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# neeed help on this sequence problem. watch

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1. ive worked out the area but cant find a formula for the second please i need some biiig time help! thanks to anyone who can figure it out
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2. Mod1Week2Activity2 (1).docx (21.6 KB, 69 views)
3. Which one exactly are you stuck on?
4. (Original post by miml)
Which one exactly are you stuck on?
Is the area of the polygon related to the number of grid points inside and/or on the polygon?

im stuck on that bit...ive been told we are meant to find some sort of formula linking the grid points to the area...but i caaant do it
5. Are we talking about that specific polygon, or a general polygon drawn on the grid?
6. (Original post by miml)
Are we talking about that specific polygon, or a general polygon drawn on the grid?
general 1..
7. (Original post by mathslover786)
general 1..
'I' conjecture...

Let p be the number of dots on the polygon and k the number of dots in the polygon.

Then the area of the polygon is given by p/2 + k - 1

Proving this may be a bit more difficult. Induction is probably the way forward.

EDIT: This is actually known as Pick's theorem.
8. (Original post by miml)
'I' conjecture...

Let p be the number of dots on the polygon and k the number of dots in the polygon.

Then the area of the polygon is given by p/2 + k - 1

Proving this may be a bit more difficult. Induction is probably the way forward.

EDIT: This is actually known as Pick's theorem.

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