OK boys, this one has been a wonderment to me for years.

 

They tell me that the ancient Greeks came up with the formula for the sine tables. Now, since these constants are expressed in numbers carried out to 7 or 8 decimal places, how did these old boys figure that shit out in the first place? How did they come up with Pi?

 

They didn't have all the stuff to take measurements that we do today. So my question is, is there some sort of natural law that they were able to apply to get the sines, cosines, tangents, etc?

I was recentlly wondering that myself. I too, would like to know that.

What kind of number system did they use?

I'm not sure, but I don't think they understood the concept of zero. That was the arabs that introduced zero.

The greeks didn't have decimal notation or zero. I can tell you they calculated pi with inscribed and circumscribed polygons and determining that pi must be bounded between those two perimiters. But calculating the perimiters takes trig functions and I don't know how they found the trig ratios.

Try

 

http://mathworld.wolfram.com/RegularPolygon.html

 

They refer to the Greeks and pi and trig functions.

Gee, they must have some kind of formula. You see it in computer programs, with sin functions. Even in programs like VB they have premade functions of sine in radians. Try asking a comp expert and he might know, although the idea seems absurd.

The formula is supposedly the McClauren (SP?) series for sine - that is

x - x^3/3! + x^5/5! -... + (-1)^k*x^(2k+1)/(2k+1)!

-Uncool-

OK boys' date=' this one has been a wonderment to me for years.

 

They tell me that the ancient Greeks came up with the formula for the sine tables. Now, since these constants are expressed in numbers carried out to 7 or 8 decimal places, how did these old boys figure that shit out in the first place? How did they come up with Pi?

 

They didn't have all the stuff to take measurements that we do today. So my question is, is there some sort of natural law that they were able to apply to get the sines, cosines, tangents, etc? [/quote']

 

Haven't read this anywhere, but I think being masters of geometry, they would just inscribe a right triangle inside of a circle. The trig functions simply express the ratios of the adj, opp and hyp sides of the triangle. They can express these ratios without knowing the complete number, much as we use PI without knowing it exactly.

wasn't it archimetese who solved pi by puting something like 20 different multisided polygons inside and outside a circle?

Yeh, he basically kept putting sides onto an octogan, nonogan, decagon etc. eventually he got 3.14 and then gave up.

OK boys' date=' this one has been a wonderment to me for years.

 

They tell me that the ancient Greeks came up with the formula for the sine tables. Now, since these constants are expressed in numbers carried out to 7 or 8 decimal places, how did these old boys figure that shit out in the first place? How did they come up with Pi?

 

They didn't have all the stuff to take measurements that we do today. So my question is, is there some sort of natural law that they were able to apply to get the sines, cosines, tangents, etc? [/quote']

 

I'm working this out in another thread syntax. There is a link to Archimedes' method there. They way I'm going to do it, is different from the method that Archimedes' used. First I am going to do it a simple way, which will connect to the concept of limit, and then I will study the link there, which explains the method which Archimedes' used.

 

There is a comment made about a German mathematician named Carl von Lindemann, and the comment is that 1852-Lindemann-1939 was the first person to prove that pi is a transcendental number. This is still new to me really. I know that a number is not transcendental if it is a root to an algebraic equation with rational coefficients.

 

Somehow, the claim is that Lindemann proved that you cannot carry out Archimedes method for computing pi, using only steps allowed by Euclid. I am working on understanding this now.

 

Kind regards