What is the name of the longest chord in a circle?
829353
the longest chord .... the one that passes through the center ... is a diameter
343495
To find arc length, you need the angle that the arc subtends and the radius of the circle.  To find the angle, you'd have to do some geometry...\n\nImagine a triangle with sides 10, 10, and 5.  This is pretty much a chord on your circle (5) and the radii from the center to the ends of the chord (10).  If you draw a line from the center perpendicular to the chord, it bisects the chord.  This gives you two right triangles, with hypotenuse 10, side 2.5 (half the chord), and side unknown (the segment from the center to the chord).  To find the angle at the center formed by the radius and the unknown, you can use the sine function:\n\nangle = arcsin(opposite/hypotenuse)\nangle = arcsin(2.5/10)\nangle = 14.48 degrees or 0.25 radians\n\nThe total angle is then 0.5 radians, since the above only found half of that total angle.\n\nThe formula for arc length is\n\narc length = radius * angle\n= 10 cm * 0.5 rad\n= 5 cm\n\nAnd this kinda makes sense - if the total circumference is 20pi, and the arc is 28.96 degrees, then the arc length can also be found by\n\narc length = angle * circumference/360\n= 28.96 * 20pi/360\n= 5 cm
428953
Pentagons occur naturally when tying knots due to the same reason that when strings are pulled taut, and a fret is placed in the middle, that the pitch that it plays on either side of the fret is a 'perfect fifth.' The idea is that the knot is exactly half the distance away from its other side within the knot itself. If one wants to see how this happens naturally, all you have to do is draw a five-pointed star, turn the page 180 degrees, and then draw another five-pointed star the others middle. This can be done ad infinitum inward or outward until physics prevents it from occurring. \n\nThe irony is: the perfect fifth is not what makes music music per se, rather it is the diminished fifth, the tri-tone, or so called devil's tone that makes music capable of changing keys from one to the next. Though, the reason that this happens is due to the natural harmonics that occur in the environment, that make the diminished fifth the actual additive center (where the perfect fifth is its multiplicative one) from the root to the octave. Knowing these two sets of mathematics and where they overlap, eerily\ncan define pretty much any physical phenomena from the Relative to the Quantum. (Unfortunately, there are very peculiar rules that establish how the sets occur whose overtones include concepts such as inverses, opposites, paradigm, zero, and the infinite.) And chances are that disarming your knots will probably find us an answer to the Zeta function. Good luck!\n\nOn a side note: it was Pythagoras who (is ironically famous for someone anonymous' theorem) started a cult around the idea of the perfect fifth, which eventually made the pentagram the infamous symbol that it is today. But this was not until after, he was murdered by a band of math conscious rioters who decided his cult was evil because they had been hiding the existence of the irrational numbers, which exist due to the multiplicative tendencies of an additive system of measurement.\n\nThat's all for which I have time.
878810
"The Devil Glitch" has been named by Guiness as the worlds longest song.  It is 69 minutes long and has 500 versus.
44921
the longest side is the one opposite the largest angle.  the shortest side is the one opposite the smallest angle.  an excellent example pertains to right triangle and the formula a^2 + b^2 = c^2  where c is the hypoteneuse and a and b are the two smaller sides.
169663
No, there is not. Circle is part of called Conic Graphs.\nA circle can be described as all points that are at the same distance (radius) of a fixed point (center). You can not give this kind of description about a triangle or square.\nNow, the truth is that you can describe -for example- an square with four lines (y=a , y=b, x=a, x=b)but you can not put everything in a single equation, besides this, this kind of lines are infinites (y=a from -inf to inf).\nThere are other kind of equations that gives you the area or perimeter of these shapes (i.e: b*h/2), but this is not what you're looking for.\nSo, again: There are NO equation of a triangle.
93089
This seems like a homework problem, so I'll give a few hints.\n\nThe arclength is radius times the angle subtended.\n\nTo find the angle subtended, consider the isosceles triangle created inside the circle where the chord is the hypotenuse and the radius of the circle is the two other legs. \n\nSince the isosceles triangle created is not a right triangle you need to use a specific formula to find the angle "C" subtended by the chord.
1141551
http://www.e-chords.com\nIt's really good and has a couple of downlodable chord charts. I use it a lot.\nHappy playing!
1048695
http://www.chordfind.com\n\nthis is where i go to look up new chords i'm not familiar with.\nhope this helps.
506532
Ahhhhhhh... isn't it great to be 30 going on 10.  Life it too short to be grown up.  Greatest shaped object huh.... okay well lets see.... you have limited my choices here, that is not fair btw. :p ~ How about a circle.  You can not invert it mathematically.  It has no beginning nor ending.  You can do so many wonderful things with it, such as foot ball, balloons, rings and what not.  It is perfect, yet can not be computed to the last digit (PI) and last but not least, because I say so.  LOL  :)
460850
http://en.wikipedia.org/wiki/Jakob_Steiner\nhttp://mathcircle.berkeley.edu/BMC3/constr2/node6.html
898544
This is a neat problem, and I am sure that there are many ways to solve it. I will be interested in seeing if the different ways to solve it end up producing answers that are at all similar.\n\nHere is what I did. I'll start with part (b), since I found it to be easier.\n\nIf x > 7, then the largest angle is the angle opposite the side having length x. This is the included angle of the sides having length 4 and 7.\n\nUse the law of cosines to relate the lengths of the two shorter sides and their included angle to the side having length x.\n\nc^2 = a^2 + b^2 - 2abcos(theta)\nx^2 = 4^2 + 7^2 - 2(4)(7)cos(theta)\n\nx^2 = 16 + 49 - 56cos(theta)\nx^2 - 65 = -56cos(theta)\ncos(theta) = (65 - x^2)/56\n\nOr, theta = arccos[(65 - x^2)/56]\n\nIn this case, x must be greater than 7 and less than 11.\n\nIf x is less than 7, then the largest angle is the angle opposite the side having length 7. This is the included angle of the sides having lengths 4 and x.\n\nMy first idea didn't work, so let's try something that could be even uglier :D\n\nCall the included angle of the sides of length 4 and 7 alpha.\n\nUsing the law of cosines, \n\nc^2 = a^2 + b^2 - 2abcos(alpha)\nx^2 = 4^2 + 7^2 - 2(4)(7)cos(alpha)\n\nx^2 = 16 + 49 - 56cos(alpha)\nx^2 - 65 = -56cos(alpha)\ncos(alpha) = (65 - x^2)/56\n\nLet's derive sin(alpha) from cos(alpha).\n\nSince sin^2(alpha) + cos^2(alpha) = 1,\n\nsin(alpha) = sqrt[1 - cos^2(alpha)]\n=sqrt{1 - [(65 - x^2)/56]^2}\n\nAt this point, you're probably wondering what this has to do with theta.\n\nNow that we know sin(alpha), we can use the law of sines on two of the sides of the triangle, and the angles opposite them.\n\na/sin(A) = b/sin(B) = c/sin(C)\n\nIn this case, theta is still the angle opposite the side having length 7. alpha is the angle opposite the side having length x.\n\nSo:\n\nx/sin(alpha) = 7/sin(theta)\n\nor\n\nsin(theta) = 7sin(alpha)/x\n\nWe know sin(alpha):\n\nsin(theta) = 7*sqrt{1 - [(65 - x^2)/56]^2}/x\n\nSo theta equals arcsin [7*sqrt{1 - [(65 - x^2)/56]^2}/x]\n\nThat's not very pretty.\n\nIn this case, x must be greater than 3 and less than 7.
543816
Yes it is !!\n\nFor proof of volume of cone, pls go to :\n\nhttp://mathforum.org/library/drmath/view/53646.html\n\n\nThe following site has got the proof for area of circle :-\n\n\nhttp://64.233.161.104/search?q=cache:FbBn10NweQkJ:www.artofproblemsolving.com/LaTeX/Examples/AreaOfACircle.pdf+area%2Bcircle%2Bproof&hl=en&gl=in&ct=clnk&cd=1
94010
since theres so many chord possibilities, i would recommend getting a piano chord dictionary. you can find them at most any music store that deals with piano at all, or online of course.  they are relatively cheap, and wil show you the fingereing for most any piano chord you can come up with
867384
http://thinkexist.com/dictionary/meaning/chord/
907992
http://www.last.fm/music/Xtension+Chords
793145
Think about what chord you are playing the most.  That would usually be the "tonic chord" and the lowest note of that chord is the name of the key. If you know the name of that chord, that is the name of the key as well.  If you don't know the name, but can hear the same note played on a guitar and piano, then match that note to a key to figure out what the name of the note is.  The white key before a group of two black keys is called C. The white keys are in order c,d,e,f,g,a,b, and then you should be at c again.  The balck notes are the same letters plus sharp if the note is higher than the white key ex. c sharp  or flat if the balck note is lower than the white key- d flat.  b and c and e and f are next to each other without a black note betwen them.  This pattern of balck and white notes on the piano keyboard repeats many times- each repeat is called an octave.