Irrational numbers

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6 total messages Started by padmanab Tue, 26 Jan 1993 01:37

#2520

Author: padmanab
Date: Tue, 26 Jan 1993 01:37

14 lines
555 bytes

Here is an interesting puzzle concerning 
irrational numbers: 

Can you find two IRRATIONAL NUMBERS P and Q such that 

                    Q 
                   P  =  rational? 

HAVE FUN!

-Prasad Padmanabhan
Dept. of ECE
University of Massachusetts
Amherst MA 01003

Re: Irrational numbers

#2524

Author: Stein Kulseth
Date: Tue, 26 Jan 1993 10:44

22 lines
1077 bytes

In article <19723.2b6495ca@ecs.umass.edu>, padmanab@ecs.umass.edu writes:
|> Here is an interesting puzzle concerning 
|> irrational numbers: 
|> 
|> Can you find two IRRATIONAL NUMBERS P and Q such that 
|> 
|>                     Q 
|>                    P  =  rational? 
|> 
|> HAVE FUN!
|> 
|> -Prasad Padmanabhan
|> Dept. of ECE
|> University of Massachusetts
|> Amherst MA 01003

e and ln2
-- 
stein.kulseth@nta.no (Norwegian Telecom Research)
   'When murders are committed by mathematics, they can be solved by
   mathematics. Most of them aren't, and this one wasn't'
   - Nick Charles (Dashiell Hammett's "The Thin Man")

Re: Irrational numbers

#2701

Author: Larry Baum
Date: Tue, 26 Jan 1993 18:16

20 lines
883 bytes

In article <19723.2b6495ca@ecs.umass.edu> padmanab@ecs.umass.edu writes:
>Here is an interesting puzzle concerning 
>irrational numbers: 
>
>Can you find two IRRATIONAL NUMBERS P and Q such that 
>
>                    Q 
>                   P  =  rational? 
>
>HAVE FUN!
>
>-Prasad Padmanabhan
>Dept. of ECE
>University of Massachusetts
>Amherst MA 01003
>

Since e**(ln x) = x, P = e, Q = ln r, will suffice for any rational.

Left to the reader: show ln r is not rational.

Re: Irrational numbers

#2693

Author: Dan Johnson
Date: Tue, 26 Jan 1993 23:16

13 lines
883 bytes

In article <19723.2b6495ca@ecs.umass.edu> padmanab@ecs.umass.edu writes:
>Can you find two IRRATIONAL NUMBERS P and Q such that 
>
>                    Q 
>                   P  =  rational? 
SPOILER:

P = e, Q = ln 2
-- 
Daniel W. Johnson                  Applied Computing Devices, Inc.
Home: 71520.367@CompuServe.COM     Work: dwj@iedv1.acd.com
      DanielJ13@aol.com                  39 25 02 N / 87 19 55 W
                - this space unintentionally left blank -

Re: Irrational numbers

#2634

Author: Joel Chan
Date: Tue, 26 Jan 1993 23:46

24 lines
1068 bytes

In article <19723.2b6495ca@ecs.umass.edu> padmanab@ecs.umass.edu writes:
>Here is an interesting puzzle concerning 
>irrational numbers: 
>
>Can you find two IRRATIONAL NUMBERS P and Q such that 
>
>                    Q 
>                   P  =  rational? 
>
>HAVE FUN!

Let P and Q both be equal to sqrt(2).

Is P^Q rational?  If it is, we're done.

If it isn't then take (P^Q)^R, where R = sqrt(2).


Joel
-- 
Joel Chan, Department of Mathematics	  	 joel@math.toronto.edu
Toronto Blue Jays: 1992 World Series Champions
"History: Those who ignore it are condemned to repeat it.  Math, too."
				    -From the comic strip "Betty"

Re: Irrational numbers

#2562

Author: stephen j uurtamo
Date: Wed, 27 Jan 1993 17:34

9 lines
553 bytes

 i(pi)
e     = -1.


ppppphhhbbbt.


steve

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