# 96 (21-Rayed Star :: Numbers 1 - 63)

learned how to create stars like this from Yetziratic Magic. the trick: any number divisible by 3 can create similar stars. if you want to create a 21-rayed star, multiply 21 by 3, arrange the numbers 1 to 63 in a magic square (i know i know, it's a rectangle) where all the columns equal the same number. take last row, write numbers clockwise on a circle, begin with lowest number: connect-the-dots.

formula to get all columns with same values is pretty simple. while it took me hours to figure out, i'm happy to save you hours of schizoid trouble.

[1] select your odd numby, that's the number of points in your star.
[2] n x 3 = P, multiply your number by three, eg, 21 x 3 = 63
[3] fire up Excel so you don't have to add manually
[4] first row: n to P, or using our example:
1-2-3-4-5-6-7-8-9-10-[11]-12-13-14-15-16-17-18-19-20-21
note: first row should end with your number
[5] 11 in brackets indicates MIDDLE NUMBER
[6] second row: take the number AFTER your number,
place it under the MIDDLE NUMBER, eg, 22.
[7] continue counting to the end of the row.
[8] begin 2nd row, 1st position, continue.
[9] third row: place P (or 63) as middle number.
[10] subtract 1 from P: P - 1 = E, eg, 63 - 1 = 62.
[11] begin 3rd row, 1st position with E, eg, 62.
[12] counting backwards, subtract 2 and enter EVEN numbers.
[13] that should get you to P (or 63).
[14] subtract 2 from P: P - 2 = E, eg, 63 - 2 = 61.
[15] to complete the row, enter ODD numbers after P (or 63).
[16] counting backwards, subtract 2 and enter ODD numbers.

all column totals should equal the same number. to draw the star:

[1] draw a circle.
[2] it's easier if you use Excel.
[3] top of circle, place first number on the third row (62).
[4] place remaining numbers clockwise.
[5] locate smallest number (43).
[6] use Curve Line drawtool on Excel's AutoShapes
[7] click on 43, click on 44, keep counting & clicking until you return to 43.

excel usually can draw a nice star for you. may take a few tries tho. when you get the shape you like, color it and stuff and you got your star.

prosper!

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