Why can’t a tetragram exist
In: 1
draw 5 points roughly evenly spaced like the points of an imaginary pentagon. As you walk clockwise around the pentagon, label them 1 through 5 in order as you encounter them.
If you draw a line from 1 to 2, 2 to 3, 3 to 4, 4 to 5, and 5 back to 1 you will have drawn a pentagon. Notice how every point is only 1 away from the previous (2-1=1, 3-2=1, 4-3=1 and 5-4=1 I won’t discuss modular arithmetic, but you can clearly see that 5 is also only one point away from 1) to get a pentagram, try connecting dots that are a gap of 2 away from each other. 1 to 3, 3 to 5, 5 to 2 (skipping over 1), 2 to 4, and 4 back to 1 (skipping over 5). Notice every line skips one number, but I didn’t list all of them because it’s obvious for those that aren’t wrapping across the first point. Here, 3-1=2, 5-3=2, and 4-2=2. And the other gaps are also 2 points away, but you’ll have to just count them.
So let’s try 4 points. If you use a gap of 1, you end up with a tetragon (square). If you choose a gap of 2, you draw one line and then become stuck. 1 to 3 (skipping 2) but then 3 can’t go back to 1 (skipping 4) because you already drew that line. So if you also connect 2 to 4, you end up with a plus sign. If you use a gap of 3, it’s the same thing as using a gap of 1 if you counted counterclockwise instead of clockwise when labeling your points. This makes a square again. And a gap of 4 isn’t possible because you skip all the points and draw no lines at all.
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