5-pointed star math investigations

GOOD MORNING

!!!

5-p0inted starBy:

Nancy B. Madarang

How many 5 pointed stars can you form in 5 points? 10 points?

15 points? 20 points? 25 points? 30 points? N points? Investigate.

Search a pattern

5points = 1 pc 5pointed star

10 points = 2pcs of 5 pointed star

15 points = 3pcs of 5 pointed star

20 points = 4pcs of 5 pointed star

25 points = 5pcs of 5 pointed star

30 points = 6pcs of 5 pointed star

Number of points number of 5 pointed stars5 110 215 320 425 530 6. .. .

n , n is a multiple of 5

Conjecture:The number of 5 pointed stars in the nth points is , where n is the number of points and a multiple of 5.

Prove the conjectureFor any number n where n is the number of points and which n is a multiple of 5, forms a 5 pointed star. Therefore, the number of 5 pointed stars used in nth is

To draw a 5-pointed star pay attention to the following steps:

1. Choose any starting point.

2. To determine the next point to connect the 5 pointed star, use this formula : ;

where n is the n is the # of points

Ex. = 1 x 2 = 2 = 2 x 2 = 43. For the next point follow step # 2. Until you form a 5-pointed star.Note: any point should have only two segments to connect.

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