How to Acquire a Conical Helix with Spheroids Image in Excel

The Tutorial

1. If you have completed the workbook from the article Acquire an N Helix with Spheroids Image, you may SAVE AS that workbook under a new appropriate name having to do with the above conical helix image I'm teaching you to create, and then modify it according to the steps below as read MODIFIED or NEW. Otherwise, open a new Excel workbook and create 3 worksheets (except Chart if you are using Chart Wizard): Data, Chart and Saves. The following article then is a copy, with modifications, of How to Acquire an N Helix with Spheroids Image, since both workbooks derive from the same workbook, "THE n-Helix Curve.xlsx".
2. MODIFIED: 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 can be done a lot. Check save external link values and use 1904 system
   6. In Error checking, check all the options.
   7. In Save, select s ave preview picture with new files and Save Autorecover 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 A14 and doing Freeze Panes.
4. Create some Defined Name Variables.

   1. Into cell A1, type AjRows.
   2. Into cell B1, type GM (for Golden Mean).
   3. Into cell C1, type Factor1.
   4. Into D1, type KEY.
   5. Into cell E1, type Number. 
5. Select cells A1:E2 and Insert Names Create in Top Row. Into cell A2, input 2880 (as the number of adjusted rows in the data-set). In cell B2, input the formula "=-(1-sqrt(5))/2" (without quote marks). This is the Golden Mean or Ratio or Proportion, known since Euclid's time, such that a:b as b:(a+b), and is quadratic and has many special properties -- it's used because it maintains in proportion the square of a number to the number such that for the Pythagorean Theorem, a given Pythagorean triplet will grow in constant proportion to itself, and since the sine and cosine functions are Pythagorean functions, it applies to them as well. In cell C2, input .125 or "=1/8". Into cell D2, input w/o quotes "=IF(Spheroids<=24, Spheroids*VLOOKUP(Spheroids,LOOKER2,2)*2,Spheroids)". Into E2 type 1.
6. Create some more Defined Name Variables.

   1. Into cell A3, type Tip.
   2. Into cell B3, type Base.
   3. Into cell C3, type Spheroids.
   4. Into cell D3, type ShrinkExpand.
   5. Into cell E3, type PiDivisor.
   6. Into cell F3, type Thickness.
   7. Into cell G3, type ShrinkExpand2
   8. Into cell H3, type Variable.
7. Select cells A3:H4 and Insert Names Create in Top Row.
8. MODIFIED  Input the formulas and values to row 4.

   1. Into cell A4, input "=Base*12/(VARIABLE*1)*PI()" -- the empty parentheses for pi are correct.
   2. Into B4, input 1712, which is 2^4 * 107 (where 2^4 means 2 raised to the power of 4).
   3. MODIFIED: Into cell C4, type 64 for now -- the lookup table that is going to be prepared is set to take any number of spheroids up to 150.
   4. MODIFIED: Into cell D4, type 1 for now. Setting up another plot column set of data with ShrinkExpand set to a different value will insert or surround one circle of spheroids with another one.
   5. Into cell E4, input 180. Differentiating this variable creates special effects.
   6. MODIFIED; Into cell F4, type 1.
   7. Into cell G4, type 2.
   8. Into cell H4, type 1.
9. Select cells A2:G2 and Format Cells Border thick line Top Bottom Sides Center and format number with 4 decimal places. Do the same for cell range A4:G4 please.
10. Put the entire sheet in font Lucida Fax size 9 by selecting the very top left cell between A and 1 for column and row and thus select the entire worksheet. Generally, viewing 4 decimal places will inform one of the differences in the sine and cosine function results.
11. MODIFIED: Create the Column Headings.

    1. Into cell A5, type Base t.
    2. MODIFIED: Into cell B5, type constant c.
    3. Into cell C5, type Cos (for cosine).
    4. Into cell D5, type Sin (for sine).
    5. Into cell E5, type Main X.
    6. Into cell F5, type Main Y.
    7. Into cell G5, type Second X.
    8. Into cell H5, type Second Y.
12. Input the t and c Formulas.

    1. MODIFIED Into cell B6, input the formula, "=(Base*24/Spheroids)". Into cell B7, type "=B6". Do Edit Go To cell range B7:B2886 and do Edit Fill Down.
    2. Into cell A6, input "=If(odd(Spheroids)=Spheroids,0,Tip)". This formula states that if the number of spheroids input is odd, result=0, else result=Tip (where Tip was defined above as 12*PI()*B4 or 1712, for a total of 64,540.8795). In the case of the result becoming 0, the column will decrement to twice Tip, negatively from 0. The number of spheroids charted will be odd, eg. 31.
13. Do Edit Go To cell range A7:A2886 and input "=(A6+(-Tip*2)/(AjRows))" into cell A7, then do Edit Fill Down. The value in cell A2886 should be decremented to -64,540.8795 if spheroids is even (eg. at 32), else it will equal 2*-64,540.8795.
14. Input the (Adjusted) Cosine and Sine formulas.

    1. Do Edit Go To cell range C6:C2886 and input into cell C6 the formula, "=Thickness*Spheroids/KEY*(COS((ROW()-6)*Number*PI()/PiDivisor*Factor1))" (without the quotation marks, as always). Do Edit Fill Down. By taking the cosine of the cell 6 rows up from cell C6, we are taking the cosine of 0 to begin with, then in subsequent rows, take the cosine up to 360 and in cycles then to 2880+6. 2880/360=8. So there are 8 cycles. Number is a variable for getting partial circle effects like animation motion likenesses when a fraction because the next piece, *PI()/PiDivisor. converts from pi radians to degrees and vice versa. Recall that PiDivisor is set to 180 degrees. Multiplying by Factor1 is taking back the 8 by 1/8th.
    2. Do Edit Go To cell range D6:D2886 and input into cell D6 the following formula: "=Thickness*Spheroids/KEY*(SIN((ROW()-6) *Number*PI()/PiDivisor*Factor1))". Do Edit Fill Down.
15. MODIFIED: Input the Main X and Main Y Formulas. Do Edit Go To cell range E6:E2886 and input into cell E6 the following formula: "=((SIN(A6/(B6*2))*GM*COS(A6)*GM*(COS(A6/(B6*2)))*GM)+U6)/ShrinkExpand". Do Edit Fill Down.

    1. MODIFIED: Do Edit Go To cell range F6:F2886 and input the formula "=((SIN(A6/(B6*2))*GM*SIN(A6)*GM*(COS(A6/(B6*2)))*GM)+W6)/ShrinkExpand". Do Edit Fill Down. You may notice the z-dimension has NOT been omitted.
16. MODIFIED: Input the Second X and Second Y Formulas. Do Edit Go To cell range G6:G2886 and input into cell G6 the following formula: "=((SIN(A6/(B6*2))*GM*COS(A6)*GM)+V6)/ShrinkExpand2". Do Edit Fill Down.

    1. MODIFIED: Do Edit Go To cell range H6:H2886 and input into cell H6 the formula "=((SIN(A6/(B6*2))*GM*SIN(A6)*GM)+W6)/ShrinkExpand2". Do Edit Fill Down.
17. Input the LOOKER table. While the sheet will now produce the chart wanted, for small numbers of spheroids like 1 or 2 or 3, they cannot appear in a ring properly. A solution for that contingency was worked out for spheroids but doesn't apply very well to helices.

    1. Do Edit Go To cell range I6:I155 and input 1 into cell I6 and then do Edit Fill Series Columns Linear, Step Value 1 and blank stop value; press OK. That should input the series from 1 to 150 in that cell range.
    2. Do Edit Go To cell range J6:J155 and input into cell J6 .125 and then do Edit Fill Down. That will input the constant value of .125 in that cell range.
    3. Do Edit Go To cell range K6:K155 and input "=I6*$K$35/$I$35" and do Edit Fill Down and then input the value .125 in cell K35.
    4. Do Edit Go To cell range I6:K155 and Insert Name Define Name Looker. Format Cells Border Red bold Outline. Input Looker in cell J5, font bold red.
    5. Go to Factor1 cell C2. Input the formula, "=VLOOKUP(ABS(Spheroids),Looker,IF(Spheroids<=24,3,2))"
18. : Input the (original) LOOKER2 vlookup table.

    1. Select cell L5 and enter LOOKER2 into it.
    2. Edit Go To cell range L6:29 and input 1 into L6 and do Edit Fill Series Column Linear Step Value 1, OK.
    3. Enter the following numbers down from cell M6 to M29: 24, 16, 8, 4, =PI(), =PI(), =PI(), 2 from M13 to M21 and enter 1 from M22 to M29.
19. MODIFIED: Enter the CONICAL HELIX DATA table constants and formulas.

    1. MODIFIED: Enter CONICAL HELIX DATA into cell N1.
    2. Enter X Stretch into cell T1. Font red.
    3. Enter Y Stretch into cell W1. Font red.
    4. MODIFIED: Enter 1 into cell T2 and format fill yellow font red and do Insert Name Define name X_Stretch to cell $T$2.
    5. MODIFIED: Enter 1.5 into cell W2 and format fill yellow font red and do Insert Name Define name Y_Stretch to cell $W$2.
    6. Enter ±6π or +/- 6 pi into cell Q4.
    7. Enter the column headings into row 5: N5: a; O5: c; P5: n; Q5: t; R5: (i); S5: z; T5: X1; U5: 90 degrees X2; V5: X3; W5: Y.
    8. MODIFIED: a, c, n: Enter "=O6*0.1" to cell N6, "=Q2889/2" into cell O6 and blank into cell P6. Select N6:P6 and Format Fill yellow for input. Enter "=N6" into cell N7 and copy it and paste it to cell range N7:P2886.
    9. MODIFIED: t: Select cell Q6 and enter "=-Q2889*PI()". Go to cell Q2889 and enter 6, font red, size 14, fill yellow. Go to cell Q2888 and enter "=PI()". Go to cell Q2887 and enter "=Q2889*Q2888" w/o quotes and do Insert Name Define Name Destiny to cell $Q$2887. Edit Go To cell range Q7:Q2886 and enter into cell Q7 w/o quotes the formula "=Destiny*2/2880+Q6" and Edit Fill Down.
    10. (i): Leave column R blank for now.
    11. z: Edit Go To cell range S6:S2886 and enter w/o quotes into S6 the formula "=Q6/(2*PI()*O6)".
    12. MODIFIED: X1: Edit Go To cell range T6:T2886 and enter w/o quotes into T6 the formula "=X_Stretch*((N6*Q6)/(2*PI()*O6))*SIN(Q6)+S6".
    13. 90 degrees X2: Edit Go To cell range U6:U2886 and enter w/o quotes into U6 the formula "=(T6-0.3-S6)". This is the column currently accessed by the chart.
    14. MODIFIED: X3: Edit Go To cell range V6:V2886 and enter w/o quotes into V6 the formula "=U6*-1".
    15. MODIFIED: Y: Edit Go To cell range W6:W2886 and enter w/o quotes into W6 the formula "=Y_Stretch*((N6*Q6)/(2*PI()*O6))*COS(Q6)+S6".
    16. MODIFIED: Edit Go To cell range N1:W2889 and Format Fill very light blue and Border Deep Purple bold Outline. Edit Go To cells N6:P6, T2, W2, Q2889  and Format Cells Fill Yellow.
20. It is also a good idea to do Insert Comment a copy of all the formulas so far into the cells so there are always the original formulas should they ever be overwritten. Do that now for cell C2 until you see the red corner flag and remember to do it for all the other formulas later please. The Abs() Absolute function allows one to input a negative number of spheroids; the effect will be to flip the graph 180 degrees horizontally (from left to right or right to left), as one can tell with an odd number of spheroids.

Explanatory Charts, Diagrams, Photos

1. (dependent upon the tutorial data above)

1. MODIFIED; Have a blank worksheet ready to copy a new chart into and expand and format it at will.

   1. Do Edit Go To cell range E6:F2886. Press the Charts button, All, or Chart Wizard. Select chart type Scatter Smoothed Line Scatter. Command c copy it and access the new worksheet and command v paste it into the new worksheet. Your chart should look like the example above except for detailing and the second helix is to be deleted as messy. Adjust the chart size by dragging the bottom right corner until you get a rectangular plot area about 5" tall by 3" wide. Get rid of the Vertical and Horizontal Axes, Legend and Grid lines via the Chart Layout tab. Clicking on the plot area will give access to the gradient style; the setting for that are Plot Area Fill Gradient Radial Centered Far Left White, 30% Ultramarine Blue, 55% Deep Navy Blue, no Line, Shadow, Glow or 3-D Format. Double-clicking on the chart plot line itself will give access to changing that under Format Selection of Chart Layout: set Series 1 Line to Ultramarine Blue, smoothed line, weight 1 pt. Glow is medium dark muddy red wine 1 pt 0 transparency 0 pt soft edges. Shadow for the line is checked, Perspective, 248 degrees, dark navy blue 33% size, 0 pt blur, 72 pt distance and 11% transparent. Chart Area Fill Gradient is Radial Centered left 41% White and fully right 100% Hot Pink Fuschia.
2. Shrink the chart on the original Data worksheet and put it at the bottom of the data.
3. Copy the Data worksheet cell range A1:W13 and paste it to the Saves worksheet at bottom, then paste it again underneath that, only this time, do Paste Special Values. Under all that data, paste a picture of the chart by going to the Chart worksheet, clicking in the Plot Area, holding down the shift key and doing Copy Picture, then lift off the shift key, go to the Saves worksheet, depress the Shift Key again and do Paste Picture. Make a note that cell O2889 equaled 6, Looker was defined to 150 and Looker2 to 24. You can make the formulas come out with no errors in the Saves worksheet by filling in the reference with 6 that is under the c in the CONICAL HELIX DATA Section and them cutting it and pasting it back above closer to the data set copies.
4. How to Acquire a Conical Helix with Spheroids Image in Excel Picture 1 Unwinding Vajra
   Finished!! This is the variation called the "Unwinding Vajra"

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.