by: Martin Sagendorf
Clocks measure time – it can be a continuous measure of events passing or the measure of the interval between two events.
After years of evolution, our modern clocks now divide the day into 24 equal length hours. And, as we know, there are two systems in use today: Americans use the “double-twelve” system while the rest of the world uses the 24 hour system.
As An Aside:
The word “hour’ comes from the Latin and Greek words meaning season, or time of day. A “minute” from the medieval Latin pars minuta prima (first minute or small part), originally described the one-sixtieth of a unit in the Babylonian system of sexagesimal fractions. And “second” from partes minutae secundae, was a further subdivision on the base of sixty – i.e. “a second minute”. (ref. Pg. 42 The Discoverers by Daniel J. Boorstin)
The “Double-Twelve” Clock Face:
Has 12 at the top – probably because at noon the sun is at its highest point in the sky.
We can make a clock with 12 o’clock anywhere we wish and the clock will still work just fine.
Here we have a clock with 12:00 where 5:00 usually is. Now, if the hour hand points to 12 and the minute hand points to 2, the time would be 10 minutes past 12.
We can rearrange the face:
We can replace the numbers:
We can divide the day into ten hours (times 2).
Suitable Clocks & How to Make Your Own Clock Face:
– Good candidates are battery operated clocks with face diameters of 8 inches or less.
– There are a variety of these clocks – all I’ve seen can be disassembled if one is careful. When a front cover face must be removed, it is usually secured by three small tabs at the inner part of the face – use a worn common screwdriver to gently pry inwards, over a tab location, between the side of the cover face and the clock body – this will release the tab and allow the cover face to be gently ‘worked’ outwards. Other clock designs are held together by multiple screws from the rear – be careful, some of these have real glass for the cover face.
– The hands can be pried-off by using one’s fingernails on opposite sides of the hub of each hand.
– A new dial face should be of ‘card stock’ (8-1/2” x 11” is readily available) – standard weight paper is too light.
– A dial face must be a little smaller (1/16” on the diameter) than the opening into which it is placed – this will prevent buckling from expansion due to high humidity.
– The dial face can be hand-drawn or computer-generated (using any of the popular computer drawing programs).
– A punch or a craft knife can be used to cut out the center hole.
– Sometimes the original dial face can be removed – sometimes not – it is not really necessary. In either case, multiple small pieces of double-sided tape are used to fasten the new dial face.
– When reinstalling the hands, they must be synchronized – the easiest way to do this is to set (press on) all the hands pointing to the (original) 12:00 position.
Over the years I, and my students, have made dozens of different clock faces – there seems to be never-ending variations. You, and your students, will think of many different ones – just think of anything that represents numbers. And, what’s neat is that each individual clock can have the maker’s name and/or school name included on its face.
Marty Sagendorf is a retired physicist and teacher; he is a firm believer in the value of hands-on experiences when learning physics. He authored the book Physics Demonstration Apparatus. This amazing book is available from Educational Innovations – it includes ideas and construction details for the creation and use of a wide spectrum of awe-inspiring physics demonstrations and laboratory equipment. Included are 49 detailed sections describing hands-on apparatus illustrating mechanical, electrical, acoustical, thermal, optical, gravitational, and magnetic topics. This book also includes sections on tips and hints, materials sources, and reproducible labels.
I am interested in a mathematical expressions clock being made for a good friend. I would like to know if you are still doing this. I have a picture that I could scan and email to you if you’d like to see it. Please let me know.
PS – In the subject line of your email, please put mathematical expressions clock.
If you were to pulse a clockwork every 730 seconds (~3^5) with a clockface displaying the 1 at top… Would seem to make an accurate