Dear Doves
I'd like to share with you how it happened that I found that
on an analogue clock, the angle between the hour-dial and the
minute-dial is 153°.
It was during our family summer vacation, where I just arrived
together with my family at our holiday destination, a village
name FIESCH. The origin of that name comes from the latin
vīcu(s) and simply means "Village". However, in retrospect I
can't un-see the FISH in this word..!
After unpacking our suitcases, I saw that there was a big
analogue clock on the wall. Unfortunately, it seemed not
working (batteries empty?). I somehow kept staring at the
clock. At the same time, I was thinking about the calculation
9x17 = 153, and at that moment I suddenly asked myself:
what is the angle between the dials at time 9:17? How cool
would it be if it was exactly 153°?
So at the first possible moment, I separated myself from my
family with a pen and a piece of paper and I started my
calculations with the time 9:17, and I figured out that it is
not a match for 153°, but it is relatively close.
Actually, in my first attempt to calculate it, I made an error
in my calculation, and I ended up with 234/11 for the seconds.
The 234 intrigued me, because it reminded me of "Vincent Tans"
number 2.34 (just search FiveDoves for Vincent Tan!). It made
me think a lot about 234 because it reminded me of "23. or 24.
September". -> see
https://www.fivedoves.com/letters/aug2025/josua831-1.htm
Later that evening, I continued researching all possible
solutions, using Grok. Even Grok made some wrong attempts in
the beginning and I had to "educate" it on how to calculate
all possible solutions. And only when it suddenly spit out
21:11 as a solution, I realized how perfectly it relates to
John 21:11! So you see, it was not my math skills, it was
simply a gift from above to "discover" this, at the right
time. All glory to God!
However, at least I want to share now how to calculate the
exact time at 21:11:xx, for those who are interested (and as
proof that Grok did not fool us! :-)).
- In 12h, the hour-dial moves 360°. Consequently, it moves 30°
per hour. Consequently, it moves 0.5° = 1/2° per minute.
- In 1h, the minute-dial moves 360°. Consequently, it moves 6°
per minute.
- At 21:11, the hour-dial is at 9x30° + 11*0.5° = 275.5°
- At 21:11, the minute-dial is at 11x6° = 66°
- As we start the angle at 12 o clock, it is easier to use the
"other angle" between the dials: 360°-153° = 207°
- 275.5° - 66° = 209.5°. -> 360°-209.5° = 150.5°. That's
close to 153°, but still 2.5° off. 2.5° is a bit less than
half a minute. So it means that 21:11 actually is a valid
solution, and about half a minute later it will be exactly
153°.
- How many seconds are left until the angle will be exactly
153°?
- The hour-dial moves 0.5°/60 = 1/120° per second.
- The minute-dial moves 6°/60 = 1/10° per second.
With that, we can finally write:
HourDial -MinuteDial -HourDialMovement +MinuteDialMovement =
207°
(note that the HourDialMovements decreases the angle, while
the MinuteDialMovement increases the angle. That's why we must
subtract the HourDialMovement)
-> 275.5 -66 -x/120 +x/10 = 207
-> 209.5 -x/120 +12x/120 = 207
-> 209.5 -11x/120 = 207
-> 209.5 -207 = 11x/120
-> 2.5 = 11x/120
-> 2.5*120 = 11x
-> 300/11 = x
-> x = 27.272727 (= 27 + 3/11) seconds
So the exact solution is indeed 21:11 with a rest of
27.27272727 seconds.
q.e.d.
Maranatha! YbiC, Josua