Why is base 60 more precise for trigonometry, can you give an example?

https://math.stackexchange.com/questions/2405480/why-is-base-60-more-precise-for-trigonometry-can-you-give-an-example

by virgilkf • 9 years ago

2 7 9 years ago

math.stackexchange.com

Counting to twelve is easy with one hand. Counting to sixty is easy with two hands. It is a modern thing to count to ten with two hands.

virgilkf• 9 years ago

what?

moonbug22• 9 years ago

Two positions per finger, three for the thumb. If you are feeling dexterous, you can count to 48.

CarolineW• 9 years ago

What you say might be true - although there are many people who doubt it, with some quoting research papers - but it simply doesn't answer the question asked, and is pretty much a complete non sequitur.

oldandtired3• 9 years ago

People use what they use. So if they use base twelve or base sixty or binary or octal or hexadecimal or base five because they have a simple way of counting in that grouping then that's what you'll see them using. Just because we don't use it today doesn't mean anything.

oldandtired3• 9 years ago

Using thumb, press on each off the three segments of the finger starting at end. ---X---X---palm. Four fingers gives twelve positions, At each twelve, fold one finger and /or thumb to palm of other hand, easy.

Have a read of Knuth for other counting systems, including binary (English Wine Merchants)

ordu• 9 years ago

With decimal numbers we can write 1/3 as 3/10+3/100+3/1000+..., it is infinite series converging to 1/3. With base 60 we can write it as 20/60, just one term of series is not null. When dealing with infinite series one would need to pick few first terms of series dropping the rest thus losing precision.

With decimal numbers we can write down exact quotient when divide by powers of 2 and 5, because 10=2 * 5. With base twelve we could write exact quotients from division by powers of 2 and 3. With base 60 we could write anything that comes from division by powers of 2, 3 and 5. It can be archieved with base 30=2 * 3 * 5, and I'm not sure that base 60 superior to 30, it do not allow to write more fractional numbers precisely. Maybe it sometimes simplifies arithmetic operations though. I believe, it is easier to divide by 4 in base 60 than in base 30.

Now we have processors that can deal with great amount of terms of series and can keep any reasonable precision we need (in the most cases at least), but back then it was hard work for skilled enough to deal with arithmetic operations.

Why is base 60 more precise for trigonometry, can you give an example?

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