How to Create a Ring of Sinewave Spheres in Excel

The Tutorial

1. Open a new Excel workbook and create 3 worksheets (except Chart if you are using Chart Wizard): Data, Chart and Saves.
2. Set Your Preferences: Open Preferences in the Excel menu and follow the directions below for each tab/icon.

   1. In General, set R1C1 to Off and select Show the 10 Most Recent Documents .
   2. In Edit, set all the first options to checked except Automatically Convert Date System . Set Display number of decimal places to blank (as integers are preferred). Preserve the display of dates and set 30 for 21st century cutoff.
   3. In View, click on show Formula Bar and Status Bar and hover for comments of all Objects . Check Show Gridlines and set all boxes below that to auto or checked.
   4. In Chart, allow show chart names and set data markers on hover and leave the rest unchecked for now.
   5. In Calculation, Make sure Automatically and calculate before save is checked. Set max change to .000,000,000,000,01 without commas as goal-seeking is done a lot. Check save external link values and use 1904 system
   6. In Error checking, check all the options.
   7. In Save, select save preview picture with new files and Save Auto-recover after 5 minutes
   8. In Ribbon, keep all of them checked except Hide group titles and Developer .
3. It helps placing the cursor at cell A16 and doing Freeze Panes. Edit Go To cell range A1:J17288 and Format Cells Number Number Decimal Places 4, Font Size 9 or 10, Fill (from the color wheel) a nice fuchsia and make the Border Dark Blue bold Outline.

4. Enter the upper Defined Name Variables Section (here's a picture):

   1. A1: Aligned left, enter Sinewave Spheres in a Ring and Format Font Apple Chancery or something fancy and nice?
   2. E1: AYE
   3. E2: BEE
   4. E3: CEE
   5. F1: 40
   6. F2: .50
   7. F3: .50
   8. Select cell range E1:F3 and Insert Name Create in Left Column, OK.
   9. G1: Stretch_y1
   10. G2: Enter w/o quotes the formula "=(8.5*(SHRINKER*10))"
   11. H1: Stretch_x1
   12. H2: Enter w/o quotes the formula "=(8.5*(SHRINKER*10))"
   13. Select cell range G1:H2 and Insert Name Create in Top Row, OK.
   14. G3: Shrinker
   15. H3: Enter w/o quotes the formula "=0.1*12/SPHERES" and Insert Name Define Name Shrinker to cell $H$3.
   16. I1: ROWS
   17. J1: "=17285-5"
   18. I2: MAGIC
   19. J2: Enter w/o quotes the formula "=J1/SPHERES"
   20. I3: SPHERES
   21. J3: 12 for now.
   22. Select cell range I1:J3 and Insert Name Create in Left Column, OK.
5. Enter the column heading of rows 4 and 5:

   1. A5: Adj Cos (for Adjusted Cosine)
   2. B5: Adj Sin
   3. C5: Indicator
   4. D5: Randy (for RandBetween)
   5. E5: t: 0 to nπ (varies from data chit)
   6. F5: z1_ (varies from data chit)
   7. G5: Adj_x1
   8. H5: Adj_y1 (varies from data chit)
   9. I4 and J4: Charting
   10. I5: x: No z
   11. J5: y: With z
   12. Command+Select cells F1:F3 and I3 and Format Fill yellow.
   13. Select cell J3 and Format Fill sky blue from the color wheel.
   14. Select cell range I4:J5 and Format Font italic.
6. Enter the column formulas:

   1. Adj Cos: Edit Go To cell range A6:A17285 and enter into A6 w/o quotes the following formula, "=17*COS((ROW()-6)*0.25/12*PI()/180)" and Edit Fill Down. The .25 is for 1440*.25 = 360. 17280/12=1440. So we are taking 1/12th of 1/4 or 1/48th of 17280 = 360, the degrees of the trig function cosine for a circle. PI()/180 converts radians to degrees. (ROW()-6) in row 6 = 0, so we start off taking the cosine of 0, which is 1, and multiplying it by 17. 17 is twice the Stretch factor, and if I recall rightly, is 1/2 the radius of the ring (the Stretch factor operates from each sphere's center). However, Shrinker is also involved, as you'll see later.
   2. Adj Sin: Edit Go To cell range B6:B17285 and enter into B6 w/o quotes the following formula,"=17*SIN((ROW()-6)*0.25/12*PI()/180)+17"and Edit Fill Down, which is different than the above one for cosine by the addition of 17 to it. All in all, that give us 4*8.5, and that is the radius, as I recall.
   3. Indicator: Select cell C6 and enter 1. Edit Go To cell range C7:C17286 and enter w/o quote the formula, "=IF((ROW()-7)/MAGIC=INT((ROW()-7)/MAGIC),1,IF((ROW()-7)=0,1,0))" and Edit Fill Down. This formula says, 'Take a look at the row I'm in, divide it by the number of rows per sphere (MAGIC) and if that number is an integer, return a 1, otherwise if I'm in the next-to-top row also return a 1, otherwise, return a 0.' So now there is an indicator of where 1 sphere ends and the next one begins, no matter how many spheres the user selects to chart.
   4. Randy: Edit Go To cell range D6:D17286 and enter into D6 w/o quotes the following formula,"=RANDBETWEEN(0,10)/100" and Edit Fill Down. Warning: Make calculation Manual before adding this variable or column into your formulas, especially as a factor, as it can take 20 minutes to calculate and draw the new chart. It is not currently employed, but a copy of its formula has been saved at the bottom of the x and y formulas. Edit Go To cell range D6:D17285 and Insert Name Define Name Randy to cell range $D$6:$D$17285.
   5. t: 0 to nπ: Select cell E6 and enter 0. Select cell E7 and enter the formula "=(2*PI()/MAGIC)". Edit Go To cell range E8:E17285 and enter w/o quotes into E8 the formula "=IF(C8=1,2*PI(),2*PI()/MAGIC+E7)" and Edit Fill Down. You may notice on the data chit the column heading states 2π but I am now recommending nπ as I noticed it works a 4π at the bottom of the worksheet just fine. It was built to increment just to 2π and begin again, so that is news to me and I have corrected my column heading.
   6. z1_: Edit Go To cell range F6:F17285 and enter w/o quotes into F6 the formula "=CEE*COS(AYE*E6)" and Edit Fill Down. Edit Go To cell range F6:F17285 and Insert Name Define Name z1_ to cell range $F$6:$F$17285.
   7. Adj_x1: Edit Go To cell range G6:G17285 and enter w/o quotes into G6 the formula "=IF(C6=1,A6,G5)" and Edit Fill Down. Edit Go To cell range G6:G17285 and Insert Name Define Name Adj_x1 to cell range $G$6:$G$17285. This makes a constant adjustment as if one were referencing a new center of every new sphere from Adj Cos, else it takes the value just above itself.
   8. Adj_y1: Edit Go To cell range H6:H17285 and enter w/o quotes into H6 the formula "=IF(C6=1,B6,H5)" and Edit Fill Down. Edit Go To cell range H6:H17285 and Insert Name Define Name Adj_y1 to cell range $H$6:$H$17285. This makes a constant adjustment as if one were referencing a new center of every new sphere from Adj Sin, else it takes the value just above itself.
   9. x: No z: Edit Go To cell range I6:I17285 and enter w/o quotes into I6 the formula "=SHRINKER^2*(Stretch_x1*(((BEE^2-CEE^2*COS(AYE*E6)*COS(AYE*E6))^0.5 *COS(E6)))+Adj_x1)" and Edit Fill Down. This is the x part of the heart of the sinewave sphere formula from the text, without the z dimension added or multiplied in, which is why it took me so long to discover how to make it work.
   10. y: With z: Edit Go To cell range J6:J17285 and enter w/o quotes into J6 the formula "=SHRINKER^2*(Stretch_y1*(((BEE^2-CEE^2*COS(AYE*E6)*COS(AYE*E6))^0.5 *SIN(E6))+z1_)+Adj_y1)" and Edit Fill Down. This is the y part of the heart of the sinewave sphere formula from the text, with the z dimension added in, which is why it took me so long to discover how to make it work. In the spirallic spheroids Garthwaite Curve, the z-dimension is multiplied into both x and y parts. Furthermore, I have made no adjustment for the GOLDEN MEAN Long Leg, which I expected to all along, until it worked without it. The other curve doesn't.
   11. Select cell I17286 and enter the formula w/o quotes "=I6" and select cell J17286 and enter the formula w/o quotes "=J6". This makes the top connecting line from the last sphere to the first.
   12. Select cell I17287 and enter "=SHRINKER^2*(Stretch_x1*(((BEE^2-CEE^2*COS(AYE* E17287)*COS(AYE*E17287))^0.5*COS(E17287)))+Adj_x1)+Randy" or *Randy, etc. Warning: this can really take a lot of processing time -- set calculation to Manual first. This is a planned error value result.
   13. Select cell J17287 and enter "=SHRINKER^2*(Stretch_y1*(((BEE^2-CEE^2*COS(AYE* E17287)*COS(AYE*E17287))^0.5*SIN(E17287))+z1_)+Adj_y1)+Randy" or *Randy, etc. Warning: this can really take a lot of processing time -- set calculation to Manual first. This is a planned error value result.
   14. Select cell D5 and Format Fill light sea green, font red, Border navy blue outline bold. Copy this cell to H17287. Then do Edit Paste Special Format of this cell to cell C6, E6, E7, I17286 and J17286 to make distinct the format of those cell's formulas/values.
   15. Edit Go To cell range I6:J17288 and do Format Fill sky blue.

Explanatory Charts, Diagrams, Photos

1. (dependent upon the tutorial data above)

1. Create the Chart:

   1. Edit Go To cell range I6:J17286 and from the Ribbon or Chart Wizard select Charts All/Other Scatter Smoothed Line Scatter and Copy or Cut the chart that is atop the data worksheet and paste it to the top left of the Chart worksheet. Hover over the lower right corner until the cursor becomes a double-headed arrow and pull it open to become a large approximate square.
   2. Click in the Plot Area and select Chart Layout from the ribbon and at far left under Current Selection select Series 1, then under that, Format Selection. Set Line to Black, Smoothed line, Weight = 1 pt. and Dashed = Solid. Set Shadow to checked Outer 45 degrees, black, Size 100%, Blur 4 pt, Distance 30 pt, Transparency 75 %. Set Glow to very light blue Size = 1 pt. 2% transparency, Soft Edges 0 pt. OK.
   3. Do Current Selection under Chart Layout as Plot Area, Format Selection. No Line, No Glow and No Shadow. Set Fill to No. Gradient to None. 3-D is all zeros. OK.
   4. Do Current Selection under Chart Layout as Chart Area, Format Selection. Fill Gradient color Prussian Blue I think they call it on left 0% to Navy Blue on right 100%, Path, 0 degrees, Transparency 0%. Line = Auto. Shadow is Unchecked/ No Glow or Soft Edges. 3-D Format is not set. OK.
   5. The version of the chart above probably will not enlarge because I set the resolution too high at 600 dpi. There is another version in Tips below that will enlarge. The Aye variable setting controls lines per sphere and 40 allowed some daylight but the version below is set for 30.

   6. 
      
      That's it!! Finished!

Helpful Guidance

1. Make use of helper articles when proceeding through this tutorial:

   1. See the article How to Create a Spirallic Spin Particle Path or Necklace Form or Spherical Border for a list of articles related to Excel, Geometric and/or Trigonometric Art, Charting/Diagramming and Algebraic Formulation.
   2. 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.