Geometrical Induction (1 Viewer)

[dawso]

in the syllabus it has an area of 'geometrical induction,' our teacher showed us this but said not to wory bout it cause it hasnt been in hsc in his memory ever, has anyone else done this stuff at their school, and or had questions in test etc

 

[CM_Tutor]

I can't think of any exam that had it off hand, but one question that could be asked is to prove that the angle sum of an n-sided polygon is (n - 2) * 180, if n > 2 is an integer.

 

[AGB]

we hav dun it in class, but were told that it would only be asked in a 4u exam....

 

[Calculon]

Originally posted by AGB
we hav dun it in class, but were told that it would only be asked in a 4u exam....

*pulls hair out, runs off screaming*

 

[~*HSC 4 life*~]

Yeah, chances are that if it hasn't been in the HSC yet, it could likely be in ours

 

[Calculon]

Originally posted by ~*HSC 4 life*~
Yeah, chances are that if it hasn't been in the HSC yet, it could likely be in ours

I'm more worried about the fact that it probably will be in 4u

 

[CM_Tutor]

Calculon, this particular proof is really fairly easy for 4u - if it's on a 4u HSC, it won't be near the end. The HSC examiners can get way more creative than this if they want to focus on induction in 4u, but it's usually OK. Most difficult 4u induction questions are difficult because of the other parts of the question.

 

[AGB]

yeah arent those ones that are sort of like 'compound' induction questions the tough 4u ones?? sorry if u dont get what i mean by compound...i cant think of another way to say it...

like the ones where you have a U1, U2, U3, and Un and u hav to use all of them...

 

[dawso]

yeah, the example we did on these questions were not hard to get out, its just heaps hard to develop what u r trying to prove wit k+1 shit

 

[CM_Tutor]

Originally posted by AGB
yeah arent those ones that are sort of like 'compound' induction questions the tough 4u ones?? sorry if u dont get what i mean by compound...i cant think of another way to say it...

like the ones where you have a U1, U2, U3, and Un and u hav to use all of them...

The phrase you are looking for is strong induction - ie. induction where the assumption must be stronger than the usual 'let k be a value of n for which the result is true', becoming things like 'let k and k + 1 be values of n for which the result is true', or even 'let k be a value of n such that the result is true for all values 1, 2, 3, ..., k'. Strong induction need not be any harder than ordinary induction, just a bit messier, although it can be. (like...

Theorem: All non-prime positive integers n can be factored into primes)

Note to Extn 1 students - strong induction (like this question) is not in your course.