The Mystic Rose Puzzle
The Mystic Rose is a geometrical construction that is so simple but goes back in time. A Spanish Catalan religious writer named Ramòn Llull created the first recorded diagram in his books on religious concerns around the year 1290. More of the story here.
You place a number of equally spaced points around a circle and draws straight lnes from each one to all the others. It is very satisfying to draw the picture for more and more points. Only when you get to about 19 points do you begin to see the flower appearing. This gives you an idea.
The puzzle is to discover a method of working out the number of lines. It is difficult counting them. There are two ways, one is practical, the other is a simple mathematical formula. To start you off here is a table of the first few numbers.
From the table you can work out that for say 10 points, the number of lines drawn equals 1+2+3+4... up to 9 (one less than 10). Counting is slow unless you use eight-year old Carl Friedrich Gauss’ solution in the year 1785. If you write 1 to 9 on the first line. then 9 to 1 below on a second line, draw an underline and add the two lines together you get the number 10 written nine times which adds up to 90. This is twice the total you want, so divide by two and the answer is 45.
This is where mathematics helps. For N points on a circle the number of lines to join them all is N x (N-1) divided by 2. For ten points, 10 x (10-1) divided by 2 = 45. Well done if you worked the formula out (or even if you worked out Carl’s method of adding numbers).
Just a thought. Have you wondered how many triangles are there in each mystic rose?
