Math Game

[Rogan Josh]

I have one for you:

let k and p be n-dimensional vectors, a and c are real numbers, and eps is a real number which is very small.

What is the n-dimensional integral of (k^2 + 2*k.p +c -i*eps)^(-a) over the infinite volume. You may take eps->0 (it only acts as a regulator).

[shade]

differential equations don't seem a problem but simple sums are

lets try an eaier one
create 20 by using four 4's.
(eg to create 8=> 4+4-4+4)
(this really is easy)

Shade

[Urban Ranger]

Originally posted by shade
differential equations don't seem a problem but simple sums are

lets try an eaier one
create 20 by using four 4's.
(eg to create 8=> 4+4-4+4)
(this really is easy)

Shade

Ha!

(4+ 4/4)*4

That's too simple

[Juggernaut]

Try this one:
A goat is tied to a pole on the circumference of a circular lawn with a 15 meter long leash. The radius of the lawn is 20 meter. How much of the lawn can the goat eat?

[Dauphin]

Originally posted by uncle_funk
Try this one:
A goat is tied to a pole on the circumference of a circular lawn with a 15 meter long leash. The radius of the lawn is 20 meter. How much of the lawn can the goat eat?

All of it - given that goats will eat anything, it would eat through the leash that was preventing it from eating all the grass

[shade]

a=Bgsin(7,5/20)
b=Pi/2 - a
==>[(4*a)/(2*Pi)]*20²*Pi
+[(2*b)/(2*Pi)]*15²*Pi - (20*(20*sin(2*a)))

voila solved

Ha!
(4+ 4/4)*4

That's too simple

well try the first one no-one even came up with a solution(only the question if it was a trickquestion and it isn't)

create 24 by using +,-,x,:
and the numbers 1,3,4,6
You may only use the numbers 1 time each and you have to use them 1 time each.

Shade

[Chowlett]

Originally posted by KrazyHorse


I guess so. Theoretically, though, you'll have to extend to functions of two variables. Shouldn't be that hard, but I've never actually done it myself.

I think we did that, and it wasn't too hard, as you suspected.

Ok, I have some problems from the Archimedeans (Cambridge mathmo society) problems drive, syndicated in the internal journal "Eureka". I'll post them one at a time. They are very hard, and I couldn't solve any of them. I do however have the answers.

1. Complete the following phrases, where each word has been replaced with its initial letter - eg 1=FP of a CM is 1 = Fixed Points in a Contraction Mapping.
a) 1729 = N of HT
b) 4.6692...=R of PD in some DS
c) 0.00000007151=P of W the NL
d) 2^3021376(2^3021377-1)=LKPN (possibly not true any more)
e) 3.14159...=LN
f) 13=AP
g) (1+æ5)/4=C of PBF
h) +æ2/12=V of RT of SO
i) 23=HP
j) 13=B of EE
k) 6=RS in FD
l) 25=PBOH

edit: arghh! The weird symbols are square roots. For some odd reason, charmap in XP no longer shows the keystrokes for the Symbol font...

[Dauphin]

d) 23021376(23021377-1)=LKPN (possibly not true any more)

Largest Known Prime Number.

That -1 gave it away.

The others appear more obsure at first glance. For example

e) 3.14159...=LN

I know its pi, but what does LN stand for? *Something* Number?

[Chowlett]

Originally posted by Big Crunch

Largest Known Prime Number.

That -1 gave it away.

Hmm, a prime number which is a product of 2^3021376 and (2^3021377-1)...

[KrazyHorse]

(sorry BC)

All in good fun.

[shade]

Originally posted by Chowlett
b) 4.6692...=R of PD in some DS

this is(translated from Dutch) 'the number of Feigenbaum'
best guess I can make for the 'english shortcut' is
Rate of periodic Dubbling in Some Dynamic Systems
those some are the unimodal images and the number is defined as
q=lim(i->infinity)[(r(i+1)-r(i))/(r(i+2)-r(i+1))]
( those (i+??) are indices)

(Noone for the simple +-*/?? )

Shade

[Dauphin]

Originally posted by Chowlett


Hmm, a prime number which is a product of 2^3021376 and (2^3021377-1)...

I made atypo

We can't all be "perfect".

[KrazyHorse]

Hmmm...that's an interesting way to construct perfect numbers. Good catch, BC.

[Q Classic]

Prove that Sqrt(11) does not exist as a rational number using only axiomatic methods.

[Dauphin]

Case for the defence

Originally posted by KrazyHorse
Hmmm...that's an interesting way to construct perfect numbers. Good catch, BC.

The -1 and the 1 diffence in the powers of two reminded me of the method for making perfect numbers. I knew that the 2ⁿ-1 number had to be prime, unfortunately I got an idée fix on prime, and said prime when I meant perfect.

Oh well.

Edit. Damned idée fix.