Additional Math Pages & Resources

Friday, October 2, 2009

Watch Your Language!

What is language? Simply stated, it's a formal means of sharing information with another person. You know that on another continent, or even in a remote neighborhood in your own town, you might hear people speaking a different language.

Most of us are multi-lingual to a certain extent. We feel angst, we can order a burrito. Our friends say Oy veycarpe diem, have a cerveza! And we usually understand if they shout, He knocked a blooper into shallow right. This isn't just slang, it's a sub-language for communicating special information.

If math is a language of counting, measurement, shapes and calculation; a language with precise and specialized terms, how does it intersect with other languages? Can we operate multi-lingually with math?

I'll give you an example.

I'm a novice watch repairman. At first I didn't know I needed to learn another language to fix watches. But I had to learn watchmaking lingo.

Watches are precision machines built for one primary function - to accurately count the passage of time. Secondarily they are fun, prestigious, glitzy and so on. Watch language supports this.

Let's look at a few watch terms, such as units of measuring size:

A unit of measure for pocket watches and mainsprings. It begins with the letter A.

An A watch = 1 inch diameter.

One sixteenth of an inch is added for each successive alpha character, so B = 1 1/16", C = 1 2/16", D = 1 3/16", etc. The most common sizes are L and N.

A unit of measure for watch movements. It begins at 0.

The 0 size = 1 and 5/30ths of an inch diameter.

One-thirtieth of an inch is added for each successive number, so  1 = 1 6/30th, 2 = 1 7/30th, etc. The most common sizes are 16 = 1 21/30" and 18 = 1 23/30".

A unit of measure for old French and Swiss PW movements. A ligne is 1/12 of an old French inch, and equals 2.256 mm (3/32nds of an inch). A Douzième ligne is 1/144th of an old French inch. An 18 ligne watch movement would be 1.5 French inches, or about 41 mm in diameter. That's the size of a men's wristwatch nowadays.

Can you imagine saying I'd like one that's 1 and 23/30ths of an inch? Much easier to say I'll have an 18 size pocket watch please.

These are math/watch terms dealing with the  function or operation of the watch:


A watch's timekeeping is maintained by a balance wheel that turns back and forth, regulating the speed of the unwinding mainspring which turns the hands. These words describe the watch's heart. It's adjusted to run at a rate of:

18,000 oscillations per hour (5 per second),
21,600 oscillations per hour (6 per second)
28,800 oscillations per hour (8 per second) or
36,000  oscillations per hour (10 per second)

This means the vibrations of a quartz crystal when stimulated by an electric current. Due to the nature of quartz, it's almost always 32,768 cycles per second (Hz). This frequency is the reference used by a quartz watch to count the time.

This word means the amount of time that a movement can run under its own power after being fully wound. Generally it's from 36-42 hours (it can run on your dresser more than 1 day but less than 2 days). Some watches run 100 hours (over the weekend), others up to 8 days. Wind-up clocks normally run either 8 days or 30 days between windings, although there are 400 day clocks (more than a year).

Here are some math/watch terms that define the purity of precious metals:

Watch cases are made of plastic, stainless steel, titanium, gold or platinum. Silver is rarely used as it quickly tarnishes. Because watches are constantly in contact with the skin, we need materials that don't corrode or cause allergic reactions. They also serve as jewelry, decoration and a sign of prosperity or good taste. For these reasons, watch cases and bracelets are often made from precious metals.

The unit of gold purity is the carat (karat). This is NOT the same carat used to weigh jewels

One K means 1/24 part of gold by weight or .042%  (24 x .0417 ≈ 1)

18 carat = 750/1000 or 75% gold by weight
14 carat = 583/1000 or 58% gold by weight

Platinum and Silver are measured in Parts Per Mil (1000).

980/1000 Mexican 98% pure silver
954/1000 Britannia 95.84% pure silver
950/1000 Japan Sterling 95% pure silver
925/1000 US / UK Sterling Silver, an alloy of 92.5% silver and 7.5% copper
900/1000 Coin silver or 90% pure silver sold in Mexico or Continental Europe
800/1000 80% silver sold outside the US, UK and France

950/1000  95% by weight (not volume) is platinum. The remaining 5% can be various elements, depending on the intended use of the piece.
900/1000  90% of the weight in platinum and 10% iridium.

Multi-Lingual Math/Watch Summary

Let's make a math sentence in this foreign language, s'il vous plait?

If your 18 ligne pocket watch with 36 hours of autonomy is beating at a rate of exactly 18,000 and is in a case marked 950, you can get a lot of money for it!

No comments:

Post a Comment

Type your comment here