Why 360 degrees?

[FrankM]

An astronomical instrument was built that used decimal degrees some 200 years ago.

The circle is divided into 400 decimal degrees numbered five by five, and each degree is then

divided into 20 parts.

decimal degree

 

A 1/400th division of a circle is a grad.

 

Many scientific calculators allow one to use deg, rad or grad in the display.

 

Grad. The grad is a metric unit of measure found on some foreign maps. There are 400 grads in

a circle (a 90-degree right angle equals 100 grads). The grad is divided into 100 centesimal minutes

(centigrads) and the minute into 100 centesimal seconds (milligrads).

The above quoted from, orienteering

 

It doesn't seem logical to adopt metric measurements for everything else, then leave angular and time

measurement linked to a base 60 system.

[Freethinker]

Originally posted by: Robust

As I recall, Freethinker, the Chaldean empire did not come into existence until about 500 BC.

OK, I already covered that in my earlier post and your off by almost a century:

Originally posted by: Freethinker

The Chaldean dynasty in Babylon during the reign of Nebuchadnezzar (605-562 BC)

You add:

The earliest pi value we have (which I believe is the correct one) dates some 5,000 years prior,

Again, what you are specifically claiming is:

 

1) you agree that the Chaldean empire existed aprox 500 (more correctly 600) BCE.

 

2) you claim pi was known "some 5,000 years prior"

 

therefore you are claiming that pi was known 5,500- 5,600 BCE. Please provide VALID FACTUAL support for this. (So far when asked for facts to prove your claim, you only give more claims)

 

The earliest written record I am aware of for pi is one Old Babylonian tablet (from ca. 1900-1680 BCE) indicates a value of 3.125 for pi.

 

You have an additional 3,600- 4,000 years to PROVE.

so the 360-degree circle, Base 10 number system, etc. dates to that period and perhaps much earlier.

First, you have yet to support your claim of pi being known over 7,500 years ago.

 

Now you also need to prove that determining the ratio PI, requires that we use either base 10 or that dividing a circle into 360 degrees would be a natural result of learning PI.

 

You have failed so far at all of this.

 

Well?

[Freethinker]

Originally posted by: Moonchild

Also, remember this:

 

In a sine wave, 360 degrees is like a full wave, which is 2pi. (4 units total on x-axis).

A sine wave is just a circle transcibed onto a linear time scale.

 

But none of this explains WHY 360 units.

[Moonchild]

OK - I want all of you, especially Freethinker, to graph a sine wave on a graphing calculator. If you don't have one, get one.

 

You will see that the first full wave is four units long. If that wave were a circle with center at origin and intersecting the axes one unit away from the origin, one full circumference would be 2pi radians. That's the same as three hundred and sixty degrees.

 

 

Maybe it would help, Robust, if you compared this circle described above with special right triangles. They correlate in some special way.

[Freethinker]

Originally posted by: Moonchild

OK - I want all of you, especially Freethinker, to graph a sine wave on a graphing calculator. If you don't have one, get one.

I was manually grafing sinewaves before calculators existed.

You will see that the first full wave is four units long.

Arbitrary divisions. It could be 2, 5, 6.8,

If that wave were a circle with center at origin

Makes no sense. "center at origin" of what?

and intersecting the axes one unit

What "unit" are you referring to? One based on arbitrarily chosen 360 degrees in a circle?

 

Back to square one.

[Robust]

Moonchild, I don't have a graphing calculator, but sure as hell going to get one now!....sounds like fun. With regard to right angle triangles, here's a formulae (2 part) I came up with for determining the quadrant chord length and distance on the arc. I call it the trianglature formulae:

 

1) r*sqrt2 describes a right angle triangle, the hypotenuse of which gives the quadrant chord length;

 

2) Hypotenuse*pi/4*sqrt2 = quadrant distance.

 

 

"All things number and harmony." - Pythagoras

[Tormod]

Try this one, it's free.

 

http://www.algebrahelp.com/calculators/function/graphing/index.jsp

[Moonchild]

Sorry, Freethinker, I meant the UNIT CIRCLE.

 

If its linear sine form is graphed, y=sin(x), then one complete "wavelenth" is four units long. The length of the wave four units to the right of the origin is 2pi, which as we now all know is equivalent to 360 degrees. So, Freethinker, sorry if I confused you.

[Robust]

Hey!...big help, Tormod...thanks much!

[FrankM]

The length of the wave four units to the right of the origin is 2pi, which as we now all know is equivalent

to 360 degrees.

 

The relationship of Pi to a circle or is representation on a linear graph does not change if the definition of

the divisions of a circle are changed. An example would be from deg to stat, the quarter wave crossovers

would be at 100, 200, 300 and 400 stats.

 

If the circle segments were broken into 1000 units, then 250, 500, 750 and 1000 would be the quarter wave

crossovers.

[Freethinker]

Originally posted by: Moonchild

If its linear sine form is graphed, y=sin(x),

If you keep using rubric based on 360 degress, you will keep getting 360 degree units.

 

This does not demand a 360 unit division to a circle.

The question is NOT, how do we work with a 360 degree circle.

 

But "WHY 360?"

then one complete "wavelenth" is four units long.

Wavelength is not measured in "four units". Wavelength is measured in distance/time.

The length of the wave four units to the right of the origin is 2pi,

Only if there is the PREsupposition of what those "units" represent that is based on a 360 degree sine function.

 

We could assign ANY arbitrary rubric to the "units" and thus "four units" could be more than one wave or less than 1/4 wave.

 

None of this explains WHY 360 divisions were arbitrarily selected.

[Freethinker]

Originally posted by: Robust

the 360-degree circle was established at least some 5,000 years before the Chaldean empire.

 

We are all still waiting for you to either prove this or admit it is wrong.

[Robust]

Freethinker, I'll readily admit to being wrong if shown to be. The oldest archeological record we have showing a pi ratio to the circle is about 5,000 BC. As stated, and as I understand it, the Chaldean empire did not come into being until about 500 BC. But allow me to carry on....

 

Relating again to the right angle triangle, here is yet another formula I came up with and which I feel further substantiates th 360-degree circle (its initial giving).

 

Diameter/180 degrees gives a right angle triangle denoting equal dimension to both the X and Y axis. As with the given trianglature formulae, the hypotenuse in this instance giving the chord length between each angular degree; its distance on the arc given by the same aforementioned conversion factor: pi/4*sqrt 2.

 

 

"All things number and harmony." - Pythagoras

[Freethinker]

Originally posted by: Robust

the 360-degree circle was established at least some 5,000 years before the Chaldean empire.

Note that first your claim was that the 360 divisioning (degrees) is dated 7,500 years ago (5,000 years before 600 BCE Chaldean Empire)

Originally posted by: Robust

Freethinker, I'll readily admit to being wrong if shown to be. The oldest archeological record we have showing a pi ratio to the circle is about 5,000 BC.

But now you want to change it to only PI?

 

Yet you have not provided the first shred of evidence to support EITHER claim.

 

Please provide verifyable refence sources to show either/ both of these, or admit you do not have them.

 

Stop making us all waste time reading the request and your red herrings in response.

[Freethinker]

Originally posted by: Robust

Relating again to the right angle triangle,

Who cares about triangles? The topic is:

 

Why 360 degrees? in a CIRCLE!

here is yet another formula I came up with and which I feel further substantiates th 360-degree circle (its initial giving).

The issue is NOT why YOU feel 360 degrees is valid.

 

Why do you keep trying to use red herrings? Dragging the discussion AWAY from the ACTUAL topic?

 

Can you SHOW us verifyable proof that the 360 degrees we currently use for a circle was used 7,500 years ago or not?

 

If not just admit it.

Diameter/180 degrees gives a right angle triangle denoting equal dimension....

Yada yada yada...

 

If you want to discuss formulas dealing with geometric shapes, start a thread for it.

 

The question here is WHEN/ WHY was the circle divided up into the 360 units we use today.

 

YOU claim it was 7,500 years ago.

 

PROVE IT!

[Moonchild]

It was the Jews.

[Robust]

What is your problem, Freethinker? I' m trying to be educative, not arguementitive. These things are all easily researched on ther web. If the pi ratio was not given to discern line an arc relationships of the circle, then what for? The right angle triangle is an intergral part of this discernment. For example, dividing a diameter of 9 by 180 degrees gives a right angle triangle with equal legs of 0.05 as giving distance on the X and Y axis and as correlating with degree-distance on the arc....as shown. Why would you think that is not relevant?