Math Problems

[Janny]

n^2 - n + 41?
1 => 41
2 => 43
3 => 47
4 => 53
5 => 61

[mithrand1r]

Originally posted by Janny
n^2 - n + 41?
1 => 41
2 => 43
3 => 47
4 => 53
5 => 61

The next number in this series is not 61.

61
Can't work out a formula tho... second row of differences, is it quadratic?

No it is not quadratic.

[Janny]

Hmm, but it worked. What is it then?

[mithrand1r]

Originally posted by Janny
Hmm, but it worked. What is it then?

The next number in this series is 59.

41, 43, 47, 53, 59

The numbers are the prime numbers (Numbers with two factors, itself and (1) One).

Prime numbers under 100:

02, 03, 05, 07, 11, 13, 17, 19, 23, 29, 31, 37, 41,
43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97

[Janny]

Ah! The irregular heartbeat of number theory!
Had I found a formula which linked all them that would have been impressive. Didn't Riemann find something to do with 41 in a prime number formula...
*runs upstairs*
Euler then... x^2 + x + 41, from x = 0 to 39 gives prime numbers. So I would have got if I'd assumed the sequence began with the 0th term.

[mithrand1r]

Originally posted by Janny
Ah! The irregular heartbeat of number theory!
Had I found a formula which linked all them that would have been impressive. Didn't Riemann find something to do with 41 in a prime number formula...
*runs upstairs*
Euler then... x^2 + x + 41, from x = 0 to 39 gives prime numbers. So I would have got if I'd assumed the sequence began with the 0th term.

Yes. But as you mentioned, it fails at n=40.
=============================================
A snail is at the bottom of a 30ft well.
Each day the snail climbs up 3 feet, but at night it slides down 2 feet.

Assuming the snail continues to climb up the well at the current pace, how many days will it take for the snail to exit the well?

[Radagast The Brown]

Originally posted by mithrand1r
Yes. But as you mentioned, it fails at n=40.
=============================================
A snail is at the bottom of a 30ft well.
Each day the snail climbs up 3 feet, but at night it slides down 2 feet.

Assuming the snail continues to climb up the well at the current pace, how many days will it take for the snail to exit the well?

27 days.

Btw, I still didn't succeed completing the 6x6 magic square.

[Valandil]

Originally posted by mithrand1r
Yes. But as you mentioned, it fails at n=40.
=============================================
A snail is at the bottom of a 30ft well.
Each day the snail climbs up 3 feet, but at night it slides down 2 feet.

Assuming the snail continues to climb up the well at the current pace, how many days will it take for the snail to exit the well?

Radagast says 27, but I think it would take 28 days. After 27 days and nights, it would be 27 feet up... which is within its 'striking distance' of 3' for the 28th day.

[Radagast The Brown]

Originally posted by Valandil
Radagast says 27, but I think it would take 28 days. After 27 days and nights, it would be 27 feet up... which is within its 'striking distance' of 3' for the 28th day.

Oh, right. My mistake.

[Valandil]

Originally posted by mithrand1r
Excellent.

That is one example of a trangle that is not 180°.

It is considered to be part of the Riemansan (sp?) space.
[Triangle has more than 180°.]

The other type of space is Lobechevsky (sp?).
[Triangle has less than 180°.]

Euclidian space.
[Triangle has exactly 180°.]
This is probably what most people had in elementary and/or secondary school.

I thought part of the definition of a triangle was that it was all in a plane though? But I'm not a mathematician... and am unfamiliar with the various 'spaces' you mention.

[Fat middle]

Originally posted by Valandil
I thought part of the definition of a triangle was that it was all in a plane though? But I'm not a mathematician... and am unfamiliar with the various 'spaces' you mention.

Well, the definition of plane also changes with the space you're considering

[Janny]

Yeah, do you mean a triangle on the surface of a sphere? I assumed you meant internally, like us minions deal with cyclic angles...

Can someone explain to me imaginary numbers? I get that they go up and down from the left right of reality, but what justification is there to say 1i squared = -1?

[Valandil]

Originally posted by Fat middle
Well, the definition of plane also changes with the space you're considering

sounds loopy to me!

[Valandil]

Originally posted by Janny
Can someone explain to me imaginary numbers? I get that they go up and down from the left right of reality, but what justification is there to say 1i squared = -1?

Whew! Now THAT was a LONG time ago... when I had THAT in school. Isn't it that i is the 'imaginary number' - and that i-squared is -1. I don't know if you really need any justification since it's all 'imaginary' anyway - right?

(EDIT: makes me wonder why they bothered teaching it to us anyway! )

[Janny]

Hmm, I thought you got numbers which were compound like 5 + 7i?
To me the whole concept seems wrong and like Pythagorous with... um.. something... irrational numbers maybe... I will deny there logical existance as long as possible! But then again I believe in God... do you need an aspect of faith to accept imaginary numbers?

[Radagast The Brown]

I have a question - this thread's aim is to ask questions about troubles you have in math (and I have many of that kind unfortunately) or to ask 'riddles' in math - like the snail one?

[Janny]

I'm doing both, but I have more thirst for knowledge than questions I can pose.
So imaginary numbers?
If they do exist, then it's saying there is a number which multiplied by itself equals the negative of itself. Right?

[mithrand1r]

Originally posted by Janny
I'm doing both, but I have more thirst for knowledge than questions I can pose.
So imaginary numbers?
If they do exist, then it's saying there is a number which multiplied by itself equals the negative of itself. Right?

i is defined as the square root of negative 1.


''i = sqrt(-1)
i^2 = -1
i^3 = - sqrt(-1)
i^4 = 1


Imaginary number exist (in your imagination )

I have seen imaginary numbers used in electrical engineering and physics. I am not sure exactly how, though.

[Count Comfect]

i was "invented" in order to let you have square roots for negative numbers, because math works much more nicely if the square root function is defined for all x

[Janny]

Yeah, I know they said things like engineering required them loads, but still. Of course now one looks at it you need to have an expression for a negative square root, but to look at it from the prespective that a number multiplied by itself to form a negative number is just a bit weird.

This may sound like a bit of a sad question, but do any of you hve a favourite proof? Are any of you as geeky as me to have that kind of thing?