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Science

hunter

(38,368 posts)

8. It wasn't an approximation, the tables ARE exact.

Reply to Binkie The Clown (Reply #6)

Sat Aug 26, 2017, 01:20 PM

Aug 2017

Last edited Sat Aug 26, 2017, 08:11 PM - Edit history (1)

There are simply no entries for angles that can't be described exactly with known fractions.

To solve problems with angles that are not exact fractions, the user of the table might make a "good enough" interpolation between the known fractions by adding a familiar (to them) sexagesimal fraction, 1/60, 2/60, 3/60.... etc.

The Babylonians handled pi in a similar fashion, using the fraction 25/8 knowing it was a little short but good enough for most work.

For more critical work 25/8 + 1/60 was a pretty good approximation.

25/8 + 1/60 = 3.141666......

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Highlight:

Babylonian trigonometry "simpler, more accurate... has clear advantages over our own." [View all] eShirl Aug 2017 OP

"only completely accurate trigonometric table" -- an exceptional claim, requiring exceptional proof. eppur_se_muova Aug 2017 #1

Maybe they figured out how to make pi3... Wounded Bear Aug 2017 #2

I defer to those who know trig eShirl Aug 2017 #4

Did you watch the video? Jim__ Aug 2017 #5

It's the kind of sci-babble that happens when they try to explain something to the uneducated Binkie The Clown Aug 2017 #6

It wasn't an approximation, the tables ARE exact. hunter Aug 2017 #8

I want to know what they mean by 'simplified' values muriel_volestrangler Aug 2017 #9

They do clarify that in the paper. Jim__ Aug 2017 #11

I think it made more sense to someone having an intimate familiarity with sexagesimal fractions hunter Aug 2017 #12

I would also like to know what they meant by that FiveGoodMen Aug 2017 #7

Sounds to me like they used the next-more-complicated version of fractional numbers. DetlefK Aug 2017 #3

The full article in Historia Mathematica is available Jim__ Aug 2017 #10

The clear advantage of the trigonometry I use over that used by the Babylonians, is that I can... NNadir Aug 2017 #13