Can the ratio of a geometric progression be 1?
920567
I do not see anything wrong with this as this meets the definition and OK. However from a practical use this does not make any useful sense.
661975
Yes, \n\nCI = P { (1+r/100)^n-1}\n\nEquate that to 2^n/3
1167304
Yes. Phi, 1.618, is the golden number. It is the ratio of two lengths such that the ratio between the longer and the shorter length is the same as the ratio between the whole and the longer length.\n\nIf a rectangle is constructed with these ratio's, it can be iteratively subdivided into smaller and smaller golden rectangles, forming an arithmetic spiral. This spiral, when copied and rotated 180 degrees, is the shape that all spiral galaxies take.\n\nPhi is related to the fibonacci sequence. 99% of sunflowers have a fibonnoci number of seeds arranged in this spiral shape.\n\nPhi is approximately the ratio between the lengths of one bone in the finger and the next.\n\nThe list goes on... too tired right now to remember more\n\nEdit - holy crap, I didn't know that about the bees. Mind so blown right now.\n\nAlso Edit - Gardener's book deals mostly with very loose claims that certain peices of ancient archetecture incorporates knowledge of the number Phi. His points are well thought out and thorough, and have discredited many specious claims about Phi's use in this area. However, the physical manifestations of Phi are very real and undeniable.
594571
3:1 ratio in favor of black
173766
same as differnce between 1 and 2
607889
can only be divided by 1 and themselves
1161642
It's approximately equal to 1.61803398874989...,\nand is equal to [1 + sq.rt.(5)] / 2.\n\nThe ancient Greeks thought it was divine because the ratio of 1:1.618... provided what they termed the perfect rectangle in architecture.  The ratio 1:1.618... is equal to 0.618...:1\n\nMathematically, it's the only number that when squared is one more than itself.  \n1.61803398874989... * 1.61803398874989... = 2.61803398874989...,\nthough the numbers are irrational, continuing infininely with no repeating pattern.\n\nThe ratio appears in regular pentagons (starfish), Archimedean spirals (seashells), and in DaVinci's proportions in drawing the human figure.\n\n[Edited to comment]\nAll of jalonzmommy's crap doesn't answer the question asked.\nAlso, check out http://en.wikipedia.org/wiki/Golden_ratio
944835
Yes, you're right.  The only way to get a parralel line w/ x=6 is another vertical line.  So if x=4, the only possible perp line is y=6. Always hated those "trick" questions!  They seem so hard, yet are ridiculously easy.
893652
with 1q, 2 ways (0,1 n)\nwith 3d, 1 ways (0 n)\nwith 2d, 3 ways (0,1,2 n)\nwith 1d, 5 ways (0,1,2,3,4 n)\nwith 0d, 7 ways (0,1,2,3,4,5,6 n)\n\nTotal of 18 ways
287856
This seems not a geometric sequence:\n\nU(1) = 6*(1/2)^1-1 = 2.0\nU(2) = 6*(1/2)^2-1 = 0.5\nU(3) = 6*(1/2)^3-1 = -0.25\n\nU(3) / U(2) is not the same as U(2) / U(1)\n\nDo you mean geometric sequence or geometric series?\n\n------- more note ---------\n\nThe answer by another user below indicated that the formula was: U(n) = 6*(1/2)^(n-1).\n\nSomeone needs to learn more about math operators and their precedence :-).
699573
Yes it is with radius of curvature = ∞\n\nHigher geometry takes this for granted
210386
I think the point may be to use synthetic division.  Look that up in your text.
991638
I don't believe it can.  This is an example of a unicursal problem and you can find some more details at the puzzle link in the reference below, you'll need to scroll down to puzzle number 51.\n\nFrom my days of O Level Maths I remember that we touched on these and I seem to recall that there was an equation to do with the number of vertices and nodes that a shape had which would determine if it was unicursal or not.\n\nBasically only unicursal shapes (those with a specific ratio of nodes and vertices) can be drawn without removing a pencil from the page and without tracing over an existing line.\n\nI'll leave further research to you.\n\nHave fun
103215
With this given data, it is not possible\n\nalthough the area is totalling to be 70 for both cases (7*10 and two pieces of 8*8 + 1*6) but with one division only, this is not possible\n\nPLEASE DO LET ME KNOW IF THERE IS SOME SOLUTION (i found it very interesting)
1030368
(a1* ... *aN)^(1/N)\n\nAs soon as you find the geometric sequence\n\n(a1 * a2 * a3 * a4 * a5 * a6)^(1/6)\nwould be an example of geometric meant, assuming you know a1 through a6\n\nLets say you had\n\n1, 2, 4, 8, 16, 32\n\nThe pattern would be 2^(n - 1)\n\nThe geometric mean would be done like this\n\n(1 * 2 * 4 * 8 * 16 * 32)^(1/6) = 32768^(1/6) = 5.6568542...
889429
1) Yup. a_1 - 5 = a_2, so a_1 must be 3.\n2) What does the common ratio actually mean? Its any term divided by the term before it. So in this case, the common ratio is just (-3)/(-2) = 1.5. Now, how would you get the first term? To go from the first term to the second you'd multiply by 1.5; thus to go from the second to the first, divide by 1.5: -2/1.5 = -4/3 is the first term.
304995
1{p+5}/u-6\n\nThe 1 can be distributed into the {p+5}\n\n{p+5}/u-6