In other words the (n-2) part means splitting the polygon into as many triangles as possible and then multiplying it by 180 to find the total sum of the angles.
I was thinking the same, if n represented I don’t 2m for all even sided shapes, that would be half the answer but that doesn’t cover the odd sided shapes
@@thebig12conference73 a triangle (n=3) has, well, 1 triangle. A quadrilateral (n=4) can be cut to 2 triangles. Suppose that an n-gon can be cut to (n-2) triangles. Let's prove that an (n+1)-gon can be cut to (n-1) triangles. Let A1A2A3...AnA(n+1) an (n+1)-gon Draw a line between Ai and A(i+2), such that the angle AiA(i+1)A(i+2)
@@seroujghazarian6343 your proof is not valid since the line AiA(i+2) may be both in and out of the polygon. Actually, if this line is wether fully in or fully out the (n+1)-gon, then your proof is working. Otherwise, it is not working. For example here is a 6-gon that invalids your proof: A1 at coordinates (0,0) A2 at coordinates (0,-1) A3 at coordinates (1,-3) A4 at coordinates (2,-1) A5 at coordinates (2,0) A6 at coordinates (1,-2) If you consider the line A2A4 it is not contained within the polygon, nor outside the polygon
This video goes in depth about the angles of a shape. Interior and exterior. I loved how much writing he did and how he explained himself. Very helpful.
People would click on this expecting an actual mathematical proof not just checking the first few patterns. Doesnt matter if you mention triangulation, you should show that if the proof relies so heavily on it.
can I ask ? how to do we get equation for interior angle in regular polygon ? cause this is just sum of all interior angles but if i want to explain to someone that it is like that, how can i surely tell him/her that it is like that? please if you understood what i meant by this reply...
The reason is that we divide the polygon into triangles by joining one point to all the other points and the number of points it can connect is the number of number triangles formed .As the adjacent sides as we can't connect adjacent points I e 2points 2less ∆ are formed so we minus 2 from it and multiply it with 180
A triangle has 3 internal angles and 3 intersect points, A B and C. czcams.com/video/g3zoeaDhjT8/video.htmlsi=Pf_6FntCF-sOiOKc This video proof sum internal triangle angle, A+B+C=180. A triangle has 3 intersection points. The sum of 3 intersection points are 3(A+B+C)=3(180). We know A+B+C=180. 3(A+B+C)=3(180) 2(A+B+C)+(A+B+C) =3(180) 2(180)+(A+B+C) =3(180) A+B+C =3(180)-2(180) A+B+C =(3-2)180 A triangle has 3 intersection points, n=3. A+B+C =(n-2)180
You are so right, Oon Han! I just rewatched the video, and the mistake is rather conspicuous. However, the point I wished to make is clear in context, and the mistake is not serious enough to prevent a viewer from misunderstanding where the formula comes from--after all, this is the principal purpose of the video. Nevertheless, I apologize for the mistake; I will strive to prevent similar ones in the future. =)
@@LetsSolveMathProblems I very much appreciate when videos with these little mistakes mention the mistake up front letting the viewer know where the mistake is, so they can look for it and know what was intended, otherwise these cause painful time loss and confusion for the unconfident viewer. I do like your video and how simple you made the intuition of the proof.
It is because like a four sided polygon have 4sides and four angles and you can see the video that shows a dour sided polygon can only cut into two triangles(i think is because the line cannot cross) So if you want to calculate how many triangle in that polygon ,just minus two and time 180°(the sum of triangle)
In other words the (n-2) part means splitting the polygon into as many triangles as possible and then multiplying it by 180 to find the total sum of the angles.
Thats not really proven at this point, there has to be shown that every n-Polygon can be devided into n-2 Triangles
I was thinking the same, if n represented I don’t 2m for all even sided shapes, that would be half the answer but that doesn’t cover the odd sided shapes
I was thinking the same thing but it gives you the right idea
@@thebig12conference73 a triangle (n=3) has, well, 1 triangle.
A quadrilateral (n=4) can be cut to 2 triangles.
Suppose that an n-gon can be cut to (n-2) triangles.
Let's prove that an (n+1)-gon can be cut to (n-1) triangles.
Let A1A2A3...AnA(n+1) an (n+1)-gon
Draw a line between Ai and A(i+2), such that the angle AiA(i+1)A(i+2)
@@seroujghazarian6343 your proof is not valid since the line AiA(i+2) may be both in and out of the polygon.
Actually, if this line is wether fully in or fully out the (n+1)-gon, then your proof is working. Otherwise, it is not working.
For example here is a 6-gon that invalids your proof:
A1 at coordinates (0,0)
A2 at coordinates (0,-1)
A3 at coordinates (1,-3)
A4 at coordinates (2,-1)
A5 at coordinates (2,0)
A6 at coordinates (1,-2)
If you consider the line A2A4 it is not contained within the polygon, nor outside the polygon
This video goes in depth about the angles of a shape. Interior and exterior. I loved how much writing he did and how he explained himself. Very helpful.
People would click on this expecting an actual mathematical proof not just checking the first few patterns. Doesnt matter if you mention triangulation, you should show that if the proof relies so heavily on it.
the way you split the shapes into triangles was very interesting
thank you so much!
can I ask ? how to do we get equation for interior angle in regular polygon ? cause this is just sum of all interior angles but if i want to explain to someone that it is like that, how can i surely tell him/her that it is like that?
please if you understood what i meant by this reply...
A channel worth subscribing to!!
It's alright bro
Keep it going on.
Thank you this helped a TON! .
The reason is that we divide the polygon into triangles by joining one point to all the other points and the number of points it can connect is the number of number triangles formed .As the adjacent sides as we can't connect adjacent points I e 2points 2less ∆ are formed so we minus 2 from it and multiply it with 180
You are the best explainer ever
3-1 = 1 wow I learned something new
thanks for the video, i've been trying to understand why the number 180 in particular was used for this theorem.
This seems to be logical inference rather than rigorous mathematical proof !
A triangle has 3 internal angles and 3 intersect points, A B and C.
czcams.com/video/g3zoeaDhjT8/video.htmlsi=Pf_6FntCF-sOiOKc
This video proof sum internal triangle angle, A+B+C=180.
A triangle has 3 intersection points. The sum of 3 intersection points are 3(A+B+C)=3(180).
We know A+B+C=180.
3(A+B+C)=3(180)
2(A+B+C)+(A+B+C) =3(180)
2(180)+(A+B+C) =3(180)
A+B+C =3(180)-2(180)
A+B+C =(3-2)180
A triangle has 3 intersection points, n=3.
A+B+C =(n-2)180
intresting
thanks, good explanation
OMG thank you for helping me understand
i have psat tmrrw and you are making my life easier
Edit: I'm still gonna kms lol
How it go
In triangle isn't it (3-2)
ye i think he made a mistake
Yip
but why
it't not a proof though... just recognition of a pattern how do you know it continues forever,
3 - 1 = 1 disliked
You are so right, Oon Han! I just rewatched the video, and the mistake is rather conspicuous. However, the point I wished to make is clear in context, and the mistake is not serious enough to prevent a viewer from misunderstanding where the formula comes from--after all, this is the principal purpose of the video. Nevertheless, I apologize for the mistake; I will strive to prevent similar ones in the future. =)
LetsSolveMathProblems OK. You have amazing videos by the way. Liked. Subbed.
@@LetsSolveMathProblems I very much appreciate when videos with these little mistakes mention the mistake up front letting the viewer know where the mistake is, so they can look for it and know what was intended, otherwise these cause painful time loss and confusion for the unconfident viewer. I do like your video and how simple you made the intuition of the proof.
Love from india
Why is it -2? How does that work visually?
It is because like a four sided polygon have 4sides and four angles and you can see the video that shows a dour sided polygon can only cut into two triangles(i think is because the line cannot cross)
So if you want to calculate how many triangle in that polygon ,just minus two and time 180°(the sum of triangle)
May have some wrong 😅
3-1=1 ??..... OMG
Yes
How it's possible
This guys stutter and mic
uhhhhhh......its unstoood why the hell you guys freakin'
Bad