how can a circle be divided into sixteenths with only five cuts?
929308
take a knife and cut 4 times thru the circle and u end up with 8 pie wedges...then line the wedges up-----<<<<<<<<------like that and cut thru on the dashed line, the fifth cut, giving u 16 wedges...not very mathematical but it works
268663
If you fold a piece of paper in half 4 times, then you  have 16 segments. Each segment has 4 holes, so the number of holes is 4x16\n\n4 x 16 = 64 holes
223610
Basically, why isn't there a rotational symmetry for 5 cells in a circle? Because there is no way you can have a single elementary cell that repeats itself covering all of the plane.\n\nTry filling a sheet of paper completely with identical cells of even-sided triangles, squares (and diamond shapes) or hexagons: no problem. Trying to do so with any other regular polygon will leave gaps. Hence only rotations with 2, 3, 4 or 6 periods will result in a lattice.
821150
first draw a circle, and then put the star in it w/ the points touching the edge. that divides the circumference of the circle into 5 equal parts. so to find the degree of each one of those section divide 360 by 5 = 72. now look at the angle that is made from the lines from the ends of the individuals sections to the point of the star it goes to, which is the inscribed angle. now that angle which is one of the acute angles is half of its intercepted arc. so that makes 72 divided by 2= 36. so since you wanted to know the measure of all the acute angles and not just one multiply 36 times 5 = 180
630158
Since you don't want to subdivide (subdivision with chi-square is perfectly valid BTW) you could try a Tukey's HSD. However if you are doing this by hand it will probably be faster to subdivide.
991890
Try the 2-2 pattern. it's the best way. The 3 is done with that criss-cross pattern, but the 2-2 allows you to continue the circle, just make it have a big radius
410760
Divide 20 by 5/2.  If you have trouble dividing by fractions, try this:  Multiplying 20 x 2 (the denominator of the fraction) = 40, and then dividing 40 by 5 (the numerator of the fraction), or 40/5 = 8.\n\nIn general, if you want to know how many A/B there are in C, the answer is (CxB)/A.  In your example, A=5, B=2, C=20, so the answer is (20x2)/5 = 40/5 = 8.
856650
This isn't the answer, but it might spark something in your mind for an answer.  If you needed to make 5 lines, with 5 trees, using a total of 19 trees, you could make a square with a diaganal line running through it.  I'll keep trying to think of another way.  May we inquire where the question came from?\n\n.1...2...3....4...5\n.6..............7...8\n.9........10......11\n12..13...........14\n15..16.17.18.19
381185
Draw a circle and a line down the middle cutting it in half.  Show that there are 2 pieces, and 1 out of two = 1/2.\n\nNow draw a line across cutting it into fourths.  Show that there are 4 pieces, and 2 out of 4 = 2/4, which is still 1/2\n\nYou can also use this circle to show that 2/2 and 4/4 equal 1 whole circle.  Anything multiplied by 1 is equal to itself (3*1=3, 5*1=5) so if you multiply a fraction by the same number on top and bottom, you are really multiplying it by 1.  Therefore, all the multiples of that fraction are equivalent.\n\nProve it with a calculator.  Take 3/4 and multiply it by 3/3 (which =9/12), 5/5 (=15/20) and then show that on the calculator all of these equal .75
235381
in dividing fractions, you just multiply them by its reciprocal.\n\nso \n\n[(x+5) / (16x)]  * [ (4x ^2) / [(3x -2)] \n\nperform the operations: \n\n[ (x+5) / 4 ] * [ x / (3x-2) ]\n\nthe answer is:\n\n[x(x+5)] / [ 4(3x-2) ]
1152243
I think it's 16 because of the math involved, you cut 16 in half and get 8, cut that in half you get 4, cut that in half and get 2, then a final winner.  Try doing that with 15 or 18
642365
The Fibonacci spiral is constructed using the arcs of demi-semi-circles of radius Fib(n) for all natural up to a given point (depending on the required size/complexity of the spiral)  This sounds confusing, doesn't it? Check out this website! It illustrates the idea pretty well!\n\nhttp://students.bath.ac.uk/ma1caab/spirals.html
845089
Ok, your question makes absolutely no sense.  Why say we can only use 1 through 16, and then say we can only use 1?\nSome ways, assuming I translated your question correctly, would include 16 + 16 +1 +1, and 16 + 15 + 3.... There are almost an infinite number of ways to add to 34 with the numbers 1-16, so please rephrase your question.
410933
Let 1 2 3 4 5 6 7 8 9 A B C D be the dots, with D in the middle. (You say 1 in the middle)\n\n1 2 3 4\n5 -- -- 6\n-- -D- --\n7 -- -- 8\n9 A B C\n\nIT CAN BE DONE WITH 5 LINE SEGMENTS AND DOESN'T NEED 6.\n\nConnect 7-5-1-2-3-4-D-9-A-B-C-8-6 in a Z-shape\n\nSo I think if it needs six lines, your question was meant to be regarding 16 dots, 4 of them in the middle. It would then be similar to your other question with 9 dots.\n\n1 2 3 4\n5 6 7 8\n9 A B C\nD E F G\n? -- -- !\n\nConnect 1-2-3-4-8-C-G-! and then proceed as for 9=dot problem, F-A-5-6-7-8-B-E-?-D-9. Six lines needed.\n\nGeneralising, an n x n square of n^2 dots will require 2n-2 lines. (for n>2)\n\nImagine a further 9 dots wrapped around the 16-dots as follows\n\nH I- J K L\n1 2 3 4 M\n5 6 7 8 N\n9 A B C 0\nD E F G P\n\nConnect G-F-E-D-0-5-1-H-I-J-K-L-  M-N-O-P and then proceed as for the 9-dot problem:\n\nC-7-2-3-4-M-8-B-E-A-6\n\nwhich is 8 lines.
993677
Well, if we consider that a pie is a 3 dimensional object we could first take 2 lines (cuts) perpendicular through the center on the top of the pie to cut it into 4 slices.  From there we could move to the side if the pie and cut evenly through it horizontally thus cutting each of the 4 pieces into a top and a bottom piece.  4 x 2 = 8.  I want dibs on the top 4 pieces...someone else can have the bottom mostly crust pieces!!  :-p
914474
well from my understanding there is 360 degrees in the circumference of a circle so divide that by 12 and you get 30 so every 30 degrees mark it.\nI hope i am not to wrong here!\n\nUnless its bigger but you can draw it down to fit that scale, that's not hard.
1021945
The first five squares are easy:\n1, 4, 9, 16, 25.\n\nRectangular:\n2, 6, 12, 20, 30\n\nTriangular:\n1, 3, 6, 10, 15\n\nPentagonals are:\n1, 5, 12, 22, 35