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Author Topic: Random Stuff  (Read 1162858 times)

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DStu

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Re: Random Stuff
« Reply #375 on: May 15, 2013, 03:15:07 pm »
+3

We need some real random stuff here.

Real Random? http://dynamic.xkcd.com/random/comic/

Edit: Bonus points if you get 221...
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Kuildeous

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Re: Random Stuff
« Reply #376 on: May 16, 2013, 10:41:34 am »
+2

I only wish that this is not from a closed thread; I'd post this there instead.

Quote
Quote
I give you a new random and likely irrational number

I feel like this is going to be hard to implement

This is an easy task.

Roll a 4-sided die.

If 1, choose e
If 2, choose pi
If 3, choose square root of 2
If 4, choose 1

Most likely, you'll randomly get an irrational number.
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gman314

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Re: Random Stuff
« Reply #377 on: May 16, 2013, 11:17:50 am »
0

I only wish that this is not from a closed thread; I'd post this there instead.

Quote
Quote
I give you a new random and likely irrational number

I feel like this is going to be hard to implement

This is an easy task.

Roll a 4-sided die.

If 1, choose e
If 2, choose pi
If 3, choose square root of 2
If 4, choose 1

Most likely, you'll randomly get an irrational number.

Had the thread not been locked, I was going to reply with "I just choose whatever integer I feel like choosing, and then take the square root of it."
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Kirian

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Re: Random Stuff
« Reply #378 on: May 16, 2013, 11:58:45 am »
0

Roll 2d6.  Multiply the numbers together.  Take the square root.
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sudgy

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Re: Random Stuff
« Reply #379 on: May 16, 2013, 11:59:58 am »
0

Roll 2d6.  Multiply the numbers together.  Take the square root.
Rolled 2d6 : 1, 1, total 2
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   Quote from: sudgy on June 31, 2011, 11:47:46 pm

sudgy

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Re: Random Stuff
« Reply #380 on: May 16, 2013, 12:00:25 pm »
0

Roll 2d6.  Multiply the numbers together.  Take the square root.
This dice roll may have been tampered with!
Rolled 2d6 : 1, 1, total 2
1 * 1 = 1, square root is 1.  HA!

And, no, I didn't plan that.
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   Quote from: sudgy on June 31, 2011, 11:47:46 pm

Kuildeous

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Re: Random Stuff
« Reply #381 on: May 16, 2013, 12:09:17 pm »
0

But if you get a perfect square, then you are left with a rational number.

I suppose you could generate a random integer and then run an algorithm.

If square root is rational, then use cube root. If cube root is rational, then…

Of course, you're screwed if your random integer happens to be 0 or 1. Negative numbers could cause problems too, but you can error-trap that.
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sudgy

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Re: Random Stuff
« Reply #382 on: May 16, 2013, 12:13:37 pm »
0

But if you get a perfect square, then you are left with a rational number.

I suppose you could generate a random integer and then run an algorithm.

If square root is rational, then use cube root. If cube root is rational, then…

Of course, you're screwed if your random integer happens to be 0 or 1. Negative numbers could cause problems too, but you can error-trap that.

Code: [Select]
if num == 0 or num == 1
num = num + 2
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   Quote from: sudgy on June 31, 2011, 11:47:46 pm

gman314

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Re: Random Stuff
« Reply #383 on: May 16, 2013, 12:21:53 pm »
0

But if you get a perfect square, then you are left with a rational number.

I suppose you could generate a random integer and then run an algorithm.

If square root is rational, then use cube root. If cube root is rational, then…

Of course, you're screwed if your random integer happens to be 0 or 1. Negative numbers could cause problems too, but you can error-trap that.

Ah, but I would still likely get an irrational. Assuming of course, that I don't lean towards choosing perfect squares.
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Kirian

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Re: Random Stuff
« Reply #384 on: May 16, 2013, 12:44:25 pm »
+1

Fine:  Roll 4d6.  Put the digits in numerical order.  Take the cube root.  There, always irrational.
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Watno

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Re: Random Stuff
« Reply #385 on: May 16, 2013, 12:52:12 pm »
0

Rolled 4d6 : 5, 4, 2, 2, total 13
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DStu

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Re: Random Stuff
« Reply #386 on: May 16, 2013, 01:00:24 pm »
+2

Fine:  Roll 4d6.  Put the digits in numerical order.  Take the cube root.  There, always irrational.
Roll d6, multiply with 7, square root.
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Awaclus

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Re: Random Stuff
« Reply #387 on: May 16, 2013, 01:20:30 pm »
0

Fine:  Roll 4d6.  Put the digits in numerical order.  Take the cube root.  There, always irrational.
But being likely irrational is enough.
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Axxle

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Re: Random Stuff
« Reply #388 on: May 16, 2013, 02:03:17 pm »
+2

Fine:  Roll 4d6.  Put the digits in numerical order.  Take the cube root.  There, always irrational.
Roll d6, multiply with 7, square root.
Get integer randomly.  Multiply with irrational number.
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Re: Random Stuff
« Reply #389 on: May 16, 2013, 02:19:58 pm »
0

Fine:  Roll 4d6.  Put the digits in numerical order.  Take the cube root.  There, always irrational.
Roll d6, multiply with 7, square root.
Get integer randomly.  Multiply with irrational number.

:O
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   Quote from: sudgy on June 31, 2011, 11:47:46 pm

Thisisnotasmile

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Re: Random Stuff
« Reply #390 on: May 16, 2013, 02:21:17 pm »
+1

Get integer randomly. Add irrational number.
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Watno

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Re: Random Stuff
« Reply #391 on: May 16, 2013, 02:23:26 pm »
+2

Fine:  Roll 4d6.  Put the digits in numerical order.  Take the cube root.  There, always irrational.
Roll d6, multiply with 7, square root.
Get integer randomly.  Multiply with irrational number.
doesn't work. 0 is an integer., but 0*i=0 isn't irrational for any irriational number i.
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Axxle

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Re: Random Stuff
« Reply #392 on: May 16, 2013, 02:36:16 pm »
+1

Fine:  Roll 4d6.  Put the digits in numerical order.  Take the cube root.  There, always irrational.
Roll d6, multiply with 7, square root.
Get integer randomly.  Multiply with irrational number.
doesn't work. 0 is an integer., but 0*i=0 isn't irrational for any irriational number i.
Stupid zero ruining everything.
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sudgy

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Re: Random Stuff
« Reply #393 on: May 16, 2013, 02:50:12 pm »
0

Get integer randomly. Add irrational number.

This works for zero.
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   Quote from: sudgy on June 31, 2011, 11:47:46 pm

Axxle

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Re: Random Stuff
« Reply #394 on: May 16, 2013, 02:54:41 pm »
+2

Get integer randomly. Add irrational number.

This works for zero.
Like I said, zero ruining everything, even my comment about it ruining everything.
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qmech

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Re: Random Stuff
« Reply #395 on: May 16, 2013, 03:21:52 pm »
0

Exercise: show that there exist irrationals a and b such that ab is rational.
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Re: Random Stuff
« Reply #396 on: May 16, 2013, 03:23:28 pm »
0

So Break of Reality is pretty good, huh?
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gman314

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Re: Random Stuff
« Reply #397 on: May 16, 2013, 03:26:36 pm »
+1

Exercise: show that there exist irrationals a and b such that ab is rational.

Let a be any irrational number. Choose ab to be a2 + 1. Then, b must be irrational. QED.

If this were actually a math assignment question, I'd add a bit more formal logic, but this isn't, so I won't. You can probably see the idea though.
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DStu

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Re: Random Stuff
« Reply #398 on: May 16, 2013, 04:11:44 pm »
0

Exercise: show that there exist irrationals a and b such that ab is rational.

Let a be any irrational number. Choose ab to be a2 + 1. Then, b must be irrational. QED.

If this were actually a math assignment question, I'd add a bit more formal logic, but this isn't, so I won't. You can probably see the idea though.
eln(2) = 2

edit: Also, I don't believe that a^b = a^2 + 1 implies b irrational for irrational a.  Take b=3, that is equivalent to a^3-a^2-1=0, which has a solution because third order polynomial, and I doubt that the solution is rational.
edit2: OK, WolframAlpha gives the solution and its irrational.
edit3: But you can save the argument by assuming a is transcendent, because this implies that a is not a solution of x^b-x^2-1=0 for rational b (because that would imply that a is algebraic).
edit4: weakened the statement a bit.
« Last Edit: May 16, 2013, 04:31:45 pm by DStu »
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qmech

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Re: Random Stuff
« Reply #399 on: May 16, 2013, 04:38:28 pm »
+1

eln(2) = 2

The trouble then is to show that log 2 is irrational.  You'd be amazed if it wasn't, but it's not obvious.

There's a fun argument that gives existence easily, but isn't constructive.

First you try √2√2.  If it's rational, you're done.  If it's irrational, then (√2√2)√2 = (√2)2 = 2.
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