Wikipedia:Reference desk/Archives/Mathematics/2007 January 2

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January 2

Nagorno-Karabakh

Hi, Dear Wikipedia!

I am from Azerbaijan. You have indicated the Nagorno-Karabakh (an integral and historical part of Azerbaijan)as an independent country in the list of World Countries. It is very erronous. It is not an independent country, you have made mistake. The Armenia republic invaded our lands.

Please make amenment to this prestiged encyclopedia.

Azerbaijan, Baku

Mr Qurban Rzayev

P.S.

Please forward this letter to the Editorial Board of Wikipedia I couldn't find their e-mail —Preceding unsigned comment added by 62.217.141.48 (talk • contribs)

Mr Rzayev - Wikipedia is written by anyone who wishes to contribute, so there is no Editorial Board - to find out more about how Wikipedia works, you might like to read Wikipedia:About and Wikipedia:Who writes Wikipedia. With regard to Nagorno-Karabakh, our article on that region says "the Nagorno-Karabakh Republic (NKR) ... remains unrecognized by any international organization or country", and Nagorno-Karabakh appears on our list of unrecognized countries. There is a note at the top of the list of countries which explains that this list includes some "countries" that are not internationally recognised. This list page also notes that Nagorno-Karabakh is a de facto (i.e. self declared) independent state which is unrecognised by any United Nations member state. Gandalf61 10:15, 2 January 2007 (UTC)

(Somehow I have the feeling that this is not a mathematics topic.) Additionally, the list of countries (which is what I presume you mean by "the list of World Countries") mentions clearly in its first sentence that the list includes states that are generally unrecognized.  --Lambiam^Talk 11:52, 2 January 2007 (UTC)

Sure it's a math question, we are debating whether Nagorno-Karabakh is a proper or improper fraction of Azerbaijan. :-) StuRat 13:29, 2 January 2007 (UTC)

Also note that Nagorno-Karabakh is an integral. -- Meni Rosenfeld (talk) 14:22, 2 January 2007 (UTC)

I would have thought that Nagorno-Karabakh culture was derivative of Azerbaijani culture. :-) StuRat 00:38, 3 January 2007 (UTC)

Radian

Ok, I feel awkward for not understanding this but I'll throw away my egoism and ask the following:

A circles length is 0.4π we roll it so it rotates up until it creates an angle of 80rad. What will be the distance that has covered? Please, give me a brief explanation along with the result, as there is more homework like this. --87.203.55.12 20:21, 2 January 2007 (UTC)

Is that really how the question is worded? —Bkell (talk) 20:30, 2 January 2007 (UTC)

Of course not, just my english are bad. Let's try again... It's a really long exercise in physics, whose mathematics part goes: on the one side of a pulley (r=0,2, so c=0,4π) we have a movable with a mass M and we let it fall. After the pulley has rotated for 80rad, how far has the movable gone from his original location? --87.203.55.12 20:37, 2 January 2007 (UTC)

A radian is the name for a length of a circle's circumference equal to the circle's radius, or for the angle defined by that measurement. If one radian of circumference has a length of one radius, then how many radiuses are there in 80 radians of circumference? --Carnildo 20:35, 2 January 2007 (UTC)

Thanks everyone for your will to help, even though you didn't understand the question. I have just called a friend and found out. Have a nice day and a happy new year! --87.203.55.12 20:56, 2 January 2007 (UTC)

Question along the lines of this: Is the circumference of a circle 2π radiands? I have read the wikipedia article but i dont really understand radians. —The preceding unsigned comment was added by 81.129.12.4 (talk) 19:46, 6 January 2007 (UTC).

Not exactly; radians should be considered a measure of angle, not distance. But you're on the right track. Consider a circle with radius R. The circumference has a length of 2πR. When R equals 1, the circumference is 2π. Now, from the center of the unit circle mark off an angle. Contained within that angle is a piece of the circumference. The numeric value of the length of that piece, which clearly is between 0 and 2π, is the radian measure of the angle. A slightly cleaner way to say this is that we consider a central angle in a circle of any radius, R, and take the radian measure of the angle to be the ratio between the length of the subtended circumference and the radius. This both eliminates the units of length and renders the size of the circle irrelevant.

As a specific example, suppose we divide a circle of radius 5 cm into 12 equal pieces. If we were working in degrees, the angle of each piece would be 360°/12, or 30°. The circumference of the circle is 2πR, or 10π cm, so each sector cuts off a circumference length of ^10π⁄₁₂ cm. Dividing by R (which is 5 cm), we find that the radian measure equivalent to 30° is ^π⁄₆.

Where degree measure artifically and arbitrarily divides the circle into 360 pieces (which was convenient in ancient Babylon), radian measure uses a natural ratio that simplifies many a trigonometric expression (which is convenient in modern mathematics).

Why 360 degrees? (1) A year has just over 360 days. (2) The integer 360 is easily divided in many ways. (3) When a circle is divided into 6 equal pieces by inscribing a regular hexagon, each side of the hexagon (which is a chord of the circle) has the same length as the radius, so a convenient multiple of 6 might be useful, with 60 the obvious multiplier in their number system. (4) Who knows?

A compelling example of the benefit of radian measure is Euler's formula,

$\exp(\mathbf {i} \theta )=\cos(\theta )+\mathbf {i} \sin(\theta ).\,\!$

This finds wide and crucial application, and only works when θ uses radian measure. --KSmrq^T 11:55, 7 January 2007 (UTC)