Math Is Fun Forum

juantheron

Member

Registered: 2011-10-19

Posts: 312

no. of parallelogram

no. of parallelogram that can be formed by using 4 parallel lines intersecting other set of 3 parallel lines

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: no. of parallelogram

hi juan

i got 4*3/2 * 3*2/2=6*3=18

---

“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
The knowledge of some things as a function of age is a delta function.

juantheron

Member

Registered: 2011-10-19

Posts: 312

Re: no. of parallelogram

anonimnystefy can you explain me

thanks

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: no. of parallelogram

___/_/_/_/___
__/_/_/_/_____
_/_/_/_/______
/  /  /  /

This is basically the picture you need,although a little butchered.

you can do this by just counting the parallelograms,but i think it's better to derive a formula for it so that it can be generalized.

we can form a parallelogram by taking any two lines from the first set of parallel lines,and two lines from the second set of parallel lines.That means that we have to calculate the number of ways to select 2 out of 4 lines in the first set of lines which is:

4 choose 2

and the number of ways we can choose 2 out of 3 lines in the second set which is:

3 choose 2

when we calculate the product of the two we get:

4 choose 2 * 3 choose 2=4*3/2 * 3*2/2=6*3=18

if we want to generalize this,it means we need to take 2 out of n lines in the first set and 2 out of m lines from the second set.The formula would be:

n choose 2 * m choose 2=n(n+1)/2 * m(m+1)/2=mn(m+1)(n+1)/4

you can check the formula by substituting n=4 and m=3

---

“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
The knowledge of some things as a function of age is a delta function.

juantheron

Member

Registered: 2011-10-19

Posts: 312

Re: no. of parallelogram

thanks anonimnystefy

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: no. of parallelogram

you're welcome!

---

“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
The knowledge of some things as a function of age is a delta function.