Math Community Quiz

[nemo]

Code: [Select]

(sqrt(5)+3)/2=phi^2→D
D is equal to phi, not phi squared.

wait: i'm wrong. my bad. i'll keep looking.

[Xeda112358]

I am fairly sure (sqrt(5)+3)/2 is phi^2 or do you mean D is supposed to be phi?

Ninja

[nemo]

oh. you forgot the ones place.

edit: well, the "phi^2 ^ 0" place. aka the ones place.

[Xeda112358]

Nope, that's not it . The decimal part is in base 10, not base phi^2 (and happens to be the "ones" place)

[nemo]

but the question asks to convert 10 into base phi^2... so if 11.52786 is in base 10 how does this answer the question? i believe 10 in base phi^2 is 110.52786... i messed up on the decimals the first time but try convert 11.52786 from phi^2 to base 10 and you will not get 10.

[ruler501]

The ones place eists in all bases. In bases it goes up to one less than the number of its base because the tens place is really the base^1 place.

@Nemo Irrational numbers can't make terminating decimals. If you add enough digits you will get more decimal places. If you add an infinite decimal places that are in an irrational number you get an irrational number as the answer a non terminating decimal. The only numbers that can be displayed without an endless decimal place are integers between it and negative it, and multiples of it

[Xeda112358]

Oh, yeah, oops. Yes, you are correct about the 110 part, but the decimal part of that is in base 10 Think about how you do decimals in binary. 11010.011101 for example...
011101/1000000 is the decimal .453125

In other words, the decimal part that you have needs to be converted to base phi^2, too. You can do this by applying basic division techniques. (long hand )

[nemo]

i've never done decimals in any other base but 10. alright, i get how that part is in base 10. so if it's in base 10 then does that answer the question or not? because it isn't in base phi^2, so it can't. does my answer work?

wait, nevermind, i see how you would do it. but i'm way too lazy to do all that math out on paper.

[ruler501]

I would write a program to do it for me if I was you guys.

[jnesselr]

I would write a program to do it for me if I was you guys.

Which is exactly what I did, and I got:
110.1021111111111111111

So the fifth digit is 1.

[ruler501]

That seems more rational than the other things we were getting I'm very tempted to believe it.
could I see your code to check it so I can see if your right?

[jnesselr]

That seems more rational than the other things we were getting I'm very tempted to believe it.
could I see your code to check it so I can see if your right?

Sure, but don't expect it to be readable or nice and tidy.  I just barely got it working, so I'm not entirely believing my answer although it should be fairly simple to check:
http://graphmastur.pastebin.com/29VSHcUX

[ruler501]

I'll give it to graphmastur His code looks right

[Xeda112358]

I believe it is correct, though I did not look at the code

(If it isn't then a month from now I will make mention of it )

[ruler501]

If it isn't right a month from now we'll all have to remove graphmastur from the game... right?

Spoiler For Spoiler:

(just kiddding)