Prove: Number of Diagonals of a Polygon

Let's develop an intuitive method for counting number of diagonals of a polygon--it will come out to be n(n-3)/2, in which n is the number of sides.

Your support is truly a huge encouragement.
Please take a second to subscribe in order to send us your valuable support and receive notifications for new videos!

Every subscriber and like are immensely appreciated.

[bhoborlina]

I love the way you say diagonals. Btw, great video!

[RasperHelpdesk]

Could use inductive proof too.

First, check for base case of n = 3. In a triangle there are 0 diagonals. And (3)(3-3)/2 = 3*0/2 = 0, so initial condition works.
Assume n sided polygon and add another vertex. The vertex can draw a diagonal to all of the original vertices except the two it borders so that is adding (n-2). It also allows a diagonal to be drawn between the two vertices it borders as they no longer share an edge, so that is adding 1.
Diagonals for n+1 = Diagonals for n + (n-2) + 1
D = (n)(n-3)/2 + (n-2) + 1 <use formula for n sided>
D = (n2 - 3n) / 2 + (n-2) + 1 <distribute the n, for ease n2 means n squared>
D = [n2 -3n + 2n - 4 + 2] /2 <common denominator>
D = [n2 - n - 2] /2 <combine terms>
D = [(n+1)(n-2)] /2 <factor>
D = [(n+1)(n+1 - 3)] /2 <change n-2 into n+1 - 3>

And there we have that if true for the n case it is true for n+1, so true for all n >= 3

[КристианКръстев-ьг]

This video was extremely helpful and I can actually explain this too using your method because I understood it! THANK YOU! <3

[RiteshKumar-bpdm]

I would be very pleased if you don't stop making videos like this 😄

[achintv]

Outstanding mind blowing awesome sir 👌👌🙏🙏

[akarsha-madhugiri]

Tqsm ...math is becoming easy by your grace ..
God bless u ...

[binodkumarchoudhary]

Thank you sir for this video. I didn't know how this formula made so I wanted to know its proof and your video explain everything that I wanted to know.

[willbishop]

Number of pairs of points - number of sides
= (n choose 2) - n
= n * (n - 1)/2 - n
= (n^2 - n - 2n) / 2
= n * (n - 3) / 2

[harshini]

Thank you much sir, you made me understand everything😅
God bless ya

[unicock]

thanks for purging me from this problem😂, love from India!!!!

[kennie]

Thank you so much sir...
Really helped me a lot.

[RiteshKumar-bpdm]

Wow such a great explanation of the formula 👏 ❤

[ranjeetashrivastava]

It was really really helpful.. thanks for uploading this video... I was searching for this since a long time

[lavendermongoose]

i was completely confused in class.. this video explained everything perfectly! Thankyou so much!!!

[chococookie]

Thank youu for such a simple explanation !😃

[jesst]

GOD BLESS YOU
THANK YOU SO MUCH
I'm going to use this

[Yperrr]

[C(n, 2)= n!/2*(n-2)!]-n
The -N at the end excludes the possibility of taking 2 contiguous vertex

[shivanighodake]

Thank SIR 😊😊😊
I DON'T KNOW THAT TRICK

[Thanos-x]

Very very much thanks to make this video.

[deepjyoti]

A new proof
If n point are given
Then total no. Of line passing through that. Is nc2 but we also counted sided along with diagonal so substract no. Of sides 'n'

Then no of diagonal =nc2-n
Which simplifies into n(n-3)/2