Math Forum Discussions

Ben Bacarisse

Posts: 1,680
Registered: 7/4/07

Re: Find the perfect square closest to n(x), i just want the perfect square above or below no decimals. Can it be solved using geometry?
Posted: Nov 1, 2013 1:19 PM

Plain Text

jonas.thornvall@gmail.com writes:

> Den fredagen den 1:e november 2013 kl. 04:01:53 UTC+1 skrev Ben Bacarisse:
>> jonas.thornvall@gmail.com writes:
<snip>
>> > The perfect square we find is subtracted from our number and now we
>> > work same approach for this smaller square. This is repeated until the
>> > full number is encoded to a series of squares + a small integer less
>> > then 4.
>>
>> Yes, this bit I've understood, but why? What's the point of doing this?

<snip>
> Main point is that it ism, i think it is a nice way express very big
> numbers without any approximation.

I have to take your word for it, since "nice" is in the eye of the beholder.

> Another is that we can encode any number making a square modular
> number system doing mathematic in,

I can't parse this.

> since it seem consistent enough doing arithmetic in, without go back
> to standard bases. So it is not just naturals it work perfectly good
> for reals.

Sorry, more trouble understanding. Do you mean that there is some
arithmetic advantage to representing numbers this way? Do mean that
arithmetic is faster/simpler/neater using your sum of squares notation
than using, say, normal binary arithmetic?

> Another point i do not which to spell out i rather implement it and
> refine it before showing. But that point is probably the reason i
> implemented it in the first case, but i think this encoding of
> numbersystem is quite useful.

I don't follow this point either.

--
Ben.