mathematical induction in geometry question (1 Viewer)

[denise1992]

could someone do this question please???


Use mathematical induction to prove that the sum of the interor angles of any polygon with n equal to or greater than 3 sides, convex or non-convex, is 180(n-2) . Begin with the induction step by choosing three adjacent vertices Pk, P(k+1) and P1 of the (k+1) polygon so that the angle of Pk, P(k+1) and P1 is acute, and joining the diagonal P1Pk to form a triangle and a polygon with k sides.


thanks

 

[lyounamu]

From the triangle property we know that triangle = 180 degrees

with that, we can prove that:

S(3) is true where

A^ + B^ + C^ = 180

We now suppose

S(4), S(5) .... are true and prove S(k+1) is true.

i.e. S(n) = 180(n-2) to S(k) = 180(k-2) where k>=3

If you draw the diagram that the question shows...you will get a triangle with p(k), p(k+1) and p(1) as vertices.

Now prove that n=k+1 holds true
LHS = S(k+1) = S(k) + p(k) + p(k+1) + p(1) = 180(k-2) + 180 = 180(k-1) = RHS

 

[jet]

I remembered doing it for someone before. Here is a diagram to accompany namu's proof.

 

[CountVonChocula]

fuck lol induction

 

[lyounamu]

I remembered doing it for someone before. Here is a diagram to accompany namu's proof.

That's the exact diagram I wanted

 

[CountVonChocula]

why the HELL do u need a diagram for induction

:mad1:

 

[lyounamu]

why the HELL do u need a diagram for induction

:mad1:

Um...because this is a mathematical induction question related to GEOMETRY

 

[EvoRevolution]

Geometrical proof by induction

 

[Kurwa]

woo go induction- those type of question will never come in the hsc !

 

[lyounamu]

woo go induction- those type of question will never come in the hsc !

Well, you never know. It's part of the 3 unit maths syllabus

 

[denise1992]

From the triangle property we know that triangle = 180 degrees

with that, we can prove that:

S(3) is true where

A^ + B^ + C^ = 180

We now suppose

S(4), S(5) .... are true and prove S(k+1) is true.

i.e. S(n) = 180(n-2) to S(k) = 180(k-2) where k>=3

If you draw the diagram that the question shows...you will get a triangle with p(k), p(k+1) and p(1) as vertices.

Now prove that n=k+1 holds true
LHS = S(k+1) = S(k) + p(k) + p(k+1) + p(1) = 180(k-2) + 180 = 180(k-1) = RHS

thankyou! it's much more easier than i thought it'd be..

 

[McLoving]

it better not

i never dun 1 in my life

 

[lyounamu]

it better not

i never dun 1 in my life

*fingers crossed* that it's in the exam

 

[McLoving]

*fingers crossed* that it's in the exam

it wont be

hav u done any past papers at all?

stupid g

 

[Kurwa]

I can assure you it wont come in the exams- think of it from teachers/ exam makers point of view..

they want everybody to do well, not everyone to FAIL..

only towards the end or towards the end of question they tend to be abit hard or tricky which is used to seperate high achievers !

 

[lyounamu]

it wont be

hav u done any past papers at all?

stupid g

I probably did more past papers in a month than you did in your whole life. I got that question twice in many past papers i have looked through.

 

[luv2luvurmama]

Well, you never know. It's part of the 3 unit maths syllabus

Suck my dick bitch, ive done the past 18 hsc 3 unit papers, and trials from the christian schools.. annddd that crap has never come up.. so now shut it!

 

[luv2luvurmama]

I probably did more past papers in a month than you did in your whole life. I got that question twice in many past papers i have looked through.

shut it whore, shove those stupid glasses up you infected fucking ass!

 

[gurmies]

Technically if they haven't asked something in the HSC before, then the likelihood of it being asked is increased...