Computer Science – Learning
Scientific paper
Aug 2006
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2006iauss...2e..87k&link_type=abstract
Innovation in Teaching/Learning Astronomy Methods, 26th meeting of the IAU, Special Session 2, 17-18 August, 2006 in Prague, Cze
Computer Science
Learning
Scientific paper
The mathematical model of the astronomical clock of Prague was developed by the professor of Prague University, Joannes Andreae, called Sindel. It was realized by Mikulas from Kadan around 1410. Over the centuries its construction has been renovated several times. The ingenuity of clockmakers of that time can be demonstrated by the following construction. The astronomical clock of Prague contains a large gear with 24 slots at increasing distances along its circumference. This arrangement allows for a periodic repetition of 1-24 strokes of the bell each day. There is also a small auxiliary gear whose circumference is divided by 6 slots into segments of arc lengths 1, 2, 3, 4, 3, 2. These numbers form a period which repeats after each revolution and their sum is s = 15. At the beginning of every hour a catch rises, both gears start to revolve and the bell chimes. The gears stop when the catch simultaneously falls back into the slots on both gears. The bell strikes 1 + 2 + ... + 24 = 300 times every day. Since this number is divisible by s = 15, the small gear is always at the same position at the beginning of each day. The large gear has 120 interior teeth which drop into a pin gear with 6 little horizontal bars that surround the centre of the small gear. The large gear revolves one time per day and therefore, the small gear revolves 20 times per day with approximately 4 times greater circumferential speed, since its circumference is 5 times smaller. This makes the regulation of strokes sufficiently precise despite the wearing out of the slots on the large gear. When the small gear revolves it generates by means of its slots a periodic sequence whose particular sums correspond to the number of strokes of the bell at each hour: 1, 2, 3, 4, 5 = 3 + 2, 6 = 1 + 2 + 3, 7 = 4 + 3, 8 = 2 + 1 + 2 + 3, 9 = 4 + 3 + 2, ... We show that we could continue in this way until infinity. However, not all periodic sequences have such a nice summation property. The astronomical clock of Prague is probably the oldest still functioning clock that contains such an apparatus.
Křížek Miroslav
Šolcová Alena
Somer L.
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