >
> > Masonically,
> > Ed K
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Re: Right Angle Times RE: Clock Hand Swap Times

Ed Kohout
--- "Palmen, KEV (Karl)" <[hidden email]> wrote:

> Dear Ed and Calendar People
>
> -----Original Message-----
> From: East Carolina University Calendar discussion List
> [mailto:[hidden email]]On Behalf Of Ed Kohout
> Sent: 16 June 2006 17:11
> To: [hidden email]
> Subject: Re: Right Angle Times RE: Clock Hand Swap Times
>
>
> Dear Karl,
>
> Unsurprising as 33/60 = .55
>
> KARL ASKS: Ed hasn't told use what is so special about .55 .
>
> Taken as fractions of an hour we get the times as
>
>  3/11
>  9/11
> 15/11  = 1 4/11 (1:22)
> 21/11  = 1 10/11 (1:55)
> 27/11  = 2 5/11
> 33/11  = 3
> 39/11  = 3 6/11 (3:33)
> 45/11  = 4 1/11
> 51/11  = 4 7/11
> 57/11  = 5 2/11 (5:11)
> 63/11  = 5 8/11 (5:44)
> and so for the other six hours
>
> So one could say
> "Unsurprising as 33/60 is close to 6/11 as they are 0.55 and
> 0.54545454 recurring respectively."
>
> I said:
> "Ed may note that although there is such a time near 3:33 there are
> none near of 1:11 or 2:22, but there is a time within the 30 seconds
> proceeding each of 5:11, 1:22, 3:33, 5:44 and 1:55:
> 05:10:54 6/11
> 01:21:49 1/11
> 03:32:43 7/11
> 05:43:38 2/11
> 01:54:32 8/11"
>
> These times and their nearest minute approximations are as follows
> when expressed as a decimal fractions of hours:
> Minute           Exact
> 5:11 5.18333...  5.18181818...
> 1:22 1.36666...  1.36363636...
> 3:33 3.55        3.54545454...
> 5:44 5.73333...  5.72727272...
> 1:55 1.91666...  1.90909090...
>
>
> ED CONTINUES:
> This is why that giant sundial in the backyard of the White House
> stands at 555.55 feet in height.
>
>
> KARL SAYS: That's taller than the spike in the front yard!
> http://www.cr.nps.gov/nr/travel/wash/dc72.htm
> which is 555.427 feet in height.


Such nit picking.  

What is special about .55 is that it's the decimal equivalent of .33.
If our western clock is anything, it's a sexigesimal relic of the
cosmologies of the ancients.  "Squaring the circle" thusly falls to
this strange number.

- Ed K
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Washington Monument and the key to time

Ed Kohout
In reply to this post by Palmen, KEV (Karl)
More on how the Washington Monument squares the circle, and how it is a
monument to time:

http://www.sonic.net/bernard/wnm-main.html

8. Let the perfect indicated height of the obelisk, 555.55' represent
the length of a Foucault pendulum. A pendulum that length would swing
back and forth one time in a period of 26.12011309 seconds.

  # Find the square root of the height: 555.55 = 23.57022604

  # The ratio of the square root of the height to the period of its
time as a pendulum generates another "perfect" number: 1.228068554

    Comment: This is a primary number in the most synchronistic sense.
It represents the unification node for a measure of time and a measure
of length. Using this perfect unit, the builder could indicate a period
of time using a linear measure of length.

  # A pendulum length of 1.228068554 feet, beats a period of time
lasting 1.228068554 seconds.

----------

- Ed
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Re: Washington Monument and the key to time

VictorEngel
Ah, but you're using feet. What's so special about feet? Suppose we use
inches instead? In inches, 555.55 feet is 6666.66 inches. Is that ominous
enough yet? But what if we use pyramid inches instead? A pyramid inch is
about 1/1.01 inches, if I recall correctly, making the monument 6733.3266
inches tall. The square root of this is 82.05685, and the ratio of this to
26.12011309 is about PI.

Or how about using meters? 555.55 feet is about 169 (13 squared) meters. And
13 is about half your 26 second period.

Does any of this mean anything? I doubt it.

Victor

> -----Original Message-----
> From: East Carolina University Calendar discussion List
> [mailto:[hidden email]]On Behalf Of Ed Kohout
> Sent: Monday, June 19, 2006 10:36 AM
> To: [hidden email]
> Subject: Washington Monument and the key to time
>
>
> More on how the Washington Monument squares the circle, and
> how it is a
> monument to time:
>
> http://www.sonic.net/bernard/wnm-main.html
>
> 8. Let the perfect indicated height of the obelisk, 555.55' represent
> the length of a Foucault pendulum. A pendulum that length would swing
> back and forth one time in a period of 26.12011309 seconds.
>
>   # Find the square root of the height: 555.55 = 23.57022604
>
>   # The ratio of the square root of the height to the period of its
> time as a pendulum generates another "perfect" number: 1.228068554
>
>     Comment: This is a primary number in the most synchronistic sense.
> It represents the unification node for a measure of time and a measure
> of length. Using this perfect unit, the builder could
> indicate a period
> of time using a linear measure of length.
>
>   # A pendulum length of 1.228068554 feet, beats a period of time
> lasting 1.228068554 seconds.
>
> ----------
>
> - Ed
>
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Re: Washington Monument and the key to time

Ed Kohout
Hi Victor,


--- "Engel,Victor" <[hidden email]> wrote:

> Ah, but you're using feet. What's so special about feet?

Well, you can't walk without them.  What's so special about 12 hour
circles?  Seriously, though, this is a monument, and any good monument
should bear some symbolic measure that tells us where we are, when we
are, and what we are looking at.

The Capitol is a veritable cornucopia of such things, and the WM is
perhaps the preeminent structure along these regards.

For instance, on a day where the shadow cast by the needle at noon is
33.33 degrees, the shadow's length is 365.25 feet.  

Furthermore, if the needle is casting a noontime shadow of 16.5
degrees, the shadow length will be 165 feet.

In English measure, the "pole" of 16.5 feet is the key to how the
system is predicated on the precise polar circumference of the Earth.



> Suppose we use inches instead?
> In inches, 555.55 feet is 6666.66 inches.

555.55 feet is 33.666 poles.




> Is that ominous
> enough yet? But what if we use pyramid inches instead? A pyramid inch
> is
> about 1/1.01 inches, if I recall correctly, making the monument
> 6733.3266
> inches tall. The square root of this is 82.05685, and the ratio of
> this to
> 26.12011309 is about PI.
>
> Or how about using meters? 555.55 feet is about 169 (13 squared)
> meters. And
> 13 is about half your 26 second period.
>
> Does any of this mean anything? I doubt it.


Well, to you it may not mean anything, but you didn't build it, did
you?

- Ed K


>
> Victor
>
> > -----Original Message-----
> > From: East Carolina University Calendar discussion List
> > [mailto:[hidden email]]On Behalf Of Ed Kohout
> > Sent: Monday, June 19, 2006 10:36 AM
> > To: [hidden email]
> > Subject: Washington Monument and the key to time
> >
> >
> > More on how the Washington Monument squares the circle, and
> > how it is a
> > monument to time:
> >
> > http://www.sonic.net/bernard/wnm-main.html
> >
> > 8. Let the perfect indicated height of the obelisk, 555.55'
> represent
> > the length of a Foucault pendulum. A pendulum that length would
> swing
> > back and forth one time in a period of 26.12011309 seconds.
> >
> >   # Find the square root of the height: 555.55 = 23.57022604
> >
> >   # The ratio of the square root of the height to the period of its
> > time as a pendulum generates another "perfect" number: 1.228068554
> >
> >     Comment: This is a primary number in the most synchronistic
> sense.
> > It represents the unification node for a measure of time and a
> measure
> > of length. Using this perfect unit, the builder could
> > indicate a period
> > of time using a linear measure of length.
> >
> >   # A pendulum length of 1.228068554 feet, beats a period of time
> > lasting 1.228068554 seconds.
> >
> > ----------
> >
> > - Ed
> >
>