Re: 64 - is this the only number that is both a sq and a cube?

From: Edwin Clark (eclark_at_math.usf.edu)
Date: 09/21/04 

Date: Tue, 21 Sep 2004 02:35:36 GMT

Bob Silverman wrote:

> On 20 Sep 2004, Michael Lockhart wrote:
>
>>"Bob Silverman" <anonymous@mathforum.org> wrote in message
>
>
> <snip>
>
>
>>I think he's just a complete layman who is looking at that as 64 = 8*8 =
>>4*4*4. In his head, he's not going to get to 3^6 = 729 = 27*27 = 9*9*9, so
>>it looks unique to him.
>
>
>
> Allow me to pontificate/editorialize a bit... No flames are
> intended except those aimed at our (U.S.) currently incompetent
> educational system.
>
> Does "complete layman" = "complete moron"??? [no flame intended
> toward original poster]
>
> The question asked is a simple one that should be able to be
> answered by anyone who has taken/passed a year of algebra. The last
> time I looked, the minimum requirement for graduating high school in the U.S. [any high school] was two years of math...
>
> Answering this question only requires simple arithmetic. If a high
> school graduate can not answer it, it speaks very poorly of the
> high school math teachers......

An argument could be made that simple arithmetic consists only in
adding, multiplying and dividing whole numbers. Something like
(x^n)^m = x^(nm) is algebra---but would you care to wager how many
beginning calculus students know this?

>
> I agree with R. Heinlein.
>

Are you referring to the recently posted excerpt from his "Expanding
Universe":

"...a state that required a bare minimum of intelligence and education -
e.g. step into the polling booth and find that the computer has
generated a new quadratic equation just for you. Solve it, the computer
unlocks the voting machine, you vote. But get a wrong answer and the
voting machine fails to unlock, a loud bell sounds, a red light goes on
over that booth - and you slink out, face red, you having just proved
yourself too stupid and/or ignorant to take part in the decisions of the
grownups. Better luck next election! No lower age limit in this system -
smart 12-yr-old girls vote every election while some of their mothers -
and fathers - decline to be humiliated twice."

On the other hand, since a large percentage of my acquaintances have
PhDs in mathematics, I have known for a long time that being able to do
advanced mathematics doesn't say much about one's ability to make good
decisions on other matters--such as voting. :-)

Edwin

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