About Stars |
We knew some stars which could be drawn i one broken line, with 5 or 8 peaks. But then my daughter Astrid-Marie, 7, discovered, that a 7-star was possible, and a further investigation showed, that there exists a great lot more.
This is related to number theory.
Here is shown the 7-star, that Astrid-Marie found (In fact there are 2)
Click on the figure to see how it is done.
Here is the second possible 7-star
Click on the figure to see how it is done.
Now we will show some of the more
conspicuous variants, with higher numbers they are not so exciting, also more tedious to carry out.
Here you see the well known 5-star
Here is the probably well known 8-star, the only one.
Here is the first 9-star of 2 possible versions:
-and here is the other
In fact there are 4
11-stars, but only one 12-star.
Here it is.
Click on the figure to see how it is done.
For the possible number of different n-stars, they are shown in the table below up to n=20.
It seems, that for any number greater than 6 there exists at least one star. With help from mr. Tom Gettys I now have a proof showing that the assumption is correct (march 2. 2005).
| Number of peaks=n | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
| Number of stars | 1 | 0 | 2 | 1 | 2 | 1 | 4 | 1 |
| 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 |
| 5 | 2 | 3 | 3 | 7 | 2 | 8 | 3 |