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**zxcvbnm123****Member**- Registered: 2013-05-08
- Posts: 15

i need to know the formula to get the coordinates that are on the perimeter and within the shape of square and rectangle. does anyone know that?

lets say square coordinates of (1,1) , (1,3) , (3,3) , (3,1)

points on perimeter would be (1,2) , (2,1) , (2,3) , (3,2) excluding the actual coordinates above.

points within shape would be (2,2)

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,468

hi zxcvbnm123

Welcome to the forum.

I seem to remember there is a formula, so I'll try to find it. Failing that, maybe I can work it out.

Back soon.

EDIT: This is the one I remembered:

http://en.wikipedia.org/wiki/Pick's_theorem

It's not quite what you want, but it'll give you a start.

Are the sides of the shapes parallel to the axes ? (Harder if not)

Bob

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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**zxcvbnm123****Member**- Registered: 2013-05-08
- Posts: 15

yes all lines and sides are parallel

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,603

Do you want just points with integer coordinates?

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

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**zxcvbnm123****Member**- Registered: 2013-05-08
- Posts: 15

yes just need point with integer . the type of answer i need is what i shown above.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,603

Well, for the points on the edges, if the square's coordinates are (a,a), (a,b), (b,a) and (b,b), they are:

(a,a+k), 0<k<b-a

(b,a+k), 0<k<b-a

(a+k,a), 0<k<b-a

(a+k,b), 0<k<b-a

As for the points inside the square, they all have coordinates of the form:

(a+k,a+l), 0<k,l<b-a

*Last edited by anonimnystefy (2013-05-08 06:28:03)*

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

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**zxcvbnm123****Member**- Registered: 2013-05-08
- Posts: 15

i am sorry, i am very new to geometry coordinates... i dont understand your formula...can give me one example how you use that formula to get the answers?

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,603

Hm, well, let's try with a=1 and b=4.

That would be the square (1,1), (1,4), (4,1), (4,4).

If draw it in the Cartesian coordinate system, you will see that the point on the edge are (1,2), (1,3), (2,1), (2,4), (3,1), (3,4), (4,2) and (4,3). By the formulas above we get:

(1,1+k), for 0<k<3, which gives (1,1+1)=(1,2) and (1,1+2)=(1,3)

(4,1+k), for 0<k<3, which gives (4,1+1)=(4,2) and (4,1+2)=(4,3)

(1+k,1), for 0<k<3, which gives (1+1,1)=(2,1) and (1+2,1)=(3,1)

(1+k,4), for 0<k<2, which gives (1+1,4)=(2,4) and (1+2,4)=(3,4)

If you compare the two sets of points, you will see we got the same points by drawing the square on the grid and by the formulas above.

Oh, just wondering, what do you need this for?

*Last edited by anonimnystefy (2013-05-08 08:26:32)*

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

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**zxcvbnm123****Member**- Registered: 2013-05-08
- Posts: 15

some homework unrelated to maths...and we need to create this formula

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,603

Programming, maybe?

Are you a bit clearer about the formulas?

Here lies the reader who will never open this book. He is forever dead.

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**zxcvbnm123****Member**- Registered: 2013-05-08
- Posts: 15

yes thank you very much , brilliant formula . rushing my work now

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**zxcvbnm123****Member**- Registered: 2013-05-08
- Posts: 15

can give me a example on how you get the answer for points within shape? and i think l is l<b not l<b-a

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,603

Well, if we take the square as in the last example, we know that the points inside the square are (2,2), (2,3), (3,2) and (3,3).

What do you get when you do

(1+k,1+l), for 0<k<3, 0<l<3?

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**zxcvbnm123****Member**- Registered: 2013-05-08
- Posts: 15

its ok i got it already

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,603

That is great!

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