**A Mystic Rose is a beautiful image created by joining together points that are equally spaced around a circle.**

Watch the animation below to see how a Mystic Rose can be constructed. You can change the number of points around the circle.

**Can you describe how to construct a Mystic Rose?**

Alison and Charlie have been working out how many lines are needed to draw a 10 pointed Mystic Rose.

Alison worked out $9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 = 45$.

Charlie worked out $\frac{10 \times 9}{2}$ = 45**Can you explain how each method relates to the construction of a 10 pointed Mystic Rose?**

How would Alison work out the number of lines needed for other Mystic Roses?

How would Charlie work them out?

**Whose method do you prefer?****How many lines are needed for a 100 pointed Mystic Rose?**

**Could there be a Mystic Rose with exactly 4851 lines? Or 6214 lines? Or 3655 lines? Or 7626 lines? Or 8656 lines?**

**How did you decide?**

## Comments

### Mystic rose

How many lines are needed foe a 100 poinyed Mystic Rose ?

Well I calculated this by logic. If you write it down the number of lines needed each time ( 1,2,3,4....98,99,100) you will found out the there are 50 pairs of 101, 100+1 99+2 98+3 ... So in total there are 101*50=5050

Could there be a Mystic Rose with exactly 4851 lines?

Well we use the formula < n/2 * (n+1) >. This means that n**2 + n is equal to 4851*2 which is equal to 9702. Then we solve the quadratic equation and we get the n is equal to 98. You can do this with any number of lines.

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### Mystic Rose

**How many lines are needed for a 100 pointed Mystic Rose? **

Well I calculated this by logic. If you write down the number of lines needed each time (1, 2, 3, 4 .... 98, 99, 100) you will find that there are 50 pairs of 101 (100+1, 99+2, 98+3, ... 51+50).

So in total there are 101x50 = 5050 lines

**Could there be a Mystic Rose with exactly 4851 lines?**

Well we use the formula $\frac{n}{2}$ x (n+1) = 4851

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### Mystic Rose

Daniel, can you explain why the number of lines needed will be 1+2+3+4+ ... +98+99+100?

And can you explain how you arrived at the formula?

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