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[who_loves_maths]

^ yes. this was my argument exactly - look at my post at the top of this page.

there is a correction that need to be made to your argument, however. you do not need to prove your 'a' is irrational - simply not an integer will suffice. ('seems' almost too easy )

so far, there are, very 'simply', two ways that can be used to prove no_arg wrong conclusively:


1) Prove [ln(pi +1) -2]/(1 - ln(pi)) is non-integral.

or,

2) Prove [6 - ln(pi +1)]/ln(pi) is non-integral.


Both seem like the blindingly obvious since you can't simplify them arithmetically into integers ... but i suppose the point is to prove that now (otherwise i assume no_arg will remain unsatisfied).

 

[Dumsum]

Y'all could take over the world with your combined maths genius...

 

[babydoll_]

CASE CLOSED

babydoll, obscene images are strictly banned on this forum.

 

[velox]

Y'all could take over the world with your combined maths genius...

Not that its useful or anything.

 

[Dumsum]

Not that its useful or anything.

My thoughts exactly, however I've said this before about something else and Slide refuted me talking about showing the interconnectedness of mathematics...it's still interesting

 

[acmilan]

ln(pi^x + pi^(x+1)) = 6 -----> ln[(pi^x)(pi + 1)] = 6
That's one wierd log law!!
ln(a+b)=ln(ab)...not true I'm afraid!

pi^x + pi^(x+1) = pi^x + pi^x.pi = pi^x(1 + pi) ?

 

[no_arg]

Apologies for the previous post log laws are OK BUT

all you've done is rewrite the question!

Clearly [ln(pi +1) -2]/(1 - ln(pi))=4

It is perfectly possible for the ln of an irrational to be rational!
Think of ln(e^2)!

When asked to calculate ln(e^(.75)) to 20 significant figs Maple returns

.74999999999999999998

Just round off

 

[who_loves_maths]

^ i doubt it would be easy for HSCers, myself included, to actually prove the irrationality of something like [6 - ln(pi+1)]/ln(pi), when most people, once again myself included, don't even know how to prove the irrationality of 'pi' (without outside reference) ...

perhaps you are demanding too much here no_arg?

however, if you can produce such a proof yourself, then maybe you can post it up so that everyone else may learn your idea of the 'proper' and 'acceptable' approach to a non-calculator proof? thnx.


Edit: btw no_arg, all it takes is for someone who actually knows the process of deriving the approximation pi^4 + pi^5 =[approx.] e^6 to end this conundrum ... so you're really just playing on the fact that ppl here so far have not found the actual derivation to refute you. but we all know it's out there; so i am still failing to see any profoundness in the point you're trying to make about using calculators and any meaningfulness in your stubbornness - i'm sure you know very well that it's an approximation.

 

[brett86]

3.14159266^4 = 97.40909182902901737436094415467536 (maybe)

???

are u honestly saying that u dont think 3.14159266⁴ = 97.40909182902901737436094415467536?

why dont u multiply it out on paper and see for yourself before making stupid comments

buchanan's argument is completely correct and so is who_loves_maths

2 people have proved u incorrect, so this continuing this thread is pointless

McLake or turtle_2468, please close this thread, thank u

 

[no_arg]

Wow

You really are keen to stop people discussing mathematical concepts aren't you!

Look at all the lovely mathematics in this thread ?

We have students solving equations in ingenious ways, considering quite deeply what it means for reals to be rational and irrational, comparing Newton's method to analytical solutions, making subtle applications of the calculus, exploring the relationships between e Pi and ln...all sorts of positive activities! Where else on this forum have you seen such open ended creative mathematical activity. It's what learning and teaching is all about! Does it really matter whether or not I actually believe that [ln(pi +1) -2]/(1 - ln(pi))=4?


And all we get from you is "close the thread, shut it down" "don't like it" "don't get it"


Experience is a harsh teacher Brett.... it gives you the test first and the lesson later.

 

[brett86]

lol, im not discouraging people from doing maths, what i am trying to do is get u to admit that pi^4 + pi^5 is not equal to e^6

im angry cause u claimed pi^4 + pi^5 = e^6 which is obviously wrong and hsc-er might believe it

also, u keep saying that buchanans argument is invalid when its perfectly correct

and btw, i encourage everyone whos interested to post whatever creative ways they come up with to disprove no_args ridiculous claims

 

[McLake]

Closed by Request