Mystic Rose

The circle below has seven points spread equally around its circumference. Press start to watch the construction of a seven pointed mystic rose. You can construct different sized roses by using the slider.

Watch the animation for some different sized mystic roses.
What did you see? Describe how to construct a mystic rose.

Now describe what a completed mystic rose looks like.

Alison and Charlie have been wondering how many lines are needed to draw a 10 pointed mystic rose.

Alison wrote down the calculation $9+8+7+6+5+4+3+2+1$.

Charlie wrote down the calculation $\frac{10 \times 9}{2}$

Who is right? Can you explain how the calculations relate to the diagram?

Investigate the number of lines needed in mystic roses of different sizes.
How would Alison work them out? How would Charlie do it?
Will they always get the same result?

What are the advantages of the alternative methods?

How many lines are needed for a 100 pointed mystic rose?

Which of the numbers below could be the number of lines needed to draw a very large mystic rose? How many points would each mystic rose have around its circumference?

• 4851

• 6214

• 3655

• 7626

• 8656

You may wish to try the problems Picturing Triangle Numbers and Handshakes. Can you see why we chose to publish these three problems together?

You may also be interested in reading the article Clever Carl, the story of a young mathematician who came up with an efficient method for adding lots of consecutive numbers.
 

Click here for a poster of this problem.