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I plan to be on November 18 in Kepler's hometown. I want to offer the Kepler Museum in this city an original wall clock for installation on the building or in the hall.
Here is a model of these clock with the solution of differential equations with a test for Kepler's second law. The clock has only a second hand. Somebody can help me make the watch and the minute and hour hands. Or some more interesting ideas!
File in Attach.
Thanks!
Physical Mathematics
Solved! Go to Solution.
Here she is.
Now capable of taking smaller resolution steps (= frames per second). Here's an example with 10 frames per second:
Mathcad file is attached.
Luc
Very nice Valery.
Note that on older clocks, so also those out of Kepler's time, the 4 is written as IIII instead of IV.
The reason for that usage is not precisely known. One argument proposed is that it would make even numbers of the different symbols on the clock. 20 I's, 4 V's and 4 X's.
Luc
Thanks Luc!
New version of the clock
I thought I'd give you(r clock) a (few more) hand(s):
It runs for over an hour (4000 seconds to be exact).
I can have it run for 9999 seconds at maximum in one animation, that's not yet 3 hours...
I haven't tried to assemble the results of multiple animations into a single animated gif. I'll see if I can do that, but it will not be before the 18'th.
Luc
It appears the minute hand moves when the second hand passes VI. I did not watch long enough to see: does the hour hand jump as the minute hand passes VI?
Ideally, the minute hand should move (less than a full step) each second. Alternatively, I would suggest that the minute hand could move a full step each time the second hand reaches XII.
Similarly, the hour hand should move (less than a full step) every minute (or every second), or a full step every 12 minutes (as the second hand reaches XII).
Regardless, your and Valery's efforts are more impressive than I could develop.
Edit: it appears the hour hand is currently programmed to move a step every 12 minutes. I was not watching as it moved to see if the second hand was passing VI or XII.
Here's some more to watch:
The hour and minute hands aren't 'programmed to move when'...
They move proportional to the time in seconds, but choose the closest one of the 60 possible positions along the perimeter of the ellipse. But the end effect of this is the same. You'll see the minute hand jump one step as soon as the second hand passes VI, and you'll see the hour hand jump one step every 12 minutes (1/5 th of an hour).
Luc
Thanks Luc!
Now I have this watch on my SmartPhone.
Send please the Mathcad sheet and/of the avi file!
Here she is.
Now capable of taking smaller resolution steps (= frames per second). Here's an example with 10 frames per second:
Mathcad file is attached.
Luc
Version 2017/11/15
I think the program needs a change, instead of round() use floor(), that makes the indication of the minutes and hours hands more true:
With this change, the minutes hands advances a step if the seconds hands passes XII, instead of VI. And the hours hands' first move will be at 12 minutes instead of at 6 minutes.
Luc.
I will discuss in Stuttgart the Idea than we will think about the realisation.
Did they like it?
@LucMeekes wrote:
Did they like it?
Yes! I have a talk with the Math prodecan of the UNI Stuttgart about this project!
Now I am in Dresden and have new Math project for Meisen porcelan factory
One math porcelan plate: (see please more https://en.wikipedia.org/wiki/Ehrenfried_Walther_von_Tschirnhaus)
The picture for the article