## Saturday, September 17, 2016

### A Basic Vandyke Edge with Two Final Vandykes

It did not take me long in my exploration of net Vandyke Edges to discover that some Vandyke Edges need more than one Vandyke to turn the corner and create a vertical edge on the last Vandyke.  With my husband's mathematical help, we discovered that there were still four types of turns; however, the directions changed slightly from when there was only one final Vandyke.

Today's sample has 11 squares in the border and 3 points on each side of the Vandykes and needs 2 Vandykes to create the last vertical edge.

The directions are as follows:

First Vandyke with straight, vertical side
1 Net 2 knots in the foundation loop. (2 loops in the row)
2 Net 1 knot in each loop except for the last loop, net 2 knots in the last loop. (3 loops in the row)
3 Net 1 knot in each loop except for the last loop, net 2 knots in the last loop. (4 loops in the row)
4 Net 1 knot in each loop except for the last loop, net 2 knots in the last loop. (5 loops in the row)
5 Net 1 knot in each loop except for the last loop, net 2 knots in the last loop. (6 loops in the row)
6 Net 1 knot in each loop except for the last loop, net 2 knots in the last loop. (7 loops in the row)
7 Net 1 knot in each loop except for the last loop, net 2 knots in the last loop. (8 loops in the row)
8 Net 1 knot in each loop except for the last loop, net 2 knots in the last loop. (9 loops in the row)
9 Net 1 knot in each loop except for the last loop, net 2 knots in the last loop. (10 loops in the row)
10 Net 1 knot in each loop except for the last loop, net 2 knots in the last loop. (11 loops in the row)
11 Net 1 knot in each loop except for the last loop, net 2 knots in the last loop. (12 loops in the row)
12 Net 1 knot in each loop. (12 loops in the row)
13 Net 1 knot in each loop except for the last loop, net 2 knots in the last loop. (13 loops in the row)
14 Net 1 knot in each loop. (13 loops in the row)
15 Net 1 knot in each loop except for the last loop, net 2 knots in the last loop. (14 loops in the row)
16 Net 1 knot in each loop. (14 loops in the row)
17 Net 1 knot in each loop except for the last loop, net 2 knots in the last loop. (15 loops in the row)
18 Net 1 knot in each loop for 12 loops; turn and net back across those loops.

Repeating Vandyke
13-18     Repeat instructions to create new Vandyke.

Final Vandykes
1 Net 1 knot in each loop except the last 2 loops, net those 2 loops together. (11 loops in the row)
2 Net 1 knot in each loop. (11 loops in the row)
3 Net 1 knot in each loop except the last 2 loops, net those 2 loops together. (10 loops in the row)
4 Net 1 knot in each loop. (10 loops in the row)
5 Net 1 knot in each loop except the last 2 loops, net those 2 loops together. (9 loops in the row)
6 Net 1 knot in each loop for 6 loops, turn the netting and begin the next row. (6 loops in the row)
7 Net 1 knot in each loop except the last 2 loops, net those 2 loops together. (5 loops in the row)
8 Net 1 knot in each loop. (5 loops in the row)
9 Net 1 knot in each loop except the last 2 loops, net those 2 loops together. (4 loops in the row)
10 Net 1 knot in each loop. (4 loops in the row)
11 Net 1 knot in each loop except the last 2 loops, net those 2 loops together. (3 loops in the row)

If you would like to know the math involved, here it is.

A. To find how many final Vandykes are needed:
1. If the number of squares in the border is less than or equal to 2 times the number of points -1 then you have just 1 final Vandyke.
2. If the number of squares in the border is greater than 2 times the number of points -1 then you need more than 1 final Vandyke.
(For this example:number of squares in the border 11 and number of points is 3, then 2 times 3 = 6, subtract 1 = 5. Since 11 is greater than 5 we will need more than 1 Vandyke.)

B. To determine how many more Vandykes are needed:
1. Subtract 2 times the number of points - 1 from the number of squares in the border (for this example 2 times 3 subtract 1 = 5)
2. Subtract that number from 11 (for this example: 11-5 = 6)
3. Divide the result by 2 times the number of points. If the answer is not a whole number, round up to the next whole number. (for this example: 6 divided by 2 times 3 = 6 divided by 6 which equals 1)
4. The whole number is how many more Vandykes are needed. (for this example the answer is 1).
B. Total number of final Vandykes needed:
1. Take the number just calculated of how many more Vandykes are needed (for this example: 1).
2. Add 1 to that number to find the total number of final Vandykes (for this example  1 + 1 = 2).

D. To determine which of the 4 types of instructions to use for the final Vandykes:
1. Double the number of points along one side of the Vandyke (for this example the answer is 6).
2. Take the answer from B4 (for this example that answer is 1).
3. Multiple the answer from D1 by the answer from D2.
4. Add the answer from B1 to the answer from D3 (for this example that answer is 5 so 6+5=11)
5. Subtract the number of squares in the border from the result (for this example 11-11 = 0)
6. The resulting number will be 0, 1, an even number greater than 0, or an odd number greater than 1.

E. Generic instructions for the final Vandykes
If your resulting number is 0, the rows are as follows:
(N= the number of points which in this example is 3)

 (N - 1) pair(s) of Decrease & Plain rows, then 1 Decrease row, the next Plain row leaves the last N loops without a knot,  turn netting and net (N - 1) pair(s) of Decrease & Plain rows,  followed by 1 Decrease row.