How to Create a Spirallic Numbers Dataset
; , Make the dataset by opening a new Excel worksheet and choosing a cell inwards and downwards about 10 rows and columns to start inputting the numbers into., Proceed sequentially outwards in a spiral.,After you have built the data set up to 100 or...
Step-by-Step Guide
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Step 1: Make the dataset by opening a new Excel worksheet and choosing a cell inwards and downwards about 10 rows and columns to start inputting the numbers into.
You may start with 0 or 1 or any number; 1 is recommended., If you want to save a little time, use a formula like "=J15+1" and copy it up, across or down off as many cells as need be.
You may then find a like formula nearby as you go outwards, which will speed things up greatly.
This will also allow you to use any originating number in the center, should you so choose..,, You might try blocking in non-primes in groups in patterns to see if you can predict primes!,, Its pattern to produce the sequence 1,3,13,31,57,91,133,183,241,307, ... is
-1*0+1=1, 1*2+1=3, 3*4+1 =13, 5*6+1 = 31, etc.
You will find a similar pattern extending to the upper left.
Notice that the second pattern is trickier: the vertical pattern that produces the sequence 1,4,15,34,61,96,139,190,249,316 is more involved.
If one takes the difference of those numbers and then the differences of the differences, one gets 8's, so one knows that a constant value of 8 is being added in the sequence.
Knowing that, a typical rate of change is produced by ((a*b)+c)+8 = result, with a being constant.
Such is the case here as it turns out, for the sequence is produced by ((4*-2)+4+8)=4, ((4*1)+3+8)=15, ((4*6)+2+8)=34, ((4*13)+1+8) = 61, etc. with the increment to b being 3,5,7,... and the increment to c being
-1, while a=4 and 8 are constants.
There's an elegant way to write that in Summation Notation with N's and K's and i's and all but it's beyond the text capacity we're operating under.
Actually, I just found another way to resolve the series: 1==((-1*0)-7)+8, 4=((1*2)-6)+8, 15=((3*4)-5)+8, 34=((5*6)-4)+8, 61=((7*8)-3)+8, 96=((9*10)-2)+8, etc. , 8's were again a constant difference of the differences but it took me awhile to find the rest of the formula.
The sequence of 11,28,53,86,127,176,233,298, ... is generated as far as I know by ((4*-5)+23)+8=11, ((4*-1)+24)+8 = 28, ((4*5)+25)+8 = 53, ((4*13)+26)+8 = 86, etc., with a=4 and 8 remaining constant while b increments by 4, 6, 8,... and c incrementing by
1.
Again, there's a more elegant way to state that.
If anyone happening to read this can help out, great.
There's another way to resolve this sequence also: 2=((2*3)-12)+8, 11=((4*5)-17)+8, 28=((6*7)-22)+8, 53=((8*9)-27)+8, 86=((10*11)-32)+8, 127=((12*13)-37)+8, 176=((14*15)-42)+8, 233=((16*17)-47)+8, and 298 =((18*19)-52)+8, etc. with element c decrementing by
-5 each time., (1*2) changed next to (3*4).
This might be the general pattern instead of working with 4's as had been, The role of d=8, the difference of the differences, was still present, so then you just need to figure out which a and b pair best approximated the answer and adjust with c accordingly, by trial and error.
It did not take long to hit upon the solutions., and also 8==((2*3)-6)+8, 23=((4*5)-5)+8, 46=((6*7)-4)+8, 77=((8*9)-3)+8, 116=((10*11)-2)+8,163=((12*13)-1)+8, 218=((14*15)-0)+8 and 281=((16*17)+1)+8.
These were done by the analytical method described above in Step 9, though it's a good hunch the problem will only yield to greater finesse than the lazy mathematician possesses., Has anyone hi-lited that yet? Might be interesting! # , For more art charts and graphs, you might also want to click on Category:
Microsoft Excel Imagery, Category:
Mathematics, Category:
Spreadsheets or Category:
Graphics to view many Excel worksheets and charts where Trigonometry, Geometry and Calculus have been turned into Art, or simply click on the category as appears in the upper right white portion of this page, or at the bottom left of the page. -
Step 2: Proceed sequentially outwards in a spiral.
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Step 3: After you have built the data set up to 100 or 324 (as in the example)
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Step 4: you're good to go!
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Step 5: You will notice right away that the prime numbers are fairly evenly distributed in the 4 quadrants at this point.
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Step 6: Notice there are a number of sequences to the columns and numbers which follow Summation Notation.
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Step 7: Notice also that the first sequence is easy -- it's the diagonal from the center to the bottom right.
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Step 8: Notice the horizontal pattern is a bit trickier to discover.
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Step 9: Notice that the diagonals take the form of ((a*b)+c)+d = Sum wherein b_sub_0 is 1 greater than a_sub_zero
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Step 10: a_sub_1 was 2 greater than a_sub_0 and b_sub_1 was 2 greater than b_sub_0
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Step 11: There are resolved 2 more sequences: 5=((2*3)-9)+8
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Step 12: 18=((4*5)-10)+8
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Step 13: 39=((6*7)-11)+8
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Step 14: Review the spirallic dataset again to see if you can spot any other sequences in it -- how about the Fibonacci Series?
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Step 15: Make use of helper articles when proceeding through this tutorial: See the article How to Datamine for Primes Using a Spirallic Dataset for a list of articles related to Excel
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Step 16: Geometric and/or Trigonometric Art
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Step 17: Charting/Diagramming and Algebraic Formulation.
Detailed Guide
You may start with 0 or 1 or any number; 1 is recommended., If you want to save a little time, use a formula like "=J15+1" and copy it up, across or down off as many cells as need be.
You may then find a like formula nearby as you go outwards, which will speed things up greatly.
This will also allow you to use any originating number in the center, should you so choose..,, You might try blocking in non-primes in groups in patterns to see if you can predict primes!,, Its pattern to produce the sequence 1,3,13,31,57,91,133,183,241,307, ... is
-1*0+1=1, 1*2+1=3, 3*4+1 =13, 5*6+1 = 31, etc.
You will find a similar pattern extending to the upper left.
Notice that the second pattern is trickier: the vertical pattern that produces the sequence 1,4,15,34,61,96,139,190,249,316 is more involved.
If one takes the difference of those numbers and then the differences of the differences, one gets 8's, so one knows that a constant value of 8 is being added in the sequence.
Knowing that, a typical rate of change is produced by ((a*b)+c)+8 = result, with a being constant.
Such is the case here as it turns out, for the sequence is produced by ((4*-2)+4+8)=4, ((4*1)+3+8)=15, ((4*6)+2+8)=34, ((4*13)+1+8) = 61, etc. with the increment to b being 3,5,7,... and the increment to c being
-1, while a=4 and 8 are constants.
There's an elegant way to write that in Summation Notation with N's and K's and i's and all but it's beyond the text capacity we're operating under.
Actually, I just found another way to resolve the series: 1==((-1*0)-7)+8, 4=((1*2)-6)+8, 15=((3*4)-5)+8, 34=((5*6)-4)+8, 61=((7*8)-3)+8, 96=((9*10)-2)+8, etc. , 8's were again a constant difference of the differences but it took me awhile to find the rest of the formula.
The sequence of 11,28,53,86,127,176,233,298, ... is generated as far as I know by ((4*-5)+23)+8=11, ((4*-1)+24)+8 = 28, ((4*5)+25)+8 = 53, ((4*13)+26)+8 = 86, etc., with a=4 and 8 remaining constant while b increments by 4, 6, 8,... and c incrementing by
1.
Again, there's a more elegant way to state that.
If anyone happening to read this can help out, great.
There's another way to resolve this sequence also: 2=((2*3)-12)+8, 11=((4*5)-17)+8, 28=((6*7)-22)+8, 53=((8*9)-27)+8, 86=((10*11)-32)+8, 127=((12*13)-37)+8, 176=((14*15)-42)+8, 233=((16*17)-47)+8, and 298 =((18*19)-52)+8, etc. with element c decrementing by
-5 each time., (1*2) changed next to (3*4).
This might be the general pattern instead of working with 4's as had been, The role of d=8, the difference of the differences, was still present, so then you just need to figure out which a and b pair best approximated the answer and adjust with c accordingly, by trial and error.
It did not take long to hit upon the solutions., and also 8==((2*3)-6)+8, 23=((4*5)-5)+8, 46=((6*7)-4)+8, 77=((8*9)-3)+8, 116=((10*11)-2)+8,163=((12*13)-1)+8, 218=((14*15)-0)+8 and 281=((16*17)+1)+8.
These were done by the analytical method described above in Step 9, though it's a good hunch the problem will only yield to greater finesse than the lazy mathematician possesses., Has anyone hi-lited that yet? Might be interesting! # , For more art charts and graphs, you might also want to click on Category:
Microsoft Excel Imagery, Category:
Mathematics, Category:
Spreadsheets or Category:
Graphics to view many Excel worksheets and charts where Trigonometry, Geometry and Calculus have been turned into Art, or simply click on the category as appears in the upper right white portion of this page, or at the bottom left of the page.
About the Author
Melissa Foster
Brings years of experience writing about pet care and related subjects.
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