As we know we can draw a pentagram in one stroke, then how to draw a heptagram in one stroke?

Here I’d like share some small discoveries.

Now let’s draw some heptagrams in one stroke

First, we draw a line, then we draw an isometric line at an angle of 77.1 ° to the first line. Repeat the operation for seveal times, then we will get:

This article we only talk about the occasion that every angels are the same.

If we change the angel to 25.7°, the graphic became:

Where the two angels came from? We have a formula.

The formula to calculate the angel of polygarm with n angels

If we use π instead of 180°, use index indicates the index of next point from current point, then the formule to calculate one angel is:

(π × (n - index * 2) / n

When the index is 1, it became the formula we used to calculate one angel of a regular polygon.

How many kinds of polygarm with n angels exist?

We can only draw one kind of hexagram, and two kinds of heptagram (the above two).

Actually, how many x-grams we can draw, depends on how many points in the left or right part of the graphic.

We can easily get this:

For odd, the amount of x-grams is (n / 2) - 1, and for even it’s (n / 2) - 2.

The minimum angle of the polygarm with n angels

The max value of index which indicates the index of next point from current point, can be calculated by the last two formulas:

For odd, the The max value of index is n / 2, and for even it’s (n / 2) - 1.

Then, according to the first formula, we get this:

For odd, the minimume angel is π / n, and for even it’s 2π / n.

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